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Photonic
Signal
Processing
Techniques and Applications
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page i 9.11.2007 7:33pm Compositor Name: BMani

OPTICAL SCIENCE AND ENGINEERING
Founding Editor
Brian J. Thompson
University of Rochester
Rochester, New York
1. Electron and Ion Microscopy and Microanalysis: Principles
and Applications, Lawrence E. Murr
2. Acousto-Optic Signal Processing: Theory and Implementation,
edited by Norman J. Berg and John N. Lee
3. Electro-Optic and Acousto-Optic Scanning and Deflection,
Milton Gottlieb, Clive L. M. Ireland, and John Martin Ley
4. Single-Mode Fiber Optics: Principles and Applications,
Luc B. Jeunhomme
5. Pulse Code Formats for Fiber Optical Data Communication:
Basic Principles and Applications, David J. Morris
6. Optical Materials: An Introduction to Selection
and Application, Solomon Musikant
7. Infrared Methods for Gaseous Measurements: Theory
and Practice, edited by Joda Wormhoudt
8. Laser Beam Scanning: Opto-Mechanical Devices, Systems,
and Data Storage Optics, edited by Gerald F. Marshall
9. Opto-Mechanical Systems Design, Paul R. Yoder, Jr.
10. Optical Fiber Splices and Connectors: Theory and Methods,
Calvin M. Miller with Stephen C. Mettler and Ian A. White
11. Laser Spectroscopy and Its Applications, edited by
Leon J. Radziemski, Richard W. Solarz, and Jeffrey A. Paisner
12. Infrared Optoelectronics: Devices and Applications,
William Nunley and J. Scott Bechtel
13. Integrated Optical Circuits and Components: Design
and Applications, edited by Lynn D. Hutcheson
14. Handbook of Molecular Lasers, edited by Peter K. Cheo
15. Handbook of Optical Fibers and Cables, Hiroshi Murata
16. Acousto-Optics, Adrian Korpel
17. Procedures in Applied Optics, John Strong
18. Handbook of Solid-State Lasers, edited by Peter K. Cheo
19. Optical Computing: Digital and Symbolic, edited by
Raymond Arrathoon
20. Laser Applications in Physical Chemistry, edited by D. K. Evans
21. Laser-Induced Plasmas and Applications, edited by
Leon J. Radziemski and David A. Cremers
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page ii 9.11.2007 7:33pm Compositor Name: BMani

22. Infrared Technology Fundamentals, Irving J. Spiro
and Monroe Schlessinger
23. Single-Mode Fiber Optics: Principles and Applications,
Second Edition, Revised and Expanded, Luc B. Jeunhomme
24. Image Analysis Applications, edited by Rangachar Kasturi
and Mohan M. Trivedi
25. Photoconductivity: Art, Science, and Technology, N. V. Joshi
26. Principles of Optical Circuit Engineering, Mark A. Mentzer
27. Lens Design, Milton Laikin
28. Optical Components, Systems, and Measurement Techniques,
Rajpal S. Sirohi and M. P. Kothiyal
29. Electron and Ion Microscopy and Microanalysis: Principles
and Applications, Second Edition, Revised and Expanded,
Lawrence E. Murr
30. Handbook of Infrared Optical Materials, edited by Paul Klocek
31. Optical Scanning, edited by Gerald F. Marshall
32. Polymers for Lightwave and Integrated Optics: Technology
and Applications, edited by Lawrence A. Hornak
33. Electro-Optical Displays, edited by Mohammad A. Karim
34. Mathematical Morphology in Image Processing, edited by
Edward R. Dougherty
35. Opto-Mechanical Systems Design: Second Edition,
Revised and Expanded, Paul R. Yoder, Jr.
36. Polarized Light: Fundamentals and Applications, Edward Collett
37. Rare Earth Doped Fiber Lasers and Amplifiers, edited by
Michel J. F. Digonnet
38. Speckle Metrology, edited by Rajpal S. Sirohi
39. Organic Photoreceptors for Imaging Systems,
Paul M. Borsenberger and David S. Weiss
40. Photonic Switching and Interconnects, edited by
Abdellatif Marrakchi
41. Design and Fabrication of Acousto-Optic Devices, edited by
Akis P. Goutzoulis and Dennis R. Pape
42. Digital Image Processing Methods, edited by
Edward R. Dougherty
43. Visual Science and Engineering: Models and Applications,
edited by D. H. Kelly
44. Handbook of Lens Design, Daniel Malacara
and Zacarias Malacara
45. Photonic Devices and Systems, edited by
Robert G. Hunsberger
46. Infrared Technology Fundamentals: Second Edition,
Revised and Expanded, edited by Monroe Schlessinger
47. Spatial Light Modulator Technology: Materials, Devices,
and Applications, edited by Uzi Efron
48. Lens Design: Second Edition, Revised and Expanded,
Milton Laikin
49. Thin Films for Optical Systems, edited by Francoise R. Flory
50. Tunable Laser Applications, edited by F. J. Duarte
51. Acousto-Optic Signal Processing: Theory and Implementation,
Second Edition, edited by Norman J. Berg
and John M. Pellegrino
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page iii 9.11.2007 7:33pm Compositor Name: BMani

52. Handbook of Nonlinear Optics, Richard L. Sutherland
53. Handbook of Optical Fibers and Cables: Second Edition,
Hiroshi Murata
54. Optical Storage and Retrieval: Memory, Neural Networks,
and Fractals, edited by Francis T. S. Yu and Suganda Jutamulia
55. Devices for Optoelectronics, Wallace B. Leigh
56. Practical Design and Production of Optical Thin Films,
Ronald R. Willey
57. Acousto-Optics: Second Edition, Adrian Korpel
58. Diffraction Gratings and Applications, Erwin G. Loewen
and Evgeny Popov
59. Organic Photoreceptors for Xerography, Paul M. Borsenberger
and David S. Weiss
60. Characterization Techniques and Tabulations for Organic
Nonlinear Optical Materials, edited by Mark G. Kuzyk
and Carl W. Dirk
61. Interferogram Analysis for Optical Testing, Daniel Malacara,
Manuel Servin, and Zacarias Malacara
62. Computational Modeling of Vision: The Role of Combination,
William R. Uttal, Ramakrishna Kakarala, Spiram Dayanand,
Thomas Shepherd, Jagadeesh Kalki, Charles F. Lunskis, Jr.,
and Ning Liu
63. Microoptics Technology: Fabrication and Applications of Lens
Arrays and Devices, Nicholas Borrelli
64. Visual Information Representation, Communication,
and Image Processing, edited by Chang Wen Chen
and Ya-Qin Zhang
65. Optical Methods of Measurement, Rajpal S. Sirohi
and F. S. Chau
66. Integrated Optical Circuits and Components: Design
and Applications, edited by Edmond J. Murphy
67. Adaptive Optics Engineering Handbook, edited by
Robert K. Tyson
68. Entropy and Information Optics, Francis T. S. Yu
69. Computational Methods for Electromagnetic and Optical
Systems,John M. Jarem and Partha P. Banerjee
70. Laser Beam Shaping,Fred M. Dickey and Scott C. Holswade
71. Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition,
Revised and Expanded, edited by Michel J. F. Digonnet
72. Lens Design: Third Edition, Revised and Expanded, Milton Laikin
73. Handbook of Optical Engineering,edited by Daniel Malacara
and Brian J. Thompson
74. Handbook of Imaging Materials: Second Edition, Revised
and Expanded,edited by Arthur S. Diamond and David S. Weiss
75. Handbook of Image Quality: Characterization and Prediction,
Brian W. Keelan
76. Fiber Optic Sensors,edited by Francis T. S. Yu and Shizhuo Yin
77. Optical Switching/Networking and Computing for Multimedia
Systems,edited by Mohsen Guizani and Abdella Battou
78. Image Recognition and Classification: Algorithms, Systems,
and Applications,edited by Bahram Javidi
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page iv 9.11.2007 7:33pm Compositor Name: BMani

79. Practical Design and Production of Optical Thin Films:
Second Edition, Revised and Expanded,Ronald R. Willey
80. Ultrafast Lasers: Technology and Applications,edited by
Martin E. Fermann, Almantas Galvanauskas, and Gregg Sucha
81. Light Propagation in Periodic Media: Differential Theory
and Design, Michel Nevière and Evgeny Popov
82. Handbook of Nonlinear Optics, Second Edition, Revised
and Expanded, Richard L. Sutherland
83. Polarized Light: Second Edition, Revised and Expanded,
Dennis Goldstein
84. Optical Remote Sensing: Science and Technology, Walter Egan
85. Handbook of Optical Design: Second Edition, Daniel Malacara
and Zacarias Malacara
86. Nonlinear Optics: Theory, Numerical Modeling,
and Applications, Partha P. Banerjee
87. Semiconductor and Metal Nanocrystals: Synthesis and
Electronic and Optical Properties, edited by Victor I. Klimov
88. High-Performance Backbone Network Technology, edited by
Naoaki Yamanaka
89. Semiconductor Laser Fundamentals, Toshiaki Suhara
90. Handbook of Optical and Laser Scanning, edited by
Gerald F. Marshall
91. Organic Light-Emitting Diodes: Principles, Characteristics,
and Processes, Jan Kalinowski
92. Micro-Optomechatronics, Hiroshi Hosaka, Yoshitada Katagiri,
Terunao Hirota, and Kiyoshi Itao
93. Microoptics Technology: Second Edition,Nicholas F. Borrelli
94. Organic Electroluminescence, edited by Zakya Kafafi
95. Engineering Thin Films and Nanostructures with Ion Beams,
Emile Knystautas
96. Interferogram Analysis for Optical Testing, Second Edition,
Daniel Malacara, Manuel Sercin, and Zacarias Malacara
97. Laser Remote Sensing, edited by Takashi Fujii
and Tetsuo Fukuchi
98. Passive Micro-Optical Alignment Methods,edited by
Robert A. Boudreau and Sharon M. Boudreau
99. Organic Photovoltaics: Mechanism, Materials, and Devices,
edited by Sam-Shajing Sun and Niyazi Serdar Saracftci
100. Handbook of Optical Interconnects, edited by Shigeru Kawai
101. GMPLS Technologies: Broadband Backbone Networks and
Systems,Naoaki Yamanaka, Kohei Shiomoto, and Eiji Oki
102. Laser Beam Shaping Applications,edited by Fred M. Dickey,
Scott C. Holswade and David L. Shealy
103. Electromagnetic Theory and Applications for Photonic Crystals,
Kiyotoshi Yasumoto
104. Physics of Optoelectronics, Michael A. Parker
105. Opto-Mechanical Systems Design: Third Edition,
Paul R. Yoder, Jr.
106. Color Desktop Printer Technology, edited by Mitchell Rosen
and Noboru Ohta
107. Laser Safety Management, Ken Barat
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page v 9.11.2007 7:33pm Compositor Name: BMani

108. Optics in Magnetic Multilayers and Nanostructures,
Sˇtefan Viˇsˇnovsky’
109. Optical Inspection of Microsystems, edited by Wolfgang Osten
110. Applied Microphotonics, edited by Wes R. Jamroz,
Roman Kruzelecky, and Emile I. Haddad
111. Organic Light-Emitting Materials and Devices, edited by
Zhigang Li and Hong Meng
112. Silicon Nanoelectronics, edited by Shunri Oda and David Ferry
113. Image Sensors and Signal Processor for Digital Still Cameras,
Junichi Nakamura
114. Encyclopedic Handbook of Integrated Circuits, edited by
Kenichi Iga and Yasuo Kokubun
115. Quantum Communications and Cryptography, edited by
Alexander V. Sergienko
116. Optical Code Division Multiple Access: Fundamentals
and Applications, edited by Paul R. Prucnal
117. Polymer Fiber Optics: Materials, Physics, and Applications,
Mark G. Kuzyk
118. Smart Biosensor Technology, edited by George K. Knopf
and Amarjeet S. Bassi
119. Solid-State Lasers and Applications, edited by
Alphan Sennaroglu
120. Optical Waveguides: From Theory to Applied Technologies,
edited by Maria L. Calvo and Vasudevan Lakshiminarayanan
121. Gas Lasers, edited by Masamori Endo and Robert F. Walker
122. Lens Design, Fourth Edition, Milton Laikin
123. Photonics: Principles and Practices, Abdul Al-Azzawi
124. Microwave Photonics, edited by Chi H. Lee
125. Physical Properties and Data of Optical Materials,
Moriaki Wakaki, Keiei Kudo, and Takehisa Shibuya
126. Microlithography: Science and Technology, Second Edition,
edited by Kazuaki Suzuki and Bruce W. Smith
127. Coarse Wavelength Division Multiplexing: Technologies
and Applications,edited by Hans Joerg Thiele
and Marcus Nebeling
128. Organic Field-Effect Transistors,Zhenan Bao and Jason Locklin
129. Smart CMOS Image Sensors and Applications,Jun Ohta
130. Photonic Signal Processing: Techniques and Applications,
Le Nguyen Binh
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page vi 9.11.2007 7:33pm Compositor Name: BMani

Photonic
Signal
Processing
Techniques and Applications
Le Nguyen Binh
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Boca Raton London New York
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page vii 9.11.2007 7:33pm Compositor Name: BMani

CRC Press
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Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page viii 9.11.2007 7:33pm Compositor Name: BMani

To the memory of my father and to my mother
To Phuong and Lam
Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page ix 9.11.2007 7:33pm Compositor Name: BMani

Binh/Photonic Signal Processing: Techniques and Applications DK6043_C000 Final Proof page x 9.11.2007 7:33pm Compositor Name: BMani

Contents
Preface................................................................................................................... xvii
Author .....................................................................................................................xix
Chapter 1
Principal Photonic Devices for Processing................................................................1
1.1 Optical Fiber Communications .........................................................................1
1.2 Photonic Signal Processors...............................................................................2
1.2.1 Photonic Signal Processing...................................................................2
1.2.2 Some Processor Components................................................................3
1.2.2.1 Optical Ampliﬁers................................................................. 3
1.2.2.2 Pumping Characteristics........................................................ 4
1.2.2.3 Gain Characteristics .............................................................. 6
1.2.3 Noise Considerations of EDFAs and Impact
on System Performance ......................................................................10
1.2.3.1 Noise Considerations .......................................................... 10
1.2.3.2 Fiber Bragg Gratings .......................................................... 13
1.3 Optical Modulators .........................................................................................15
1.3.1 Introductory Remarks .........................................................................15
1.3.2 Lithium Niobate Optical Modulators..................................................16
1.3.2.1 Optical-Diffused Channel Waveguides .............................. 16
1.3.2.2 Linear Electro-Optic Effect................................................. 28
1.3.3 Electro-Absorption Modulators ..........................................................35
1.3.3.1 Electro-Absorption Effects.................................................. 35
1.3.3.2 Rib Channel Waveguides ................................................... 38
1.3.4 Operational Principles and Transfer Characteristics...........................42
1.3.4.1 Electro-Optic Mach–Zehnder Interferometric
Modulator............................................................................ 42
1.3.5 Modulation Characteristics and Transfer Function ............................51
1.3.5.1 Transfer Function................................................................ 51
1.3.5.2 Extinction Ratio for Large Signal Operation...................... 54
1.3.5.3 Small Signal Operation....................................................... 55
1.3.5.4 DC Bias Stability and Linearization................................... 55
1.3.6 Chirp in Modulators............................................................................56
1.3.6.1 General Aspects .................................................................. 56
1.3.6.2 Modulation Chirp................................................................ 58
1.3.7 Electro-Optic Polymer Modulators.....................................................59
1.3.8 Modulators for Photonic Signal Processing .......................................62
1.4 Remarks ..........................................................................................................64
References................................................................................................................64
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xi

Chapter 2
Incoherence and Coherence in Photonic Signal Processing....................................71
2.1 Introduction.....................................................................................................71
2.2 Incoherent Fiber-Optic Signal Processing ......................................................72
2.2.1 Fiber-Optic Delay Lines .....................................................................73
2.2.2 Fiber-Optic Directional Couplers........................................................74
2.2.3 Fiber-Optic and Semiconductor Ampliﬁers........................................75
2.3 Coherent Integrated-Optic Signal Processing .................................................76
2.3.1 Integrated-Optic Delay Lines..............................................................79
2.3.2 Integrated-Optic Phase Shifters ..........................................................80
2.3.3 Integrated-Optic Directional Couplers................................................80
2.3.4 Integrated-Optic Ampliﬁers ................................................................83
2.4 Summary .........................................................................................................84
References................................................................................................................85
Chapter 3
Photonic Computing Processors ..............................................................................89
3.1 Incoherent Fiber-Optic Systolic Array Processors..........................................90
3.1.1 Introduction.........................................................................................90
3.1.2 Digital-Multiplication-by-Analog-Convolution Algorithm
and Its Extended Version....................................................................91
3.1.2.1 Multiplication of Two Digital Numbers ............................. 91
3.1.2.2 High-Order Digital Multiplication ...................................... 92
3.1.2.3 Sum of Products of Two Digital Numbers......................... 94
3.1.2.4 Twos-Complement Binary Arithmetic................................ 95
3.1.3 Elemental Optical Signal Processors ..................................................96
3.1.3.1 Optical Splitter and Combiner ............................................ 96
3.1.3.2 Binary Programmable Incoherent Fiber-Optic
Transversal Filter ................................................................ 98
3.1.4 Incoherent Fiber-Optic Systolic Array Processors
for Digital Matrix Multiplications ....................................................100
3.1.4.1 Matrix–Vector Multiplication ........................................... 100
3.1.4.2 Matrix–Matrix Multiplication ........................................... 102
3.1.4.3 Cascaded Matrix Multiplication........................................ 104
3.1.5 Performance Comparison..................................................................106
3.1.5.1 Fiber-Optic Systolic Array Processors Using
Nonbinary Data................................................................. 107
3.1.5.2 High-Order Fiber-Optic Systolic Array Processors.......... 109
3.1.6 Remarks ............................................................................................109
3.2 Programmable Incoherent Newton–Cotes Optical Integrator.......................111
3.2.1 Introductory Remarks .......................................................................111
3.2.2 Newton–Cotes Digital Integrators ....................................................112
3.2.2.1 Transfer Function.............................................................. 112
3.2.2.2 Synthesis ........................................................................... 114
3.2.2.3 Design of a Programmable Optical
Integrating Processor......................................................... 115
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xii

3.2.2.4 Analysis of the FIR Fiber-Optic Signal Processor ........... 120
3.2.2.5 Analysis of the IIR Fiber-Optic Signal Processor ............ 121
3.2.3 Remarks ............................................................................................124
3.2.3.1 Conclusions....................................................................... 129
3.3 Higher-Derivative FIR Optical Differentiators .............................................129
3.3.1 Introduction.......................................................................................129
3.3.2 Higher-Derivative FIR Digital Differentiators..................................132
3.3.3 Synthesis of Higher-Derivative FIR Optical Differentiators ............133
3.3.4 Remarks ............................................................................................136
3.3.4.1 First-Derivative Differentiators ......................................... 136
3.3.4.2 Second-Derivative Differentiators .................................... 138
3.3.4.3 Third-Derivative Differentiators ....................................... 140
3.3.4.4 Fourth-Derivative Differentiators...................................... 142
3.3.5 Remarks ............................................................................................147
Appendix A: Generalized Theory of the Newton–Cotes Digital Integrators........149
A.1 Deﬁnition of Numerical Integration.............................................................149
A.2 Newton’s Interpolating Polynomial .............................................................150
A.3 General Form of the Newton–Cotes Closed Integration Formulas .............152
A.4 Generalized Theory of the Newton–Cotes Digital Integrators ....................153
References..............................................................................................................155
Chapter 4
Ultrashort Pulse Photonic Generators....................................................................159
4.1 Optical Dark-Soliton Generator and Detectors.............................................159
4.1.1 Introduction.......................................................................................159
4.1.2 Optical Fiber Propagation Model .....................................................161
4.1.3 Design and Performance of Optical Dark-Soliton Detectors ...........162
4.1.3.1 Design of Optical Dark-Soliton Detectors........................ 162
4.1.3.2 Performance of the Optical Differentiator ........................ 163
4.1.3.3 Performance of the Butterworth Lowpass
Optical Filter ..................................................................... 165
4.1.4 Design of the Optical Dark-Soliton Generator .................................166
4.1.4.1 Design of the Optical Integrator ....................................... 166
4.1.4.2 Design of an Optical Dark-Soliton Generator .................. 169
4.1.5 Performance of the Optical Dark-Soliton Generator
and Detectors ....................................................................................171
4.1.5.1 Performance of the Optical Dark-Soliton
Generator........................................................................... 171
4.1.5.2 Performance of the Combined Optical Dark-Soliton
Generator and Optical Differentiator ................................ 172
4.1.5.3 Performance of the Combined Optical Dark-Soliton
Generator and Butterworth Lowpass Optical Filter.......... 174
4.1.6 Remarks ............................................................................................176
4.2 Mode-Locked Ultrashort Pulse Generators ..................................................178
4.2.1 Regenerative Mode-Locked Fiber Lasers.........................................179
4.2.2 Ultrahigh Repetition Rate Fiber Mode-Locked Lasers ....................182
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xiii

4.2.2.1 Mode-Locking Techniques and Conditions
for Generation of Transform Limited Pulses
from a Mode-Locked Laser .............................................. 183
4.2.2.2 Experimental Setup and Results ....................................... 186
4.2.2.3 Remarks ............................................................................ 192
4.2.3 Active Mode-Locked Fiber Ring Laser by Rational
Harmonic Detuning...........................................................................193
4.2.3.1 Rational Harmonic Mode Locking ................................... 193
4.2.3.2 Experimental Setup ........................................................... 194
4.2.3.3 Phase Plane Analysis ........................................................ 195
4.2.3.4 Results and Discussion ..................................................... 199
4.2.3.5 Remarks ............................................................................ 202
4.2.4 Repetition Rate Multiplication Ring Laser Using Temporal
Diffraction Effects.............................................................................202
4.2.4.1 GVD Repetition Rate Multiplication Technique.............. 206
4.2.4.2 Experimental Setup ........................................................... 207
4.2.4.3 Phase Plane Analysis ........................................................ 208
4.2.4.4 Demonstration ................................................................... 213
4.2.4.5 Remarks ............................................................................ 214
4.2.5 Multiwavelength Fiber Ring Lasers .................................................218
4.2.5.1 Theory ............................................................................... 219
4.2.5.2 Experimental Results and Discussion............................... 222
4.2.6 Multiwavelength Tunable Fiber Ring Lasers ...................................225
4.2.6.1 Remarks ............................................................................ 229
References..............................................................................................................230
Chapter 5
Dispersion Compensation Using Photonic Filters.................................................235
5.1 Dispersion Compensation Using Optical Resonators...................................235
5.1.1 Signal-Flow Graph Application in Optical Resonators....................237
5.1.2 Stability .............................................................................................244
5.1.3 Frequency and Impulse Responses...................................................244
5.1.3.1 Frequency Response ......................................................... 244
5.1.3.2 Impulse and Pulse Responses ........................................... 245
5.1.3.3 Cascade Networks............................................................. 247
5.1.3.4 Circuits with Bidirectional Flow Path .............................. 247
5.1.3.5 Remarks ............................................................................ 247
5.1.4 DCDR Circuit under Temporal Incoherent Condition .....................247
5.1.4.1 Transfer Function of the DCDR Circuit........................... 248
5.1.4.2 Circulating-Input Intensity Transfer Functions................. 250
5.1.4.3 Analysis............................................................................. 251
5.1.4.4 Remarks ............................................................................ 272
5.1.5 DCDR under Coherence Operation..................................................273
5.1.5.1 Field Analysis of the DCDR Circuit ................................ 273
5.1.5.2 Output–Input Field Transfer Function.............................. 273
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xiv

5.1.5.3 Circulating-Input Field Transfer Functions ...................... 275
5.1.5.4 Resonance of the DCDR Circuit ...................................... 275
5.1.5.5 Transient Response of the DCDR Circuit ........................ 278
5.1.6 Photonic Resonator as a Dispersion Equalizer.................................285
5.1.6.1 Group Delay and Dispersion of the DCDR Resonator .... 289
5.1.6.2 Optical Eigenﬁlter as Dispersion Compensators .............. 297
5.1.6.3 Remarks ............................................................................ 297
5.2 Eigenﬁlter Design for Dispersion Compensation .........................................300
5.2.1 Formulation of Dispersive Optical Fiber Channel .........................300
5.2.2 Formulation of Optical Dispersion Eigencompensation.................300
5.2.3 Design .............................................................................................302
5.2.4 Performance Comparison of Eigenﬁlter and Chebyshev
Filter Techniques ............................................................................305
5.2.5 Synthesis of Optical Dispersion Eigencompensators .....................305
5.2.6 IM/DD Transmission System Model..............................................307
5.2.7 Performance Comparison of Optical Dispersion
Eigencompensator and Chebyshev Optical Equalizer....................310
5.2.8 Eigencompensated System with Parameter Deviations
of the Optical Dispersion Eigencompensator .................................314
5.2.9 Trade-Off between Transmission Distance
and Eigenﬁlter Bandwidth ..............................................................315
5.2.10 Compensation Power of Eigencompensating Technique ...............317
5.2.11 Remarks ..........................................................................................319
References..............................................................................................................319
Chapter 6
Tunable Optical Filters ..........................................................................................325
6.1 Introduction...................................................................................................325
6.2 Basic Structures of Tunable Optical Filters..................................................326
6.2.1 First-Order All-Pole Optical Filter..................................................326
6.2.2 First-Order All-Zero Optical Filter .................................................328
6.2.3Mth-Order Tunable Optical Filter...................................................331
6.3 Tunable Optical Filters .................................................................................332
6.3.1 Design Equations for Tunable Optical Filters ................................332
6.3.2 Design of Second-Order Butterworth Tunable
Optical Filters..................................................................................333
6.3.3 Tuning Parameters of the Lowpass and Highpass Tunable
Optical Filters..................................................................................335
6.3.4 Tuning Parameters of Bandpass and Bandstop
Tunable Optical Filters ...................................................................338
6.3.5 Summary of Tuning Parameters of Tunable Optical Filters ..........338
6.3.6 Magnitude Responses of Tunable Optical Filters with Variable
Bandwidth and Fixed Center Frequency Characteristics................339
6.3.7 Magnitude Responses of Tunable Optical Filters with Fixed
Bandwidth and Variable Center Frequency Characteristics ...........342
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6.3.8 Summary of Filtering Characteristics of Tunable
Optical Filters....................................................................................342
6.3.9 Discussions .......................................................................................344
6.4 An Experimental First-Order Butterworth Lowpass and Highpass
Tunable Filters ..............................................................................................345
6.5 Remarks ........................................................................................................347
Appendix: Fundamental Characteristics of Recursive Digital Filters ...................349
References..............................................................................................................352
Index......................................................................................................................353
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Preface
Photonic signal processing (PSP) is very attractive because it has the potential to
overcome the electronic limits for processing ultra-wideband signals. Furthermore,
PSP provides signal conditioning that can be integrated in-line withﬁber optic
systems. Several techniques have been proposed and reported for the implementation
of the photonic counterparts of conventional electronic signal processing systems.
Signal processing in the photonic domain offers signiﬁcant improvement of signal
quality.
This book was written to address the emerging techniques of processing and
manipulating of signals propagating in an optical domain. This means the pulses or
signal envelopes are complex or modulating the optical carriers. Naturally, the
applications of such processing techniques in photonics are essential to illustrate
their usefulness. The change of the transmission cable from coaxial and metallic
waveguide toﬂexible optically transparent glassﬁber has allowed the processing of
ultra-high-speed signals in the microwave and millimeter-wave domain to the photo-
nic domain in which the delay line can be implemented in theﬁber lines, which are
very lightweight and space efﬁcient.
Chapter 1 gives a brief historical perspective of PSP and an introduction to a number
of photonic components essential for photonic processing systems, including, but not
exclusively, optical ampliﬁcation devices, opticalﬁbers, and optical modulators. Chap-
ter 2 discusses the representation of photonic circuits using signal-ﬂow graph tech-
niques, which have been employed in electrical circuits since the 1960s; however, they
have been adapted for photonic domains in which the transmittance of a photonic
subsystem determines the optical transfer function of a photonic subsystem. The
coherent and incoherent aspects of photonic circuits are important in terms of whether
theﬁeld or the power of the lightwaves should be used as well as because the length of
the photonic processors must be less than that of the coherence length.
Photonic signal processors such as differentiators and integrators are described in
Chapter 3. Their applications in the generation of solitons and in optically ampliﬁed
ﬁber transmission systems are described in Chapter 4. Chapter 5 illustrates the
compensation of dispersion using photonic processors. Chapter 6 explains the design
of opticalﬁlters using photonic processing techniques.
Many individuals have contributed, either directly or indirectly, to this book.
Thanks are due to Associate Professor John Ngo of Nanyang Technological Univer-
sity (NTU
candidate at Monash University; Associate Professor Shum Ping of the School of
Electrical and Electronic Engineering of NTU; Dr. Wenn Jing Lai; and Steven Luk.
I appreciate the help of my CRC Press=Taylor & Francis editor, Taisuke Soda, and
the encouragement of his colleague, Theresa Delforn. Last but not least, I thank my
wife Phuong and my son Lam for their support and for putting up with my busy
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xvii

writing schedule of the book and my daily teaching and research commitments at the
university, which certainly took away a large amount of time that we could have
spent together.
Le Nguyen Binh
Melbourne, Australia
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xviii

Author
Le Nguyen Binh, Ph.D.,received a B.E.(Hons.) and a Ph.D. in electronic engin-
eering and integrated photonics in 1975 and 1980, respectively, both from the
University of Western Australia, Nedlands, Western Australia. He has worked
extensively in theﬁelds of optical communication systems and networks and photo-
nic signal processing in academic and industrial environments, including the
advanced technology research laboratories of Siemens and Nortel Networks. He is
currently director of the Center for Telecommunications and Information Engineer-
ing and a reader in the Department of Electrical and Computer Systems Engineering
of Monash University. He has made outstanding contributions in theﬁelds of
integrated optics, optical communication systems and networks, and photonic
signal processing, and has published more than 150 papers in leading journals and
refereed conferences. He holds numerous patents related to photonics and optical
communications.
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1
Principal Photonic
Devices for Processing
This opening chapter provides the fundamentals of some principal photonic devices
that are essential for processing of ultrafast electrical and electronic signals in the
photonic domain, including optical communications and microwave photonics. It
describes the basic structures, the beneﬁts, and the needs of photonic signal process-
ing for the advancement of such systems. The device structures, fabrication, and
characteristics of operating functions of the optical ampliﬁers, opticalﬁlters, and
optical modulators are examined. The transmittance of photonic components can be
represented, in Chapter 2, in the form of signalﬂow and blocks of photonic signal
subsystems.
1.1 OPTICAL FIBER COMMUNICATIONS
The proposed dielectric waveguides for guiding lightwaves by Kao and Hockham in
1966 [1] have revolutionized the transmission of broadband signals and ultrahigh
capacity over ultra-long global telecommunication systems and networks. In the
1970s, the reduction of theﬁber losses over the visible and infrared spectral regions
was extensively investigated. The demonstration of the pure and low loss silica-
based glassﬁber was achieved in the early 1970s. Since then, the reduction of the
ﬁber dispersion with the theoretical development and manufacturing of weakly
guiding single-modeﬁbers were extensively conducted. The research, development,
and commercialization of opticalﬁber communication systems were then progressed
with practical demonstrations of higher and higher bit rates and longer and longer
transmission distance. Signiﬁcantly, the installation of opticalﬁber systems was
completed in 1978 [2]. Since then,ﬁber systems have been installed throughout
the world and interconnecting all continents of the globe with terrestrial and undersea
systems.
The primary reason for such exciting research and development is that the
frequency of the lightwave is in the order of a few hundred terahertz and the low
loss windows of glassﬁber are sufﬁciently wide so that several tens of terabits per
second capacity of information can be achieved over ultra-long distance, whereas the
carrier frequencies of the microwave and millimeter-wave are in the tens of gigahertz.
Indeed in the 1980s, the transmission speed and distance were limited because
of the ability of regeneration of information signals in the optical or photonic domain.
Data signals were received and recovered in the electronic domain; then the lightwave
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1

sources for retransmission were modulated. The distance between these regenerators
was limited to 40 km for installedﬁber transmission systems. Furthermore, the
dispersion-limited distance was longer than that of the attenuation-limited distance,
and no compensation of dispersion was required.
The repeaterless distance could then be extended to another 20 km with the use
of coherent detection techniques in the mid-1980s; heterodyne and homodyne
techniques were extensively investigated. However, the complexity and demands on
the extreme narrow line width of the lightwave source at the transmitter and the local
oscillator for mixing at the receiver restrict the applications of coherent processing.
This attenuation was eventually overcome with the invention of the optical
ampliﬁers in 1987 [3,4] using Nd or Er doping in silicaﬁber. Optical gain of
20–30 dB can be easily obtained. Hence, the only major issue was the dispersion
of lightwave signals in long-haul transmission. This leads to extensive search for the
management methods for compensation of dispersion. The simplest method can
be the use of dispersion compensatingﬁbers inserted in each transmission span,
hence the phase reversal of the lightwave and compensation in the photonic domain.
This is a form of photonic signal processing.
This leads to the development of high and ultrahigh bit rate transmission system.
The bit rate has reached 10, 40, and 80 Gb=s per wavelength channels in the late
1990s. Presently, the transmission systems of several wavelength channels each
carrying 40 Gb=s are practically proven and installed in a number of routes around
the world.
Recently, 10 Gb=s Ethernet has been standardized and the 100 Gb=s rate is
expected to be implemented in the future. Furthermore, soliton systems are also
attracting much attention with bit rate reaching 160 or 320 Gb=s with an ultrashort
pulse generating from mode-locked (ML) lasers [5]. At this ultrafast speed, the
processing of signals in the electronic domain is no longer possible and thus signal
processors in the photonic domain are expected to play a major role in these systems.
1.2 PHOTONIC SIGNAL PROCESSORS
1.2.1 P
HOTONICSIGNALPROCESSING
The term signal processing means extracting or modifying information from signals
at the receiver end [6]. This requires the modiﬁcation of the frequency, phase,
and amplitude of the received signals [7–30]. This function is essential in all commu-
nication systems as the signals arrived at the receiver end usually contain both
information and disturbances, such as distortion and noises that must beﬁltered and
eliminated. In addition, if the information data are transmitted at ultrahigh speed then it
may be very useful to down convert the signals to a lower frequency region so that the
manipulation and detection of the signals can be then recovered in the electronic
domain. This down conversion process is normally termed as photonic mixing. The
noise removal process isﬁltering. Other photonic processing processes can be
frequency discrimination, phase comparison, signal correlation, photonic differenti-
ation and integration, analog-to-digital optical conversion, etc. [29,31] which are
emerging as potential processors for future ultrafast photonic systems. Implementing
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2 Photonic Signal Processing: Techniques and Applications

these photonic processors for processing signals at speed above 10 GHz would offer
signiﬁcant advantages and overcome the bottlenecks caused by conventional elec-
tronic signal processors. Furthermore, the all in-lineﬁber-optic and integrated optic
structures of photonic signal processors are inherently compatible with opticalﬁber
transmission and microwaveﬁber-optic systems, hence ease of connectivity with
built-in signal conditioning. Photonic signal processing functions can also be imple-
mented in parallel as photons do not interact in a linear optical medium and hence,
lightwaves can be implemented in parallel in the same optical pipeline.
Unlike the traditional approach, the idea of photonic signal processing is to
process the signals while they are still in the photonic domain. Therefore, these
processors can be located in-line within theﬁber-optic transmission or photonic
systems. In a simple photonic system, there would be an optical transmitter consisting of
a laser source, which is modulated either directly or externally by an optical modulator
of electro-optic (EO =
guiding optical medium, optical devices, such as ampliﬁers, phase comparators using
interferometric devices.
Theﬁrst proposal of the processing of signals in the photonic domain was coined
by Wilner and van der Heuvel in 1976 [7] indicating that the low loss and broadband of
the transmittance of the single-mode opticalﬁbers would be the most favorable
condition for processing of broadband signals in the photonic domain. Since then,
several topical developments in theﬁeld, including integrated optic components,
subsystems, and transmission systems have been reported and contributed to optical
communications [32–42]. Almost all traditional functions in electronic signal pro-
cessing have been realized in the photonic domain.
1.2.2 SOMEPROCESSORCOMPONENTS
Ever since the proposal and invention of photonic signal processor was developed,
the structures of these processors have continuously been evolved to the invention of
new photonic devices, such as optical amplifying devices, photonicﬁlters of either
ﬁber resonance circuits orﬁber Bragg gratings (FBG). These components provide a
strong inﬂuence on the implementation of photonic signal processors. It is thus
important to understand the operation principles and characteristics of these photonic
devices. We brieﬂy describe here the operation principles and characteristics, their
circuit representation in the form of the photonic transmittance transfer functions
would then be given in the next chapter.
1.2.2.1 Optical Ampliﬁers
An optical ampliﬁer is an important component in incoherentﬁber-optic signal proces-
sors because it can compensate for optical losses as well as providing designﬂexibility
resulting in potential applications. Optical ampliﬁers can provide signal ampliﬁcation
directly in the optical domain. The operational principles, characteristics, and perform-
ances of the optical ampliﬁers are described. The gain of an optical ampliﬁer is
generated by the processes of stimulated scattering induced by nonlinear (NL
ing in an opticalﬁber, or stimulated emission caused by a population inversion in a
lasing medium. The former process is utilized by stimulated Raman scatteringﬁber
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Principal Photonic Devices for Processing 3

ampliﬁers and stimulated Brillouin scattering and parametricﬁber ampliﬁers; the
later types are based on NL effects inﬁbers. The latter process is employed by semi-
conductor laser ampliﬁers (SLAs ﬁber ampliﬁers. Furthermore,
integrated optic waveguides employing silica on silicon planar technology can be
doped with erbium (Er ﬁers [43–71]. In this section,
we give a brief description of theﬁber Er-doped ampliﬁers, which is mostly widely used
in current long-haul optically ampliﬁed transmission systems and processing networks.
Other than compensating for the transmission loss, boosting optical power, and
increasing the receiver sensitivity, the EDFA is attractive due to its high gain (30 dB
typically gain), low noise, large optical bandwidth, and polarization insensitivity
characteristics. One example is the incorporating of the EDFA in a recirculating loop
using a directional coupler and its compensating for the coupler splitting power,
hence generating a lightwave oscillator. If a pulse is coupled to this oscillator then a
periodic train of signals can then be generated from each round of circulation of the
lightwave signals.
Figure 1.1 shows the schematic diagram of an EDFA incorporating the pump
lasers, the gain medium silica-based doped with Er. Figure 1.2 shows the relevant
energy level diagram of Er ions in a silica host. Although the Er ions can be
pumped at various lengths to obtain population inversion in a 1550 nm transition
occurring between
4
I
13=2and
4
I
15=2, only two longest pump wavelengths at 980 and
1480 nm shown in Figure 1.2 are of practical interest. For these pump wavelengths, the
gain efﬁciency with respect to the pump power is at maximum and the available
semiconductor pump sources at these wavelengths are available.
1.2.2.2 Pumping Characteristics
Depending on the selected pump wavelength, Er-dopedﬁber can be approximately
described as a three- or two-level laser system. Figure 1.3 shows the absorption and
Isolator
Amplified (+ noise) signal out
Er
+
-doped fiber
Signal in
Isolator
Monitoring diode
WDM coupler
High pump source
Monitoring diode
l
p
FIGURE 1.1Schematic diagram of a forward-pumped erbium (Erﬁber ampliﬁer.
WDM multiplexer combines signal and pump wavelengths into the erbium-dopedﬁber.
Monitoring diodes are used for feedback control of the ampliﬁcation factor through adjusting
the pump power level.
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4 Photonic Signal Processing: Techniques and Applications

emission of the Er ion with respect to wavelength. Theﬁber host is GeO2-doped
silicaﬁber. To theoretically analyze, optimize the design and characteristics of
Er-dopedﬁber ampliﬁers (EDFA
ence the Stark effect resulting in splitting of the energy levels. Since the energy
levels are split with an uneven internal subpopulation, distribution makes it possible
to pump Er
þ
:glass directly in an
4
I13=2level and to achieve overall population
20
4
I
11/2
4
I
13/2
I
15/2
Energy level
2
H
11/2
4
S
3/2
4
F
9/2
0 514 532 667 800
Wavelength (nm)
980 1480 1550
FIGURE 1.2Energy level diagram of erbium-doped silica glass.
1.46 1.48 1.5 1.52 1.54 1.56 1.58
0
2
4
6
8
10
12
Wavelength (µm)
Absorption/gain coefficient (dB/m)
Gain and absorption coefficient spectral profile of Ge:SiO
2
EDFA
Absorption
Gain
FIGURE 1.3Absorption and gain (emission) spectra of a typical Er-doped alumina-germano-silicate
ﬁber. Note the gain is greater than the absorption in the wavelength range 1510–1560 nm where
theﬁber loss is also at minimum.
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Principal Photonic Devices for Processing 5

inversion between
4
I13=2and
4
I15=2levels. This pumping scheme, corresponding to the
1480 nm pump wavelength, would not be possible if the levels were not split by
the Stark effect. This energy splitting level also contributes to a certain tolerance to
the pump wavelengths (roughly 980 nm with a tolerance ofþ10 andﬁ10 nm and
þ15 andﬁ15 nm at 1480 nm) and to a broadened ampliﬁcation line width. Optical
ampliﬁcation occurs between the metastable
4
I13=2and ground
4
I15=2levels from
the inversion of the Er ions population due to the absorption of the pump photons.
The Er ions in the metastable level are de-excited down to the ground level by
stimulated emission (providing optical gain) and spontaneous emission (resulting in
noises). Pumping efﬁciency of about 0.8 dB=m was been obtained at 820 nm.
Although it is smaller by an order of magnitude compared with 980 and 1480 nm
pumping, 30 dB gain can be realized with 40–50 mW of pumping power, level has
already possible by using GaAs semiconductor laser.
1.2.2.3 Gain Characteristics
Figure 1.3 shows the absorption and emission spectrum exhibited by Er ions in a
typical Al
2O:GeO
2silicaﬁber over the 1450–1600 nm spectral range. The gain
spectrum is dependent on the presence of the dopants, alumina or Germania within
the core region. The plots clearly illustrate the possibility to achieve gain between
1530 and 1560 nm, where the loss of single-mode silica-based opticalﬁbers is at
minimum.
The ampliﬁcation of input signal to the Er-dopedﬁber combines the two effects,
the conﬁnement of the pump beam to the core-doped regions and the absorption of
energy of the pump beam. Depending on the pump wavelength the single-mode
Er-dopedﬁber can support a single-mode or few-order-mode operating region. That
means a nonuniformly pumped or inverted over its whole length. This situation
requires a speciﬁc model, which is based on a standard atomic rate equation. A
thorough and extensive description of this modeling of the EDFA can be found in
Ref. [3] [35].
The gain provided at the wavelengthlby an Er-dopedﬁber of lengthLcan be
described by
G
dB(l)¼s e(l)N2ﬁsa(l)N1 (1:1)
withN
i¼
1
N
t
ð
L
0
Ni(z)dzfori¼1, 2
where
s
e(l) ands a(l) are the stimulated emission and ionic absorption cross sections,
respectively N
1andN
2are the excited and ground state population densities
N
tis the total density of Er
þ
ions
Lthe length of the dopedﬁber
Now let us assume that the pump beam propagates in the same direction as the signal, referred as forward pumping or a copropagating scheme. Such a
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6 Photonic Signal Processing: Techniques and Applications

pumping and signal input scheme is shown in Figure 1.1. The input and pump beams
are multiplexed in a WDM coupler to propagate in the same direction.
The monitoring diodes are used to control the pump power at an appropriate
level for the signal input power to ensure that the signal is not ampliﬁed in the
saturation region.
If the pump power is too small with respect to the lengthLof the dopedﬁber,
signal photons are ampliﬁed in theﬁrst portion of the positive gain, then reabsorbed
in the secondﬁber portion of the negative gain. This is because of the decay of the
pump beam along the length, leading to noninverted populations in the second
section of the gain medium.
Increasing the pump power will guarantee a total population inversion over the
whole length of the doped amplifyingﬁber and a higher gain. Once that inverted
population is achieved by large pump power and regardless of the input signal
power, there is no beneﬁt to increase the pump power. This means that the length
of the dopedﬁber must be optimized for a maximum gain with respect to the pump
power and operational input power.
For large signal input powerP
in
s
, i.e., the saturation regime, the maximum output
power that can be extracted from the ampliﬁer is maximum for a 1480 nm pumping
wavelength, compared to a 980 nm pumping wavelength, since the photon energy of
the former is 1.34310
ﬁ19
J and the later is 2.03310
ﬁ19
J. Theseﬁgures must be
compared to the photon energy of the signal at 1550 nm of 1.28310
ﬁ19
J. This
follows the principle of energy conservation expressed in terms of photonﬂuxf, the
number of photons per second.
Letf
in
p
andf
in
s
,f
out
s
theﬂuxes of the pump photons and signal photons at the
input and output of the dopedﬁber, respectively, we then have, by deﬁnition
f
in
p
¼
P
in
p
hnp
(1:2)
f
in s
¼
P
in
s
hns
(1:3)
f
out
s
¼
P
out
s
hns
(1:4)
wherehis Planck’s constant. Theﬂuxes of photons must fulﬁll according to the
conservation of energy
P
out
s
hns
ﬂ
P
in
p
hnp
þ
P
in
s
hns
(1:5a)
or
P
out
s
ﬂP
in
s
þP
in
p
lp
ls
(1:5b)
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Principal Photonic Devices for Processing 7

Equation 1.5b shows that the maximum output power can be extracted by selecting
the wavelength ratio between the pump and signal beams. For a given pump power,
the larger the pump wavelength the higher the signal power output. This is the reason
for the use of the 1480 nm pump beam together with the reason that theﬁber would
operate in the single-mode region. However, at this wavelength there is a need to
ﬁlter the pump signal at the output of theﬁber to avoid the mixing of the pump and
signal power beam at the receiver.
The power spectral density of the forward ampliﬁed spontaneous emission
(ASE
S
ASE¼2n sphn(G EDFﬁ1)Dn (1:6)
where
G
EDFis the small signal optical gain of the Er-dopedﬁber
Dnis the effective bandwidth (in Hz) in whichS
ASEis expressed, the spontane-
ous emission bandwidth
The spontaneous emission factors related to the inversion of Er ions population by
n
sp(ls,lp)¼
ﬁsN2
ﬁsN2ﬁN1
(1:7)
whereh
s¼se(ls)=sa(ls). In the limit of the high pumping power, when the spon-
taneous emission factorn
spreaches its minimum value we have
n
min
sp
(ls,lp)¼
1
1ﬁ
se(lp)sa(ls)
s
a(lp)se(ls)
ﬁﬂ (1:8)
The spontaneous emission factor of Equation 1.8 is achieved if the emission is non-
radiative, i.e.,s
e(l
p)¼0. This corresponds to the three-level laser system with
l
p¼980 nm where the decay is nonradiative from the level
4
I11=2. When 1480 nm
wavelength laser pumping is used,s
e(lp)6¼0 the spontaneous emission factorn spis
greater than 1 and we expect a degradation of the signal-to-noise ratio (SNR
degradation of the SNR is commonly referred as the EDF noiseﬁgure (NF
lower limit is 3 dB, the so-called quantum limit. In practicen
spis always greater than
1 (even at 980 nm) and the input coupling lossC
1from the transmissionﬁber to the
amplifyingﬁber has to be taken into account for actual EDFA modules. Therefore,
the NF of EDFA is expressed as 2n
sp=C
1.
NF
EDFA¼2n sp=C1 (1:9)
Ampliﬁed spontaneous emission is generated over a continuum of wavelengths
spanning the entire spectrum of theﬁber gain spectrum. Because of the nonuniform
spectral response of then
spandG
EDFover the ampliﬁcation bandwidth, the spectral
distribution ofS
ASEis notﬂat. This ASE is then the source of optical noises, leading
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8 Photonic Signal Processing: Techniques and Applications

to different noise term of the electrical signal after the optoelectronic conversion in
the photodetector. The quantity of the ASE depends strongly on the gain value
required for signal ampliﬁcation.
When the input power is increased, the optical ampliﬁer is progressively reach-
ing saturation: the gain and subsequently the power spectral density are decreased
and vice versa for the noise. This noise behavior has a crucial impact on the design of
optical-ampliﬁedﬁber systems. In the case of long concatenated optical ampliﬁers,
the ASE noises generated at each EDFA section are accumulated and further
ampliﬁed at these succeeding ampliﬁers. If in-line optical ampliﬁers are operated
with constant output total power, the signal power will gradually decrease along the
chain to the worst effect of the increase in optical noises power. In addition, the
spectrum of the ASE noise at the end of spectrum leads to self-ﬁltering effects and
thus limits the useful optical bandwidth of the signal. This is critical for designing the
wavelength-division multiplexed (WDM
Typical properties of the Er-dopedﬁber are the Er ions doped in conﬁned region
of 2–4mm core diameter as shown in Figure 1.4. The Er ions concentration is a few
hundreds ppm, leading to a typical attenuation of about 10 dB=m at 1532 nm when
the dopedﬁber is in an unpumped mode of operation. The modeﬁeld diameter of the
dopedﬁber is about 4mm that is much smaller than that of standard opticalﬁbers
(for optical communication systems). Thus, a splicing loss of about 2 dB is expected
from these two mismatchedﬁbers. This splicing loss can be reduced if the standard
ﬁber is tapered; the loss can be as low as 0.2 dB. Optical isolator may be added to the
two ends of the dopedﬁbers in order to prevent the ampliﬁcation medium from
oscillating and behaving as a laser.
Signal
Erbium ions
Unguided spontaneous
emission
Er
+
-doped fiber core
ASE
FIGURE 1.4Generation of an ampliﬁed spontaneous emission (ASE ﬁer.
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Principal Photonic Devices for Processing 9

1.2.3 NOISECONSIDERATIONS OFEDFAS ANDIMPACT ONSYSTEMPERFORMANCE
1.2.3.1 Noise Considerations
Optical ampliﬁcation is obtained in the expense of the optical noise added to output
signal of the systems. The optical ASE noise is spreading over the entire spectrum
much wider than the signal itself. This noise density is integrated over the noise
spectrum of the photodetector and thus it has a major effect on the receiver noise
characteristics. To avoid such an integrated effect, an opticalﬁlter is usually placed
in front of an opticalﬁlter whose bandwidth is sharp and covering that of the signals.
Whether optical ampliﬁers are used as an in-line ampliﬁers, power ampliﬁers, or
preampliﬁers, the noises fallen into the signal bandwidth will severely limit the
maximum repeaterless distance. The predominant noise term generated by optical
ampliﬁers, namely the signal-ASE beat noise, is directly related to the EDFA gain
and NF.
An optoelectronic ampliﬁer consists of a photodiode, an electronic preampliﬁer,
an AGC control circuit, a low passﬁlter, and a decision circuit. The received signals
are sampled by a clock recovery circuitry. The photodiode converts the incoming
optical power into a photocurrenti
s(t) according to the square law:
i
s(t)¼G<E s(t)hi (1:10)
where
Gis the average avalanche gain factor
<is the photodiode responsivity
E
s(t) is the electromagneticﬁeld of the incoming optical waves
Thisﬁeld is effectively the sum of the signalﬁeld and the ASEﬁeld. Thus, we
have
E
2
(t)¼E
2
s
(t)þ2E s(t)EASE(t)þE
2
ASE
(t)( 1:11)
where
E
2
s
(t) is the mean optical power of the signal
2E
s(t)E
ASE(t) is the beating of the signal with the ASE
E
2
ASE
(t) is the beating of all ASE components with themselves
The mean noise power spectral current densities are given by
.Shot noises
For signal:d(i
2
s
-s
)¼½2qG
2þx
<(GPsþPspþId)df (1:12a)
For ASE:d(i
2
s
-ASE
)¼½2qG
2þx
<SASEDndf (1:12b)
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10 Photonic Signal Processing: Techniques and Applications

.Beat noises
For signal-ASE:d(i
2
b
-ASE
)¼½2qG
2þx
<
2
SASEPsﬃdf (1:12c)
For ASE-ASE:d(i
2
SE
-ASEA
)¼½4<
2
G
2þx
S
2
ASE
Dnﬃdf (1:12d)
where
qis the electronic charge
Gis the avalanche gain of the photodiode
xis the multiplication factor of the photodiode
P
sandS
ASEare the detected signal power and noise spectral density,
respectively
Dnis the optical bandwidth of the opticalﬁlter placed in front of the
photodetector
dfis the differential frequency interval when measuring the noise power
spectrum
The electronic noises of preampliﬁerS
eqto give the total equivalent noise current at
the input of the electronic ampliﬁer are denoted as d(i
2
Neq
); this is included in the
signal noise current or can be treated separately. The total noise power can then be
found by integrating it over the system bandwidth.
The unit ofS
ASEis usually expressed in dBm=(0.1 nm) because the opticalﬁlter
and useable optical bandwidth are in order of much less than 1.0 nm and the
optical power noise is measured in microwatts. The main purpose of the optical
ﬁlter is to reject the unwanted ASE power on either side of the signal wavelength and
to reduce the ASE-ASE beating noises. In practical systems, the noise terms of
the remnant pump power or the relative intensity noise of the laser transmitter are
negligible.
The shot noises of the signals are depending on whether a 0 or a 1 is received.
The total currents generated at the optical receiver with optical ampliﬁers are thus
given by integrating the noise density over the electrical bandwidth of the systems
(normally about 0.7 of the bit rate for a PCM modulation hierarchy). These noise
currents (square) are given by
i
2
SN
(‘‘1’’)¼
X
d(i
2
N
(‘‘1’’)
hi
B e (1:13a)
i
2
SN
(‘‘1’’)¼
X
d(i
2
N
(‘‘0’’)
hi
B e (1:13b)
whereB
eis the 3 dB bandwidth of the electrical low passﬁlter placed after the
electronic preampliﬁer, or effectively the bandwidth of the electronic preampliﬁer.
We can thus integrate the total spectral densities over the electrical bandwidth. Once
the total noises generated by the ASE and the total quantum shot noises and
electronic noises equivalent current are known, the bit error rate (BER
found with ease. The BER is thus given by
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Principal Photonic Devices for Processing 11

BER¼Q(d)( 1:14a)
wheredis given by
d¼
i1ﬁi0
iSN(‘‘1’’)þi SN(‘‘0’’)
(1:14b)
The average photo currents corresponding to the‘‘low’’or mark and‘‘high’’or space
levels are detected by the photodetector. The signal generated currents are related to
the mean signal power as
i
1¼<GP
‘‘
1’’
s
¼<G
2Tex
1þT ex
Ps (1:15a)
i
0¼<GP
‘‘
0’’
s
¼<G
2
1þT
ex
Ps (1:15b)
whereT
exis an extension ratio between‘‘1’’and‘‘0’’photocurrents. It is also
assumed that the equal probability between‘‘0’’and‘‘1’’digital levels for optimum
threshold level of the decision circuit. Thus, once the signal powerP
scan be found
the required optical power at the input of the optical ampliﬁed electronic receiver can
be converted into the receiver sensitivity for a certain bit rate and BER.
Thedfactor can also be expressed as a function of the SNR which is usually
expressed in dB=(0.1 nm) as
SNR¼10log
Ps
SASEDn
(1:16)
whereDn¼0.1 nm, i.e., 1.25310
10
at 1550 nm (normally the passband of the
opticalﬁlter is placed immediately after the EDFA to reduce ASE noise). The optical
SNR corresponds to the ratio between the signal power and the ASE power at the signal wavelength. To guarantee negligible degradation caused by the EDFA noise during data stream ampliﬁcation, SNR must be greater than 20 dB=(0.1 nm)
at the input of the photodetector at 2.5 Gb=s.
Typical DFB semiconductor transmitters deliver power in the range of 0–3 dBm.
An EDFA can be used as a power ampliﬁer within the transmitter to boost the
launched power and to extend theﬁber span of the systems. In practical systems,
the input power is normally about 0 dBm and the EDFA is deeply saturated. The generated ASE power is low, resulting in a large SNR and in a nonsigniﬁcant amount
of ASE-signal beating at the photodiode level. In the optical receiver terminal, the opticalﬁber ampliﬁer can be used to optimize the receiver sensitivity, hence theﬁber
length of a repeaterless span.
To perform as an efﬁcient optical ampliﬁer, the gain of EDFA must be sufﬁ-
ciently large to make all the noise term much smaller than that of the ASE-beat term. In this case, we have the signal-dependent electronic noises (i
Neq) no longer the
dominating noise of the total noise. Thus from Equation 1.13b, we have
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12 Photonic Signal Processing: Techniques and Applications

dmax¼
(2<GP
‘‘
1’’
is
GEDF)
2
2G
2
<
2
SASEBoGEDFP
‘‘
1’’
is
Be
(1:17a)
where
P
isis the input optical signal power at the input of the EDF ampliﬁer
G
EDFis the optical power gain
or
d
max
¼
P
‘‘
1’’
is
GEDF
2qSASEBoBe
(1:17b)
We note that as soon as the ampliﬁer gainG
EDFin dB reaches 20 dB, thed-factor
reaches the maximum value; thus, it is not beneﬁcial to increase the optical gain
higher than 20 dB.
Therefore, the new receiver sensitivity for a preoptical ampliﬁer receiver can be
found by converting theP
isto dBm for a value ofdcorresponding to a certain BER
(e.g., BER¼10
ﬁ9
ford¼6).
1.2.3.2 Fiber Bragg Gratings
With the discovery of the photosensitivity of silicaﬁber, especially the Ge-doped
silica, by Hill et al. in 1978 [72], a new type ofﬁber-based component has been
created by writing patterns so that there are regions in which the refractive index can
be increased or decreased. Hence, if an interference pattern is imposed on theﬁber, a
grating can be generated. Hence, lightwaves can be reﬂected if the period of the
grating matches that of the lightwave. Thus, the phase matching condition would
lead to theﬁltering effects on the reﬂected spectrum. The center of the passband
happens exactly when the phase matching is at the Bragg wavelengthl
B.
l
B¼2n effﬁ (1:18)
where
Lis the period of the grating
n
effis the effective refractive index of the guided mode, i.e., the ratio of the
propagation of the guided lightwave along theZ-direction and that of the wave
vector
The grating reﬂection coefﬁcient can be determined during the fabrication of the
grating, usually depending on the exposure time of the silicaﬁber under the UV
illumination.
The wavelength-dependent reﬂection property makes FBG a very attractive
sampling element used for the construction of discrete time signal photonic proces-
sors. In the case of grating-based photonic signal processors, the sampling time
can be controlled via the spacing of the grating, usually by pyroelectric effects or
by stressing the FBG. Thus, the center wavelength can be selective and thus a
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Principal Photonic Devices for Processing 13

tunable wavelength processing system can be generated or demultiplexing of differ-
ent wavelength lightwave channels in a WDM system [73,74]. Chirpedﬁber
grating can also be employed in which the period is continuously varied. This allows
the simultaneous reﬂection of different wavelength lightwaves but different delay
time, hence dispersion compensation of modulated lightwave channels. Arrays of
FBGs can be formed in cascade or parallel to generate discrete photonic signal
processors.
The reﬂectance transfer function of a uniform FBG of lengthLis given by [75]
ﬂ¼
ﬁksinh
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
L
p
s
2
sinh
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
L
p
þj
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
p
cosh
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
L
p (1:19)
wherekis the AC coupling coefﬁcient given by
k¼
p
l
ndn
eff (1:20)
wheredn
effis the average change of the effective index of the grating over the whole
length of the FBG.^sis the DC self-coupling coefﬁcient and is related to a detuning
factor (¼dþs) given by
d¼2pn
eff
1
l
ﬁ
1
l
B

(1:21)
s¼
2p
l
dn
eff (1:22)
Under the operating condition of incoherence processor, the reﬂection in power is
given as the modulus (magnitude) of the transmittance transfer function which can be
written as
r¼
sinh
2
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
L
p
cosh
2
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k
2
ﬁ^s
2
L
p
ﬁ
^s
2
k
2
(1:23)
The phase change of the reﬂection transfer function can be found as
ﬃ¼tan
ﬁ1
Im(ﬂ)
Re(ﬂ)
ﬁﬂ
(1:24)
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14 Photonic Signal Processing: Techniques and Applications

The maximum reﬂectance is thus given as
r¼tanh
ﬁ1
kL (1:25)
This shows that the grating reﬂectivity can be increased monotonically as a function
of the length of the grating. The dimensionless productkLis the measure of the
grating strength.
1.3 OPTICAL MODULATORS
1.3.1 I
NTRODUCTORYREMARKS
The engineering of optical transmission systems has been pushed to the maximum
limit. We have witnessed the transmission bit rate increases from 2.5 Gb=s in the
mid-1980s to 40 G and even 160 Gb=s in the 1990s and the early twenty-ﬁrst century
[37,38,76–99]. These transmission rates are beyond the capability of direct modula-
tion of the laser sources. External modulation technique is the method, which would
modulate the lightwaves generated from the laser sources whose line width must also
be very narrow, usually around 100 MHz.
Most of advanced optical modulators are operating based on two principal
physical effects: the linear electro-optic effect (EOE
effect (EAE ﬁeld, which makes the
modulators as voltage-controlled devices. The appliedﬁeld changes the refractive
index or the absorption rate via the EOE and the EAE, respectively. This is used in
changing the phase of the optical waves along the propagation path of an interfero-
meter and hence the constructive or destructive output.
Lightwaves can have various characteristics, which can be modulated for carry-
ing information, including the intensity, the frequency, the phase, and the polariza-
tion. Among these, the intensity modulation is very popular in the normal ON–OFF
keying (OOK) and until recently the phase modulation has been considered for
efﬁcient bandwidth. Optical sources of different carrier frequencies, particularly
their stability plays a very important role in WDM and DWDM opticalﬁber
communications. The spacing between the centers of the wavelengths of operation
is naturally very critical in system and network performance. Thus, it is very crucial
for both simulation and hardware implementation to ensure that the optical carriers
generated represent the true physical picture of the practical optical sources.
Unlike direct modulation of the laser diodes, external modulation modulates the
lightwaves continuously generated by the laser; the lithium niobate (LiNbO
3) modu-
lators can be designed to be chirp free, adjustable chirp, negative or positive chirp
which can be employed to compensate for theﬁber dispersion. In analog systems, the
linearization of the external modulator can provide very low modulation distortion.
This section introduces the principles of modulation of the lightwaves using EO,
electro-absorption (EA
3uniaxial or polymer
materials systems. The waveguides can be either diffused or rib structures. Some
numerical designs of optical waveguides are given. The modulation phenomena are
described for the EA and Mach–Zehnder interferometric modulators (MZIMs).
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Principal Photonic Devices for Processing 15

1.3.2 LITHIUMNIOBATEOPTICALMODULATORS
The maturity of LiNbO
3technology has warranted the realization of devices that
provide high speed switching and modulation. Among the more mature and widely
used devices that provide broadband modulation are the modulators, which are based
on interferometric and directional coupler structure [76]. Our interest in this section
is the design and applications of theY-branch interferometric modulators.
There exist two versions of interferometric type modulators. One is the Mach–
Zehnder type structure that employs a 232 directional couplers as splitter and
combiner, whereas the other one is the 3 dB (i.e., symmetric)Y-branch splitting
and combining interferometer. TheY-branch interferometer is the most popular
structure for optical modulation devices when only one input and one output optical
ports are required. In this section, we outline the relevant LiNbO
3technology and the
operational principles of such modulators.
1.3.2.1 Optical-Diffused Channel Waveguides
1.3.2.1.1 Property of LiNbO
3
Optical waveguide devices based upon LiNbO3substrates are presently in an
advanced state and employed as the external modulators in most photonic transmitters
in advanced optical communication systems. LiNbO
3has several important charac-
teristics that make it attractive for waveguide devices. It is relatively easily processed
and its material properties have been studied and documented extensively [78].
LiNbO
3is a dielectric crystal which belongs to the rhombohedral space group,
3 mm. It possesses a high Curie temperature point, large EO and acousto-optic effects,
large nonlinear optical coefﬁcients, and high birefringence. The LiNbO
3crystal is
deﬁned in three dimensions with three principal axes namely theX,Y, andZ(orC-)
axes. The axes form the basis of specifying the particular orientation or cutting of the
wafers. AnX-cut crystal implies that the direction normal to theﬂat surface of
the wafer is parallel to theX-principal axis, whereas aZ-cut crystal indicates that the
direction normal to theﬂat surface of the wafer is parallel to theZorC-principal axis.
Owing to its birefringence or doubly refracting properties, LiNbO
3as an uniaxial
birefringent type has two refractive indices, known, respectively, as the ordinary and
extraordinary refractive indices, which can be represented by an ellipsoid in the three-
dimensional (3-D Z-axis would see the extraordinary
index, whereas for light polarized in theX-orY-crystal axis, the ordinary index would
be effective. The refractive index seen by polarization in any direction other than
a principal axis would depend on the direction of polarization with respect to the
principal axes.
Figure 1.5 shows the index ellipsoid of the LiNbO
3uniaxial crystal. Alterna-
tively in the plane of the wave propagation, we have the refractive index contours for
a positive uniaxial material, such as LiNbO
3crystal as shown in Figure 1.6. The
diagrams are drawn relative to theC-axis as the principal axis. Lightwaves traveling
in the device are not propagating along a principal axis, but in some arbitrary
direction. In LiNbO
3optical modulators, we usually use the crystals with the cuts
in eitherX-orY-axes as illustrated in Figures 1.6b and c, respectively. These
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16 Photonic Signal Processing: Techniques and Applications

X
Y
Z
n
3
Index
ellipse
n
a
n
b
D
b
D
a
n
3
n
2
u
^
FIGURE 1.5Index ellipsoid with ordinary indexn
o(n
2) andn
e(n
3) the extraordinary index.
naandnbare refractive indices seen by lightwaves polarized other than the principal crystal axis.
n
o
n
o
n
o
n
e
n
e
n
e
Z or C-axis
Z
(a
(c)
Z
Z
X
Y
X
Y
FIGURE 1.6Refractive index contours for LiNbO3crystal withZ-orC-denoted as the
principal axis. (a Z-axis polarized alongY-cut LiNbO
3,
(b Z-axis andX-cut crystal, (cY-prop andY-cut crystal.
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Principal Photonic Devices for Processing 17

effective refractive indices as seen by the lightwaves are critical when one uses it as
an EO or acousto-optic modulator so as to maximize the tensor coefﬁcients of the
relevant effect. Furthermore, the propagation direction is also dependent on the
guidance of such lightwaves in optical wave guides, which are fabricated by in-,
out-diffusion or proton exchange methods. In the next section, the fabrication
techniques of the optical waveguides in LiNbO3are brieﬂy described.
1.3.2.1.2 Fabrication of Optical Channel Waveguide
The formation of waveguide in the LiNbO
3substrate involves the creation of a
region of higher refractive index relative to that of the substrates. Several techniques
[81] have been employed to form waveguides in LiNbO3. Initially, the waveguide
was formed by thermal out-diffusion of Li2O which results in an increased refractive
index for the extraordinary index,ne. This technique involves the placing of the
LiNbO3substrate in a furnace at a temperature of in the region of 9808C–10758C for
5–10 h [81,82] that causes the out-diffusion of Li2O from the substrate, hence
creating a layer of region of higher refractive index at the surface of the substrate.
In addition to being limited to guiding light in only one polarization, the achievable
index change is small and therefore provides waveguide modes whose conﬁnement
is relatively weak. Furthermore, channel waveguides cannot be formed conveniently
except by etching the substrate to form ridge waveguides.
The above problems can be overcome by creating waveguides based on the in-
diffusion of a thin metallic layer, e.g., titanium, to raise the refractive index of the
substrate on the surface and graded along the diffusion depth. This technique is by
far the most popular and established method since 1976.
Optical channel waveguides in LiNbO
3can also be formed by an exchange
process similar to that used for glass substrates. Proton exchange using benzoid
and other acids has also been employed. As in the case of out-diffused waveguides,
only the extraordinary indexneis increased. However, very large index difference
in only one direction can be achieved using proton exchange technique.
The fabrication of titanium-diffused waveguides is quite straightforward.
Although there are slight variations, a typical step of the fabrication of the
channel waveguides is by liftoff patterning shown in Figure 1.7. The polished and
1. Expose waveguide pattern
Photoresist
2. Deposit titanium dopant
Ti metal film
3. Liftoff 4. Diffuse
w
t
t ~ 5–10 µm
w ~ 0.05–0.1 µm
Diffused waveguide
LiNbO
3
T ~ 1000ﬁC –1050ﬁC
t ~ 4–12 h
FIGURE 1.7Steps of fabrication of Ti-diffused optical waveguide in LiNbO3.
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18 Photonic Signal Processing: Techniques and Applications

cleaned crystal is spun coated with a thin layer of photoresist. A mask with the
desired waveguide pattern is placed in contact with the crystal and then exposed to
UV light. Upon developing to remove the exposed photoresist, a window corre-
sponding to the waveguide pattern is left in the photoresist. Titanium (Ti
deposited over the entire crystal by rf-sputtering, by e-beam deposition or by using a
resistively heated evaporator. The crystal is then placed in a photoresist solvent,
which removes the photoresist and the unwanted titanium, leaving the desired
strip of titanium. Instead of liftoff, the patterning can also be achieved by depositing
Ti over the entire surface and selectively removing it outside the desired waveguide
region.
The Ti-patterned substrate is then placed in a diffusion furnace under oxygenﬂow
for diffusion at temperatures that range from 9808C to 10508C for typical diffusion
times of 5–10 h. The lower limit (temperature) results in an overly long diffusion time,
while the upper limit is set by the desire to remain below the Curie temperature
(~11258C) to avoid the need to repole the crystal after diffusion. Various ambient
conditions have been used for the diffusion. Historically, the heating and diffusion
cycles were performed in an atmosphere ofﬂowing argon bubbled through a water
column. A process of cool down after diffusion is performed inﬂowing oxygen to
allow reoxidation of the crystal to compensate for oxygen loss during diffusion. The
water vapor treatment was initially employed to reduce the photorefractive effect.
Later, it was realized that this process also reduces Li
2O out-diffusion that can cause
unwanted planar guiding for the extraordinary polarization. Typically, 80% relative
humidity in theﬂow gas is sufﬁcient to eliminate unwanted guiding at diffusion
temperature as high as 10508C.
Diffusion process is controlled so that a single-mode waveguide with a low
coupling loss, i.e., matched spot size with that of the opticalﬁber, can be achieved
[85,86]. Various fabrication parameters and conditions can be varied independently
to control important waveguide parameters, such as waveguide width, effective
depth, and peak index change. The waveguide depth depends upon the diffusion
time, the diffusion temperature, and to a lesser extent on the Ti strip width. The
waveguide width is photolithographically deﬁned although increased somewhat by
lateral diffusion. Most importantly, the peak waveguide-substrate index change
depends, forﬁxed diffusion temperature and time, upon the Ti and density.
1.3.2.1.3 Guided Modes of Ti:LiNbO
3Channel Waveguide
The mode distribution of Ti:LiNbO
3channel waveguide, a graded index waveguide,
plays a signiﬁcant role in the design of the optical modulators and switches. Efﬁcient
design and fabrication of such optical devices require good knowledge of the modal
characteristics of the relevant channel waveguide. The key features of the fabrication
of Ti:LiNbO
3waveguide can be understood, and hence the modulation efﬁciency for
Mach–Zehnder optical modulator.
Over the past decades, much work has been done in fabricating low loss,
minimum mode size Ti-diffused channel waveguide [30,34]. From these references,
the diffusion process involved in the fabrication of LiNbO
3waveguide and its
relevant diffusion proﬁle can be used for the design of diffused channel optical
waveguides.
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Principal Photonic Devices for Processing 19

1.3.2.1.4 Refractive Index Proﬁle of Ti:LiNbO 3Waveguide
When the Ti metal is diffused, Ti-ion distribution spreads more widely than the initial
strip width. The proﬁles can be described by the sum of an error function, while the
Ti-ion distributions perpendicular to the substrate surface can be approximated by a
Gaussian function [86]. This, of course, is true only if the diffusion time is long enough
to diffuse all the Ti metal into the substrate. We consider this case as having theﬁnite
dopant source. However, if the total diffusion time is shorter than needed to exhaust
the Ti source, the lateral diffusion proﬁle would take up the sum of the complementary
error function while the depth index proﬁle is given by the complementary function
[83]. This case is considered to have had an inﬁnite doping source [12]. In our study,
we would assume that there is sufﬁcient time for the source to be fully diffused because
in most practical waveguide, it is undesirable to have Ti residue deposited on the
surface of the waveguide because this will increase the propagation loss. This
increase in propagation loss is a result of stronger interaction with the LiNbO
3surface
(and thus an increased scattering loss) as the modes become more weakly guided.
In general, the two-dimensional (2-D
guiding channel waveguide
n(x,y)¼n
bþDn(x,y)¼n bþDn 0f(x)g(y)( 1:26)
where
n
bis the refractive index of the bulk (substrate
Dn(x,y) is the variation of the refractive index in the guiding region in the
vertical and lateral directions
Dn(x,y) in our diffusion model is essentially a separable function wheref(x) andg(y)
are the functions that describe the lateral and perpendicular diffusion proﬁle andDn
0
is known as the surface index change after the diffusion time. The surface index
change is deﬁned as the change of refractive index on the substrate just below the
center of the Ti strip. In other words, it is the refractive index when bothf(x) andg(y)
assume unity value. The variation of the refractive index can be represented as [12]
Dn(x,y)¼
dn
dc
t
ð
w=2
ﬁw=2
2
d
y
ﬃﬃﬃﬃ
p
pexpﬁ
y
d
y

2
"#
1
d
x
ﬃﬃﬃﬃ p
pexpﬁ
xﬁu
d
x

2
"#
du
¼Dn
0f(x)g(y)( 1:27)
where
f(x)¼
1
2
erfxþ
w
2
.
d
x
hi
ﬁerfxﬁ
w
2
.
d
x
hino
erf
w
2d
x
(1:28)
g(x)¼expﬁ
y
d
y

2
"#
(1:29)
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20 Photonic Signal Processing: Techniques and Applications

and
Dn0¼
dn
dc
2
ﬃﬃﬃﬃ
p
p
t
dy
erf
w
2dx

(1:30)
with
dx¼2
ﬃﬃﬃﬃﬃﬃﬃ
Dxt
p
and
dy¼2
ﬃﬃﬃﬃﬃﬃﬃ
Dyt
p
(1:31)
where
tis the total diffusion time
cis the Ti concentration
(dxanddy) and (DxandDy) are the diffusion lengths and constants in thexandy
directions, respectively
tandware the initial Ti strip thickness and width, respectively
dn=dcis the change of index per unit change in Ti metal concentration
Figures 1.8 and 1.9 show the diffusion proﬁle across and into the LiNbO3substrate.
The diffusion conditions are the same for both cases. Figure 1.10 shows the variation
of the surface index with respect to the initial Ti strip width. The change of surface
index would reach a saturated value when increasing the width. The change of
surface index can be given by
Dn0¼
dn
dc
2
ﬃﬃﬃﬃ
p
p
t
dy
(1:32)
Diffusion into substrate with different diffusion time
0
0.005
0.01
0.015
0.02
0.025
0.03
0 1 2 3 4 5 6 7 8 9 10 11 12
y (µm)
Change of refractive index
t = 4 h
t = 6 h
t = 8 h
t =10 h
t =12 h
t =12 h
t =10 h
t = 8 h
t = 6 h
t = 4 h
FIGURE 1.8Depth index variation with increasing diffusion time.
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Principal Photonic Devices for Processing 21

Any increase in the surface index must be from a higher thickness of the Ti strip, or a
decrease in diffusion depth,dy, which involves either an increase or decrease in
diffusion temperature. According to the work of Fukuma and Noda [83], the
diffusion length is very close to one another in both lateral and depth directions
(isotropic diffusion) at 10258C forZ-cut LiNbO3crystal. An increase in temperature
greater than that would result in a higher diffusion constant in the depth direction and
lower value for lateral diffusion and vice versa for diffusion temperature lower than
10258C. The diffusion length can also be changed by controlling the diffusion time.
Essentially, longer diffusion time would means a lower surface index change as most
of the Ti source would be diffused deeper into the substrate. Again, we could predict
Lateral diffusion with different Ti strip width (model 1)
0
0.005
0.01
0.015
0.02
0.025
−14−12−10−8−6−4−2 0 2 4 6 8 10 12 14
x (µm)
Change of refractive index
w = 2.5
w = 4
w = 6
w = 8
w =10
w = 2.5
w = 4.0
w = 6.0
w = 8.0
w = 10.0
FIGURE 1.9Lateral diffusion variation with increasing Ti strip width.
25
20
15
10
y (µm)
x (µm)
5
025
20
15
10
5
0
0
0.5
1
Normalized E
y
FIGURE 1.10Typical (transverse magnetic) TM modalﬁeld of a diffused channel waveguide.
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22 Photonic Signal Processing: Techniques and Applications

that a higher change of surface index since not all the Ti metal is exhausted. Typical
fabrication condition and parameters are assumed to beT¼10258C,t¼1100 Å,
dn=dc¼0.625,d
xandd yare both equal to 3.2mm. We can observe that by
controlling the width of the initial Ti strip width, one can vary the change of
refractive index and the relative size of the channel waveguide, thus enabling us to
control the number of mode and the mode spot size that can be supported by the
diffused channel waveguide.
In general, a narrow initial Ti width would give a near cutoff mode for the
refractive index change would be too small. The optical mode would be weakly
conﬁned, thus giving a larger mode size. As we increase the Ti width, the refractive
index difference would be higher and the waveguide mode would be better conﬁned
and has a smaller mode size. This is important to minimize the coupling loss between
the single-modeﬁber and the modulator waveguide. However, the mode size would
increase with further increase in Ti width due to a larger physical size of the
waveguide. The change of surface index can also be controlled by varying the
thickness of the Ti strip. As implied in Equation 1.32, the surface index change is
proportional to the Ti strip thickness,t. Penetrable Ti thickness at 10008C–10508C
for 6 h would be around 50–80 nm [30]. If the Ti strip is too thin, the refractive index
change approaches cutoff conditions. All these characteristics and the distribution of
the guided modes are illustrated in the next section.
1.3.2.1.5 Mode Distribution: Numerical and Experimental
The parameters of the diffusion proﬁle can be used for simulation and design of the
modal characteristics of Ti:LiNbO
3waveguide. Experimental work reported by
Suchoski and Ramaswamy [89] in the fabrication of minimum mode size low loss
Ti:LiNbO
3channel waveguide can be conﬁrmed with simulated waveguide modes.
We analyze theZ-cutY-propagating material as shown in Figure 1.11 and likewise in
Figure 1.12 for different crystal orientations. For this particular crystal cut, the
relevant opticalﬁeld would be (transverse magnetic) TM polarized, which corres-
ponds to the polarization along the extraordinary index axis of the crystal. Hence, the
change of refractive index of the extraordinary index,n
e, is expected. The TM-
polarized mode width and depth, which is deﬁned as 1=e intensity full width and full
depth, are measured for Ti:LiNbO
3waveguides fabricated under the condition where
T¼10258C for 6 h. The sample waveguides have Ti thickness ranging from 500 to
1100 Å, and Ti strip widths ranging from 2.5 to 10mm. We thus can see that the
mode size increases as the Ti strip width is decreased from 4 to 2.5mm. This increase
is more pronounced especially with the thinner Tiﬁlms, hence smallerDn, because
the waveguides become closer to cutoff. The TM mode depth and width decrease as
the Ti thickness is increased from 500 to 800 Å. However, for 4mm strip widths, the
mode size does not decrease further for Tiﬁlms thicker than 800 Å. This is an
indication that it is not possible to diffuse any more Ti into the substrate for Ti
thickness of more than 800 Å for 6 h diffusion time. It can be focused on Ti thickness
that ranges between 700 and 800 Å because it is the thickness that gives minimum
mode sizes, which is ideal for the design of optical modulator for maximizing the
overlap integral between the guided mode and the applied modulatingﬁeld. To
achieve this, we mustﬁrst estimate the suitable diffusion parameter to be used in the
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Principal Photonic Devices for Processing 23

simulation. Various values of dn=dchave been reported [24]. Measurements reported
by Minakata et al. [81] show the change of extraordinary indexneper Ti concen-
tration as
dne
dc
¼0:625 (1:33)
The nominal values for diffusion constants,DxandDy, obtained from the work of
Fukuma and Noda [83] were both measured to be 1.2310
Γ4
mm
2
=s at the nomin-
ated temperature which is 10258C giving both diffusion length ofd
xandd
ythe value
of 3.2mm. With these nominal parameters, the optical channel waveguides with a Ti
thickness,tof 700 Å can be simulated. The followingﬁgures are the result of our
simulation compared to the experimental one and some illustrations of the TM mode
proﬁle. Figure 1.13 shows that the simulated results appear to have overestimated
bothGxandGy. Such discrepancy is anticipated fabrication of diffused waveguide is
subjected to many changes. Various reports [76–88] have shown that even though
the nominal diffusion condition can be very much the same, the measured diffusion
parameters can still differ greatly from one another due to possible differences in
stoichiometry between different crystals and measurement techniques. Therefore,
there would certainly be some uncertainties that lie in fabrication parameters and also
the application of the refractive index model. Such uncertainty can be compensated
by adjusting the value of dn=dcand alsoDxandDy.Weﬁnd that by adjusting the
following diffusion parameters where dn=dc¼0.8,Dx¼1.4310
Γ4
mm=s
2
and
Optical waveguide
20 mm
8 µm
(a)
(b)
Metal
electrode
T
EL
G
EL
W
EL(gnd)
d
OPT
G
OPT
W
OPT
Z
Y
X
W
ELO(bo1)
T
Buffer
Adhesion
layer
Buffer
layer
LiNbO
3
substrate
FIGURE 1.11A schematic diagram of a dual-drive Mach–Zehnder intensity modulator:
(a
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24 Photonic Signal Processing: Techniques and Applications

D
y¼1.1310
4
mm=s
2
, the properties of the estimated modes correspond well
within design limit with the experimental waveguides for the case where the wave-
guide is well guided as shown in Figure 1.13. The plots with circular graph markers
are extracted from Ref. [30] whereas the plots with square graph markers are
simulated results. The simulated and measured result matches to within 5%. The
results show that the mode width,Gxcorresponds well to the experimental result with
differences of less than 3%. The mode depth,Gy, however, matches only to within
8%. Effectively, the larger initial mode spot size is because of the lower refractive
Optical mode
Optical mode
Optical mode
Optical mode
gg w
gg w
Z
X
Air
Air
Air
LiNbO
3
LiNbO
3
LiNbO
3
LiNbO
3
SiO
2
SiO
2
SiO
2
SiO
2
X-cut CPW
X
Z
Z-cut CPW
gw
Z
X
Z-cut ACPS
gw
Air
Z
X
Z-cut CPS
W
FIGURE 1.12Commonly used electrode structure and crystal orientation in LiNbO3.
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Principal Photonic Devices for Processing 25

index change resulted from a much narrower Ti width, thus causing the optical mode
to be less conﬁned. As the Ti strip becomes wider, it gives a higher change of
refractive index, hence a better conﬁned optical mode. The mode width, however,
would increase further as we increase the Ti width simply because of the increase in
the physical width of the waveguide. At the same time, the larger physical width
would enable the waveguide to support higher-order modes.
Figure 1.14 shows a typical dispersion relation of the normalized mode indexbas
a function of the width of the Ti thin-ﬁlm layer before the diffusion, deﬁned as [37]
b¼
(n
2
eff
ﬁn
2
s
)
2Dnns
(1:34)
It is shown that the waveguide becomes more strongly guided as we increase the Ti
width. At the same time, higher-order mode begins to settle in as the strip width
becomes signiﬁcantly larger than 6mm. The modal depth, however, continues to
decrease with the wider Ti strip width because any wider Ti strip width does not
affect the diffusion depth. It only increases the surface index, thus giving smaller
modal depth. The surface index, however, only reaches a maximum value as we
increase Ti widthw. This is shown in Figure 1.17. Therefore, as the Ti strip width is
increased to a certain point, the modal depth ceases to decrease further at any
apparent rate, as shown by both the experimental and simulated results. At this
point, lateral diffusion dominates. It is worth to be reminded that the limiting case of
increasing width in Ti width is a planar waveguide. Similarly, with the same
diffusion parameter, the experiment where Ti thickness is increased to 800 Å can
be compared. Fouchet et al. [85] had shown the relation between refractive index
changeDn
e,o(Z) and Ti concentrationC(Z) in the mathematical form of
Variation of mode size with Ti strip width (t = 750 Å)
0
1
2
3
4
5
6
234567891011
Ti strip width (µm)
Γ
x
Γ
y
Ref. [30]
SVMM
SVMML
Ref. [30]
Γ
x
, Γ
y
(µm)
FIGURE 1.13Comparison of simulated and experimental mode sizes fort¼700 Å.
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26 Photonic Signal Processing: Techniques and Applications

Dne,o(Z)¼Ae,o(Co,l)C(Z)?
ae,o
(1:35)
The expression shows that the proportionality coefﬁcientA
e,odepends not only on
the wavelengthlbut also on the diffusion parameters which are characterized byCo,
the Ti surface concentration.
The mode intensity distribution of a higher-order mode is illustrated in Figure 1.15
and itsﬁeld in Figure 1.16. The diffusion proﬁle of Ti ions in the substrate can be seen as
Normalized index, b as a function of Ti strip width, w (t = 750 Å)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
012345678910
Ti strip width, w (µm)
Normalized mode index, b
TM
11
TM
21
TM
31
FIGURE 1.14Normalized mode index,bas a function of Ti strip width,w.
Refractive index distribution across substrate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
−16−14−12−10−8−6−4−20246810121416
X (µm)
Normalized refractive index

FIGURE 1.15Lateral diffusion proﬁle of Ti ions.
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Principal Photonic Devices for Processing 27

shown in Figure 1.17. The surface concentration of Ti is shown in Figure 1.18 and the
variation of the modeﬁeld distribution with respect to the diffusion time is shown in
Figure 1.19.
1.3.2.2 Linear Electro-Optic Effect
The linear electro-optic (Pockels) effect, which is the basis for active wave guide
device control, provides a change in refractive index proportional to the applied
electricﬁeld. The way in which this index change results in optical switching,
intensity modulation,ﬁlter tuning, etc., and depends upon the device conﬁgurations.
A voltageVapplied to the electrodes placed over or alongside the waveguide,
25
20
15
10 y (µm)
x (µm)
5
025
20
15
10
5
0
−1
−0.5
0
0.5
3-D plot for TM-polarized mode
1
Normalized E
y
FIGURE 1.16TM21mode:t¼750 Å,w¼10mm.
Refractive index distribution into substrate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
01234567891011121314 15
Substrate depth, y (µm)
Normalized refractive index
FIGURE 1.17Depth of the Ti diffusion proﬁle.
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28 Photonic Signal Processing: Techniques and Applications

as shown in Figure 1.20, created an internal electricﬁeld of approximate magnitude
jEjV=G, Gbeing the width of the electrode gap [76,87,88].
The linear change in the coefﬁcients of the index ellipsoid due to an applied
electricﬁeld (Ej) along the principal crystal axis is [76]
D
1
n
2
i

¼
X
3
j¼1
rijEjor (Dn)
i?ﬁ
n
3
2
X
3
j¼1
rijEj (1:36)
Change of surface index versus Ti strip width
0
0.005
0.01
0.015
0.02
0.025
012345678910
Initial Ti width (µm)
Change of surface index
FIGURE 1.18Change of surface index as a function of initial Ti width.
Lateral diffusion with different diffusion time
0
−16−14−12−10−8−6−4−2 0 2 4 6 8 10 12 14 16
x (µm)
Change of refractive index
t = 4
t = 6
t = 8
t = 10
t = 12
t = 8
t = 6
t = 4
t = 10
0.006
t = 12
0.01
0.015
0.02
0.03
0.026
FIGURE 1.19Lateral diffusion variation of Ti with increasing diffusion time.
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Principal Photonic Devices for Processing 29

Exploring the Variety of Random
Documents with Different Content

CHAPTER XIII
THE EVOLUTION OF THE WORLD
The Notion of Creation—Miracles—Creation of the Whole Universe
and of its Various Parts—Creation of Substance (Cosmological
Creation)—Deism: One Creative Day—Creation of Separate
Entities—Five Forms of Ontological Creationism—Theory of
Evolution—I. Monistic Cosmogony—Beginning and End of the
World—The Infinity and Eternity of the Universe—Space and
Time—Universum perpetuum mobile—Entropy of the Universe—
II. Monistic Geogeny—History of the Inorganic and Organic
Worlds—III. Monistic Biogeny—Transformism and the Theory of
Descent: Lamarck and Darwin—IV. Monistic Anthropogeny—
Origin of Man
The greatest, vastest, and most difficult of all cosmic problems is
that of the origin and development of the world—the “question of
creation,” in a word. Even to the solution of this most difficult world-
riddle the nineteenth century has contributed more than all its
predecessors; in a certain sense, indeed, it has found the solution.
We have at least attained to a clear view of the fact that all the
partial questions of creation are indivisibly connected, that they
represent one single, comprehensive “cosmic problem,” and that the
key to this problem is found in the one magic word—evolution. The
great questions of the creation of man, the creation of the animals
and plants, the creation of the earth and the sun, etc., are all parts
of the general question, What is the origin of the whole world? Has it
been created by supernatural power, or has it been evolved by a
natural process? What are the causes and the manner of this
evolution? If we succeed in finding the correct answer to one of
these questions, we have, according to our monistic conception of

the world, cast a brilliant light on the solution of them all, and on the
entire cosmic problem.
The current opinion as to the origin of the world in earlier ages was
almost a universal belief in creation. This belief has been expressed
in thousands of interesting, more or less fabulous, legends, poems,
cosmogonies, and myths. A few great philosophers were devoid of it,
especially those remarkable free-thinkers of classical antiquity who
first conceived the idea of natural evolution. All the creation-myths,
on the contrary, were of a supernatural, miraculous, and
transcendental character. Incompetent, as it was, to investigate for
itself the nature of the world and its origin by natural causes, the
undeveloped mind naturally had recourse to the idea of miracle. In
most of these creation-myths anthropism was blended with the
belief in the miraculous. The creator was supposed to have
constructed the world on a definite plan, just as man accomplishes
his artificial constructions; the conception of the creator was
generally completely anthropomorphic, a palpable “anthropistic
creationism.” The “all-mighty maker of heaven and earth,” as he is
called in Genesis and the Catechism, is just as humanly conceived as
the modern creator of Agassiz and Reinke, or the intelligent
“engineer” of other recent biologists.
Entering more fully into the notion of creation, we can distinguish as
two entirely different acts the production of the universe as a whole
and the partial production of its various parts, in harmony with
Spinoza’s idea of substance (the universe) and accidents (or modes,
the individual phenomena of substance). This distinction is of great
importance, because there are many eminent philosophers who
admit the one and reject the other.
According to this creationist theory, then, God has “made the world
out of nothing.” It is supposed that God (a rational, but immaterial,
being) existed by himself for an eternity before he resolved to create
the world. Some supporters of the theory restrict God’s creative
function to one single act; they believe that this extramundane God
(the rest of whose life is shrouded in mystery) created the substance

of the world in a single moment, endowed it with the faculty of the
most extensive evolution, and troubled no further about it. This view
may be found, for instance, in the English Deists in many forms. It
approaches very close to our monistic theory of evolution, only
abandoning it in the one instant in which God accomplished the
creation. Other creationists contend that God did not confine himself
to the mere creation of matter, but that he continues to be operative
as the “sustainer and ruler of the world.” Different modifications of
this belief are found, some approaching very close to pantheism and
others to complete theism. All these and similar forms of belief in
creation are incompatible with the law of the persistence of matter
and force; that law knows nothing of a beginning.
It is interesting to note that E. du Bois-Reymond has identified
himself with this cosmological creationism in his latest speech (on
“Neovitalism,” 1894). “It is more consonant with the divine
omnipotence,” he says, “to assume that it created the whole material
of the world in one creative act unthinkable ages ago in such wise
that it should be endowed with inviolable laws to control the origin
and the progress of living things—that, for instance, here on earth
rudimentary organisms should arise from which, without further
assistance, the whole of living nature could be evolved, from a
primitive bacillus to the graceful palm-wood, from a primitive
micrococcus to Solomon’s lovely wives or to the brain of Newton.
Thus we are content with one creative day, and we derive organic
nature mechanically, without the aid of either old or new vitalism.”
Du Bois-Reymond here shows, as in the question of consciousness,
the shallow and illogical character of his monistic thought.
According to another still prevalent theory, which may be called
“ontological creationism,” God not only created the world at large,
but also its separate contents. In the Christian world the old Semitic
legend of creation, taken from Genesis, is still very widely accepted;
even among modern scientists it finds an adherent here and there. I
have fully entered into the criticism of it in the first chapter of my
Natural History of Creation. The following theories may be

enumerated as the most interesting modifications of this ontological
creationism:
I. Dualistic creation.—God restricted his interference to two creative
acts. First he created the inorganic world, mere dead substance, to
which alone the law of energy applies, working blindly and aimlessly
in the mechanism of material things and the building of the
mountains; then God attained intelligence and communicated it to
the purposive intelligent forces which initiate and control organic
evolution.
[26]
II. Trialistic creation.—God made the world in three creative acts: (a)
the creation of the heavens—the extra-terrestrial world, (b) the
creation of the earth (as the centre of the world) and of its living
inhabitants, and (c) the creation of man (in the image and likeness
of God). This dogma is still widely prevalent among theologians and
other “educated” people; it is taught as the truth in many of our
schools.
III. Heptameral creation; a creation in seven days (teste Moses).—
Although few educated people really believe in this Mosaic myth
now, it is still firmly impressed on our children in the biblical lessons
of their earliest years. The numerous attempts that have been made,
especially in England, to harmonize it with the modern theory of
evolution have entirely failed. It obtained some importance in
science when Linné adopted it in the establishment of his system,
and based his definition of organic species (which he considered to
be unchangeable) on it: “There are as many different species of
animals and plants as there were different forms created in the
beginning by the Infinite.” This dogma was pretty generally held until
the time of Darwin (1859), although Lamarck had already proved its
untenability in 1809.
IV. Periodic creation.—At the beginning of each period of the earth’s
history the whole population of animals and plants was created
anew, and destroyed by a general catastrophe at its close; there
were as many general creative acts as there are distinct geological

periods (the catastrophic theory of Cuvier [1818] and Louis Agassiz
[1858]). Palæontology, which seemed to support this theory in its
more imperfect stage, has since completely refuted it.
V. Individual creation.—Every single man—and every individual
animal and plant—does not arise by a natural process of growth, but
is created by the favor of God. This view of creation is still often met
with in journals, especially in the “births” column. The special talents
and features of our children are often gratefully acknowledged to be
“gifts of God”; their hereditary defects fit into another theory.
The error of these creation-legends and the cognate belief in
miracles must have been apparent to thoughtful minds at an early
period; more than two thousand years ago we find that many
attempts were made to replace them by a rational theory, and to
explain the origin of the world by natural causes. In the front rank,
once more, we must place the leaders of the Ionic school, with
Democritus, Heraclitus, Empedocles, Aristotle, Lucretius, and other
ancient philosophers. The first imperfect attempts which they made
astonish us, in a measure, by the flashes of mental light in which
they anticipate modern ideas. It must be remembered that classical
antiquity had not that solid groundwork for scientific speculation
which has been provided by the countless observations and
experiments of modern scientists. During the Middle Ages—
especially during the domination of the papacy—scientific work in
this direction entirely ceased. The torture and the stake of the
Inquisition insured that an unconditional belief in the Hebrew
mythology should be the final answer to all the questions of
creation. Even the phenomena which led directly to the observation
of the facts of evolution—the embryology of the plant and the
animal, and of man—remained unnoticed, or only excited the
interest of an occasional keen observer; but their discoveries were
ignored or forgotten. Moreover, the path to a correct knowledge of
natural development was barred by the dominant theory of
preformation, the dogma which held that the characteristic form and

structure of each animal and plant were already sketched in
miniature in the germ (cf. p. 54).
The science which we now call the science of evolution (in the
broadest sense) is, both in its general outline and in its separate
parts, a child of the nineteenth century; it is one of its most
momentous and most brilliant achievements. Almost unknown in the
preceding century, this theory has now become the sure foundation
of our whole world-system. I have treated it exhaustively in my
General Morphology (1866), more popularly in my Natural History of
Creation (1868), and in its special application to man in my
Anthropogeny (1874). Here I shall restrict myself to a brief survey of
the chief advances which the science has made in the course of the
century. It falls into four sections, according to the nature of its
object; that is, it deals with the natural origin of (1) the cosmos, (2)
the earth, (3) terrestrial forms of life, and (4) man.
I.—MONISTIC COSMOGONY
The first attempt to explain the constitution and the mechanical
origin of the world in a simple manner by “Newtonian laws”—that is,
by mathematical and physical laws—was made by Immanuel Kant in
the famous work of his youth (1755), General History of the Earth
and Theory of the Heavens. Unfortunately, this distinguished and
daring work remained almost unknown for ninety years; it was only
disinterred in 1845 by Alexander Humboldt in the first volume of his
Cosmos. In the mean time the great French mathematician, Pierre
Laplace, had arrived independently at similar views to those of Kant,
and he gave them a mathematical foundation in his Exposition du
Système du Monde (1796). His chief work, the Mécanique Céleste,
appeared a hundred years ago. The analogous features of the
cosmogony of Kant and Laplace consist, as is well known, in a
mechanical explanation of the movements of the planets, and the
conclusion which is drawn therefrom, that all the cosmic bodies were
formed originally by a condensation of rotating nebulous spheres.

This “nebular hypothesis” has been much improved and
supplemented since, but it is still the best of all the attempts to
explain the origin of the world on monistic and mechanical lines. It
has recently been strongly confirmed and enlarged by the theory
that this cosmogonic process did not simply take place once, but is
periodically repeated. While new cosmic bodies arise and develop
out of rotating masses of nebula in some parts of the universe, in
other parts old, extinct, frigid suns come into collision, and are once
more reduced by the heat generated to the condition of nebulæ.
Nearly all the older and the more recent cosmogonies, including
most of those which were inspired by Kant and Laplace, started from
the popular idea that the world had had a beginning. Hence,
according to a widespread version of the nebular hypothesis, “in the
beginning” was made a vast nebula of infinitely attenuated and light
material, and at a certain moment (“countless ages ago”) a
movement of rotation was imparted to this mass. Given this “first
beginning” of the cosmogonic movement, it is easy, on mechanical
principles, to deduce and mathematically establish the further
phenomena of the formation of the cosmic bodies, the separation of
the planets, and so forth. This first “origin of movement” is Du Bois-
Reymond’s second “world-enigma”; he regards it as transcendental.
Many other scientists and philosophers are equally helpless before
this difficulty; they resign themselves to the notion that we have
here a primary “supernatural impetus” to the scheme of things, a
“miracle.”
In our opinion, this second “world-enigma” is solved by the
recognition that movement is as innate and original a property of
substance as is sensation. The proof of this monistic assumption is
found, first, in the law of substance, and, secondly, in the discoveries
which astronomy and physics have made in the latter half of the
century. By the spectral analysis of Bunsen and Kirchhoff (1860) we
have found, not only that the millions of bodies, which fill the infinity
of space, are of the same material as our own sun and earth, but
also that they are in various stages of evolution; we have obtained

by its aid information as to the movements and distances of the
stars, which the telescope would never have given us. Moreover, the
telescope itself has been vastly improved, and has, in alliance with
photography, made a host of scientific discoveries of which no one
dreamed at the beginning of the century. In particular, a closer
acquaintance with comets, meteorites, star-clusters, and nebulæ has
helped us to realize the great significance of the smaller bodies
which are found in millions in the space between the stars.
We now know that the paths of the millions of heavenly bodies are
changeable, and to some extent irregular, whereas the planetary
system was formerly thought to be constant, and the rotating
spheres were described as pursuing their orbits in eternal regularity.
Astro-physics owes much of its triumph to the immense progress of
other branches of physics, of optics, and electricity, and especially of
the theory of ether. And here, again, our supreme law of substance
is found to be one of the most valuable achievements of modern
science. We now know that it rules unconditionally in the most
distant reaches of space, just as it does in our planetary system, in
the most minute particle of the earth as well as in the smallest cell
of our human frame. We are, moreover, justified in concluding, if we
are not logically compelled to conclude, that the persistence of
matter and force has held good throughout all time as it does to-day.
Through all eternity the infinite universe has been, and is, subject to
the law of substance.
From this great progress of astronomy and physics, which mutually
elucidate and supplement each other, we draw a series of most
important conclusions with regard to the constitution and evolution
of the cosmos, and the persistence and transformation of substance.
Let us put them briefly in the following theses:
I. The extent of the universe is infinite and unbounded; it is empty in
no part, but everywhere filled with substance.
II. The duration of the world is equally infinite and unbounded; it
has no beginning and no end: it is eternity.

III. Substance is everywhere and always in uninterrupted movement
and transformation: nowhere is there perfect repose and rigidity; yet
the infinite quantity of matter and of eternally changing force
remains constant.
IV. This universal movement of substance in space takes the form of
an eternal cycle or of a periodical process of evolution.
V. The phases of this evolution consist in a periodic change of
consistency, of which the first outcome is the primary division into
mass and ether—the ergonomy of ponderable and imponderable
matter.
VI. This division is effected by a progressive condensation of matter
as the formation of countless infinitesimal “centres of condensation,”
in which the inherent primitive properties of substance—feeling and
inclination—are the active causes.
VII. While minute and then larger bodies are being formed by this
pyknotic process in one part of space, and the intermediate ether
increases its strain, the opposite process—the destruction of cosmic
bodies by collision—is taking place in another quarter.
VIII. The immense quantity of heat which is generated in this
mechanical process of the collision of swiftly moving bodies
represents the new kinetic energy which effects the movement of
the resultant nebulæ and the construction of new rotating bodies.
The eternal drama begins afresh. Even our mother earth, which was
formed of part of the gyrating solar system millions of ages ago, will
grow cold and lifeless after the lapse of further millions, and,
gradually narrowing its orbit, will fall eventually into the sun.
It seems to me that these modern discoveries as to the periodic
decay and re-birth of cosmic bodies, which we owe to the most
recent advance of physics and astronomy, associated with the law of
substance, are especially important in giving us a clear insight into
the universal cosmic process of evolution. In their light our earth
shrinks into the slender proportions of a “mote in the sunbeam,” of

which unnumbered millions chase each other through the vast
depths of space. Our own “human nature,” which exalted itself into
an image of God in its anthropistic illusion, sinks to the level of a
placental mammal, which has no more value for the universe at
large than the ant, the fly of a summer’s day, the microscopic
infusorium, or the smallest bacillus. Humanity is but a transitory
phase of the evolution of an eternal substance, a particular
phenomenal form of matter and energy, the true proportion of which
we soon perceive when we set it on the background of infinite space
and eternal time.
Since Kant explained space and time to be merely “forms of
perception”—space the form of external, time of internal, sensitivity
—there has been a keen controversy, which still continues, over this
important problem. A large section of modern metaphysicians have
persuaded themselves that this “critical fact” possesses a great
importance as the starting-point of “a purely idealist theory of
knowledge,” and that, consequently, the natural opinion of the
ordinary healthy mind as to the reality of time and space is swept
aside. This narrow and ultra-idealist conception of time and space
has become a prolific source of error. It overlooks the fact that Kant
only touched one side of the problem, the subjective side, in that
theory, and recognized the equal validity of its objective side. “Time
and space,” he said, “have empirical reality, but transcendental
ideality.” Our modern monism is quite compatible with this thesis of
Kant’s, but not with the one-sided exaggeration of the subjective
aspect of the problem; the latter leads logically to the absurd
idealism that culminates in Berkeley’s thesis, “Bodies are but ideas;
their essence is in their perception.” The thesis should be read thus:
“Bodies are only ideas for my personal consciousness; their
existence is just as real as that of my organs of thought, the
ganglionic cells in the gray bed of my brain, which receive the
impress of bodies on my sense-organs and form those ideas by
association of the impressions.” It is just as easy to doubt or to deny
the reality of my own consciousness as to doubt that of time and
space. In the delirium of fever, in hallucinations, in dreams, and in

double-consciousness, I take ideas to be true which are merely
fancies. I mistake my own personality for another (vide p. 185);
Descartes’ famous Cogito ergo sum applies no longer. On the other
hand, the reality of time and space is now fully established by that
expansion of our philosophy which we owe to the law of substance
and to our monistic cosmogony. When we have happily got rid of the
untenable idea of “empty space,” there remains as the infinite
“space-filling”-medium matter, in its two forms of ether and mass. So
also we find a “time-filling” event in the eternal movement, or
genetic energy, which reveals itself in the uninterrupted evolution of
substance, in the perpetuum mobile of the universe.
As a body which has been set in motion continues to move as long
as no external agency interferes with it, the idea was conceived long
ago of constructing an apparatus which should illustrate perpetual
motion. The fact was overlooked that every movement meets with
external impediments and gradually ceases, unless a new impetus is
given to it from without and a new force is introduced to counteract
the impediments. Thus, for instance, a pendulum would swing
backward and forward for an eternity at the same speed if the
resistance of the atmosphere and the friction at the point it hangs
from did not gradually deprive it of the mechanical kinetic energy of
its motion and convert it into heat. We have to furnish it with fresh
mechanical energy by a spring (or, as in the pendulum-clock, by the
drag of a weight). Hence it is impossible to construct a machine that
would produce, without external aid, a surplus of energy by which it
could keep itself going. Every attempt to make such a perpetuum
mobile must necessarily fail; the discovery of the law of substance
showed, in addition, the theoretical impossibility of it.
The case is different, however, when we turn to the world at large,
the boundless universe that is in eternal movement. The infinite
matter, which fills it objectively, is what we call space in our
subjective impression of it; time is our subjective conception of its
eternal movement, which is, objectively, a periodic, cyclic evolution.
These two “forms of perception” teach us the infinity and eternity of

the universe. That is, moreover, equal to saying that the universe
itself is a perpetuum mobile. This infinite and eternal “machine of
the universe” sustains itself in eternal and uninterrupted movement,
because every impediment is compensated by an “equivalence of
energy,” and the unlimited sum of kinetic and potential energy
remains always the same. The law of the persistence of force proves
also that the idea of a perpetuum mobile is just as applicable to, and
as significant for, the cosmos as a whole as it is impossible for the
isolated action of any part of it. Hence the theory of entropy is
likewise untenable.
The able founder of the mechanical theory of heat (1850), Clausius,
embodied the momentous contents of this important theory in two
theses. The first runs: “The energy of the universe is constant”—that
is one-half of our law of substance, the principle of energy (vide p.
230). The second thesis is: “The energy of the universe tends
towards a maximum.” In my opinion this second assertion is just as
erroneous as the first is true. In the theory of Clausius the entire
energy of the universe is of two kinds, one of which (heat of the
higher degree, mechanical, electrical, chemical energy, etc.) is partly
convertible into work, but the other is not; the latter energy, already
converted into heat and distributed in the cooler masses, is
irrevocably lost as far as any further work is concerned. Clausius
calls this unconsumed energy, which is no longer available for
mechanical work, entropy (that is, force that is directed inward); it is
continually increasing at the cost of the other half. As, therefore, the
mechanical energy of the universe is daily being transformed into
heat, and this cannot be reconverted into mechanical force, the sum
of heat and energy in the universe must continually tend to be
reduced and dissipated. All difference of temperature must
ultimately disappear, and the completely latent heat must be equally
distributed through one inert mass of motionless matter. All organic
life and movement must cease when this maximum of entropy has
been reached. That would be a real “end of the world.”

If this theory of entropy were true, we should have a “beginning”
corresponding to this assumed “end” of the world—a minimum of
entropy, in which the differences in temperature of the various parts
of the cosmos would be at a maximum. Both ideas are quite
untenable in the light of our monistic and consistent theory of the
eternal cosmogenetic process; both contradict the law of substance.
There is neither beginning nor end of the world. The universe is
infinite, and eternally in motion; the conversion of kinetic into
potential energy, and vicissim, goes on uninterruptedly; and the sum
of this actual and potential energy remains constant. The second
thesis of the mechanical theory of heat contradicts the first, and so
must be rejected.
The representatives of the theory of entropy are quite correct as
long as they confine themselves to distinct processes, in which,
under certain conditions, the latent heat cannot be reconverted into
work. Thus, for instance, in the steam-engine the heat can only be
converted into mechanical work when it passes from a warmer body
(steam) into a cooler (water); the process cannot be reversed. In
the world at large, however, quite other conditions obtain—
conditions which permit the reconversion of latent heat into
mechanical work. For instance, in the collision of two heavenly
bodies, which rush towards each other at inconceivable speed,
enormous quantities of heat are liberated, while the pulverized
masses are hurled and scattered about space. The eternal drama
begins afresh—the rotating mass, the condensation of its parts, the
formation of new meteorites, their combination into larger bodies,
and so on.
II.—MONISTIC GEOGENY
The history of the earth, of which we are now going to make a brief
survey, is only a minute section of the history of the cosmos. Like
the latter, it has been the object of philosophic speculation and
mythological fantasy for many thousand years. Its true scientific

study, however, is much younger; it belongs, for the most part, to
the nineteenth century. The fact that the earth is a planet revolving
round the sun was determined by the system of Copernicus (1543);
Galilei, Kepler, and other great astronomers, mathematically
determined its distance from the sun, the laws of its motion, and so
forth. Kant and Laplace indicated, in their cosmogony, the way in
which the earth had been developed from the parent sun. But the
later history of the earth, the formation of its crust, the origin of its
seas and continents, its mountains and deserts, was rarely made the
subject of serious scientific research in the eighteenth century, and
in the first two decades of the nineteenth. As a rule, men were
satisfied with unreliable conjectures or with the traditional story of
creation; once more the Mosaic legend barred the way to an
independent investigation.
In 1822 an important work appeared, which followed the same
method in the scientific investigation of the history of the earth that
had already proved the most fertile—the ontological method, or the
principle of “actualism.” It consists in a careful study and
manipulation of actual phenomena with a view to the elucidation of
the analogous historical processes of the past. The Society of
Science at Göttingen had offered a prize in 1818 for “the most
searching and comprehensive inquiry into the changes in the earth’s
crust which are historically demonstrable, and the application which
may be made of a knowledge of them in the investigation of the
terrestrial revolutions which lie beyond the range of history.” This
prize was obtained by Karl Hoff, of Gotha, for his distinguished work,
History of the Natural Changes in the Crust of the Earth in the Light
of Tradition (1822-34). Sir Charles Lyell then applied this ontological
or actualistic method with great success to the whole province of
geology; his Principles of Geology (1830) laid the firm foundation on
which the fabric of the history of the earth was so happily erected.
The important geogenetic research of Alexander Humboldt, Leopold
Buch, Gustav Bischof, Edward Süss, and other geologists, were
wholly based on the empirical foundation and the speculative
principles of Karl Hoff and Charles Lyell. They cleared the way for

purely rational science in the field of geology; they removed the
obstacles that had been put in the path by mythological fancy and
religious tradition, especially by the Bible and its legends. I have
already discussed the merits of Lyell, and his relations with his friend
Charles Darwin, in the sixteenth and seventeenth chapters of my
Natural History of Creation, and must refer the reader to the
standard works on geology for a further acquaintance with the
history of the earth and the great progress which dynamical and
historical geology have made during the century.
The first division of the history of the earth must be a separation of
inorganic and organic geogeny; the latter begins with the first
appearance of living things on our planet. The earlier section, the
inorganic history of the earth, ran much the same course as that of
the other planets of our system. They were all cast off as rings of
nebula at the equator of the rotating solar mass, and gradually
condensed into independent bodies. After cooling down a little, the
glowing ball of the earth was formed out of the gaseous mass, and
eventually, as the heat continued to radiate out into space, there
was formed at its surface the thin solid crust on which we live. When
the temperature at the surface had gone down to a certain point,
the water descended upon it from the environing clouds of steam,
and thus the first condition was secured for the rise of organic life.
Many million years—certainly more than a hundred—have passed
since this important process of the formation of water took place,
introducing the third section of cosmogony, which we call biogeny.
III.—MONISTIC BIOGENY
The third phase of the evolution of the world opens with the advent
of organisms on our planet, and continues uninterrupted from that
point until the present day. The great problems which this most
interesting part of the earth’s history suggests to us were still
thought insoluble at the beginning of the nineteenth century, or, at
least, so difficult that their solution seemed to be extremely remote.

Now, at the close of the century, we can affirm with legitimate pride
that they have been substantially solved by modern biology and its
theory of transformism; indeed, many of the phenomena of the
organic world are now interpreted on physical principles as
completely as the familiar physical phenomena of inorganic nature.
The merit of making the first important step in this difficult path and
of pointing out the way to the monistic solution of all the problems
of biology must be accorded to the great French scientist, Jean
Lamarck; it was in 1809, the year of the birth of Charles Darwin,
that he published his famous Philosophie Zoologique. In this original
work not only is a splendid effort made to interpret all the
phenomena of organic life from a monistic and physical point of
view, but the path is opened which alone leads to the solution of the
greatest enigma of this branch of science—the problem of the
natural origin of organic species. Lamarck, who had an equally
extensive empirical acquaintance with zoology and botany, drew the
first sketch of the theory of descent; he showed that all the
countless members of the plant and animal kingdoms have arisen by
slow transformation from simple, common ancestral types, and that
it is the gradual modification of forms by adaptation, in reciprocal
action with heredity, which has brought about this secular
metamorphosis.
I have fully appreciated the merit of Lamarck in the fifth chapter,
and of Darwin in the sixth and seventh chapters, of the Natural
History of Creation. Darwin, fifty years afterwards, not only gave a
solid foundation to all the essential parts of the theory of descent,
but he filled up the lacunae of Lamarck’s work by his theory of
selection. Darwin reaped abundantly the success that Lamarck had
never seen, with all his merit. His epoch-making work on The Origin
of Species by Natural Selection has transformed modern biology
from its very foundations, in the course of the last forty years, and
has raised it to a stage of development that yields to no other
science in existence. Darwin is the Copernicus of the organic world,
as I said in 1868, and E. du Bois-Reymond repeated fifteen years
afterwards.
[27]

IV.—MONISTIC ANTHROPOGENY
The fourth and last phase of the world’s history must be for us men
that latest period of time which has witnessed the development of
our own race. Lamarck (1809) had already recognized that this
evolution is only rationally conceivable as the outcome of a natural
process, by “descent from the apes,” our next of kin among the
mammals. Huxley then proved, in his famous essay on The Place of
Man in Nature, that this momentous thesis is an inevitable
consequence of the theory of descent, and is thoroughly established
by the facts of anatomy, embryology, and palæontology. He
considered this “question of all questions” to be substantially
answered. Darwin followed with a brilliant discussion of the question
under many aspects in his Descent of Man (1871). I had myself
devoted a special chapter to this important problem of the science of
evolution in my General Morphology (1866). In 1874 I published my
Anthropogeny, which contains the first attempt to trace the descent
of man through the entire chain of his ancestry right up to the
earliest archigonous monera; the attempt was based equally on the
three great “documents” of evolutionary science—anatomy,
embryology, and palæontology. The progress we have made in
anthropogenetic research during the last few years is described in
the paper which I read on “Our Present Knowledge of the Origin of
Man” at the International Congress of Zoologists at Cambridge in
1898.
[28]

CHAPTER XIV
THE UNITY OF NATURE
The Monism of the Cosmos—Essential Unity of Organic and
Inorganic Nature—Carbon-Theory—The Hypothesis of
Abiogenesis—Mechanical and Purposive Causes—Mechanicism
and Teleology in Kant’s Works—Design in the Organic and
Inorganic Worlds—Vitalism—Neovitalism—Dysteleology (the
Moral of the Rudimentary Organs)—Absence of Design in, and
Imperfection of, Nature—Telic Action in Organized Bodies—Its
Absence in Ontogeny and Phylogeny—The Platonist “Ideas”—No
Moral Order Discoverable in the History of the Organic World, of
the Vertebrates, or of the Human Race—Prevision—Design and
Chance
One of the first things to be proved by the law of substance is the
basic fact that any natural force can be directly or indirectly
converted into any other. Mechanical and chemical energy, sound
and heat, light and electricity, are mutually convertible; they seem to
be but different modes of one and the same fundamental force or
energy. Thence follows the important thesis of the unity of all
natural forces, or, as it may also be expressed, the “monism of
energy.” This fundamental principle is now generally recognized in
the entire province of physics and chemistry, as far as it applies to
inorganic substances.
It seems to be otherwise with the organic world and its wealth of
color and form. It is, of course, obvious that a great part of the
phenomena of life may be immediately traced to mechanical and
chemical energy, and to the effects of electricity and light. For other
vital processes, however, especially for psychic activity and

consciousness, such an interpretation is vigorously contested. Yet
the modern science of evolution has achieved the task of
constructing a bridge between these two apparently irreconcilable
provinces. We are now certain that all the phenomena of organic life
are subject to the universal law of substance no less than the
phenomena of the inorganic universe.
The unity of nature which necessarily follows, and the demolition of
the earlier dualism, are certainly among the most valuable results of
modern evolution. Thirty-three years ago I made an exhaustive
effort to establish this “monism of the cosmos” and the essential
unity of organic and inorganic nature by a thorough, critical
demonstration, and a comparison of the accordance of these two
great divisions of nature with regard to matter, form, and force.
[29]
A
short epitome of the result is given in the fifteenth chapter of my
Natural History of Creation. The views I put forward are accepted by
the majority of modern scientists, but an attempt has been made in
many quarters lately to dispute them and to maintain the old
antithesis of the two divisions of nature. The ablest of these is to be
found in the recent Welt als That of the botanist Reinke. It defends
pure cosmological dualism with admirable lucidity and consistency,
and only goes to prove how utterly untenable the teleological system
is that is connected therewith. According to the author, physical and
chemical forces alone are at work in the entire field of inorganic
nature, while in the organic world we find “intelligent forces,”
regulative or dominant forces. The law of substance is supposed to
apply to the one, but not to the other. On the whole, it is a question
of the old antithesis of a mechanical and a teleological system. But
before we go more fully into it, let us glance briefly at two other
theories, which seem to me to be of great importance in the decision
of that controversy—the carbon-theory and the theory of
spontaneous generation.
Physiological chemistry has, after countless analyses, established the
following five facts during the last forty years:

I. No other elements are found in organic bodies than those of the
inorganic world.
II. The combinations of elements which are peculiar to organisms,
and which are responsible for their vital phenomena, are compound
protoplasmic substances, of the group of albuminates.
III. Organic life itself is a chemico-physical process, based on the
metabolism (or interchange of material) of these albuminates.
IV. The only element which is capable of building up these
compound albuminates, in combination with other elements
(oxygen, hydrogen, nitrogen, and sulphur), is carbon.
V. These protoplasmic compounds of carbon are distinguished from
most other chemical combinations by their very intricate molecular
structure, their instability, and their jelly-like consistency.
On the basis of these five fundamental facts the following “carbon-
theory” was erected thirty-three years ago: “The peculiar chemico-
physical properties of carbon—especially the fluidity and the facility
of decomposition of the most elaborate albuminoid compounds of
carbon—are the sole and the mechanical causes of the specific
phenomena of movement, which distinguish organic from inorganic
substances, and which are called life, in the usual sense of the word”
(see The Natural History of Creation). Although this “carbon-theory”
is warmly disputed in some quarters, no better monistic theory has
yet appeared to replace it. We have now a much better and more
thorough knowledge of the physiological relations of cell-life, and of
the chemistry and physics of the living protoplasm, than we had
thirty-three years ago, and so it is possible to make a more confident
and effective defence of the carbon-theory.
The old idea of spontaneous generation is now taken in many
different senses. It is owing to this indistinctness of the idea, and its
application to so many different hypotheses, that the problem is one
of the most contentious and confused of the science of the day. I
restrict the idea of spontaneous generation—also called abiogenesis

or archigony—to the first development of living protoplasm out of
inorganic carbonates, and distinguish two phases in this “beginning
of biogenesis”: (1) autogony, or the rise of the simplest protoplasmic
substances in a formative fluid, and (2) plasmogony, the
differentiation of individual primitive organisms out of these
protoplasmic compounds, in the form of monera. I have treated this
important, though difficult, problem so exhaustively in the fifteenth
chapter of my Natural History of Creation that I may content myself
here with referring to it. There is also a very searching and severely
scientific inquiry into it in my General Morphology (1866). Naegeli
has also treated the hypothesis in quite the same sense in his
mechanico-physiological theory of descent (1884), and has
represented it to be an indispensable thesis in any natural theory of
evolution. I entirely agree with his assertion that “to reject
abiogenesis is to admit a miracle.”
The hypothesis of spontaneous generation and the allied carbon-
theory are of great importance in deciding the long-standing conflict
between the teleological (dualistic) and the mechanical (monistic)
interpretation of phenomena. Since Darwin gave us the key to the
monistic explanation of organization in his theory of selection forty
years ago, it has become possible for us to trace the splendid variety
of orderly tendencies of the organic world to mechanical, natural
causes, just as we could formerly in the inorganic world alone.
Hence the supernatural and telic forces, to which the scientist had
had recourse, have been rendered superfluous. Modern metaphysics,
however, continues to regard the latter as indispensable and the
former as inadequate.
No philosopher has done more than Immanuel Kant in defining the
profound distinction between efficient and final causes, with relation
to the interpretation of the whole cosmos. In his well-known earlier
work on The General Natural History and Theory of the Heavens he
made a bold attempt “to treat the constitution and the mechanical
origin of the entire fabric of the universe according to Newtonian
laws.” This “cosmological nebular theory” was based entirely on the

mechanical phenomena of gravitation. It was expanded and
mathematically established later on by Laplace. When the famous
French astronomer was asked by Napoleon I. where God, the
creator and sustainer of all things, came in in his system, he clearly
and honestly replied: “Sire, I have managed without that
hypothesis.” That indicated the atheistic character which this
mechanical cosmogony shares with all the other inorganic sciences.
This is the more noteworthy because the theory of Kant and Laplace
is now almost universally accepted; every attempt to supersede it
has failed. When atheism is denounced as a grave reproach, as it so
often is, it is well to remember that the reproach extends to the
whole of modern science, in so far as it gives a purely mechanical
interpretation of the inorganic world.
Mechanicism (in the Kantian sense) alone can give us a true
explanation of natural phenomena, for it traces them to their real
efficient causes, to blind and unconscious agencies, which are
determined in their action only by the material constitution of the
bodies we are investigating. Kant himself emphatically affirms that
“there can be no science without this mechanicism of nature,” and
that the capacity of human reason to give a mechanical
interpretation of phenomena is unlimited. But when he came
subsequently to give an elucidation of the complex phenomena of
organic nature in his critique of the teleological system, he declared
that these mechanical causes were inadequate; that in this we must
call final causes to our assistance. It is true, he said, that even here
we must recognize the theoretical faculty of the mind to give a
mechanical interpretation, but its actual competence to do so is
restricted. He grants it this capacity to some extent; but for the
majority of the vital processes (and especially for man’s psychic
activity) he thinks we are bound to postulate final causes. The
remarkable §79 of the critique of judgment bears the characteristic
heading: “On the Necessity for the Subordination of the Mechanical
Principle to the Teleological in the Explanation of a Thing as a
Natural End.” It seemed to Kant so impossible to explain the orderly
processes in the living organism without postulating supernatural

final causes (that is, a purposive creative force) that he said: “It is
quite certain that we cannot even satisfactorily understand, much
less elucidate, the nature of an organism and its internal faculty on
purely mechanical natural principles; it is so certain, indeed, that we
may confidently say, ‘It is absurd for a man to conceive the idea
even that some day a Newton will arise who can explain the origin of
a single blade of grass by natural laws which are uncontrolled by
design’—such a hope is entirely forbidden us.” Seventy years
afterwards this impossible “Newton of the organic world” appeared
in the person of Charles Darwin, and achieved the great task that
Kant had deemed impracticable.
Since Newton (1682) formulated the law of gravitation, and Kant
(1755) established “the constitution and mechanical origin of the
entire fabric of the world on Newtonian laws,” and Laplace (1796)
provided a mathematical foundation for this law of cosmic
mechanicism, the whole of the inorganic sciences have become
purely mechanical, and at the same time purely atheistic. Astronomy,
cosmogony, geology, meteorology, and inorganic physics and
chemistry are now absolutely ruled by mechanical laws on a
mathematical foundation. The idea of “design” has wholly
disappeared from this vast province of science. At the close of the
nineteenth century, now that this monistic view has fought its way to
general recognition, no scientist ever asks seriously of the “purpose”
of any single phenomenon in the whole of this great field. Is any
astronomer likely to inquire seriously to-day into the purpose of
planetary motion, or a mineralogist to seek design in the structure of
a crystal? Does the physicist investigate the purpose of electric force,
or the chemist that of atomic weight? We may confidently answer in
the negative—certainly not, in the sense that God, or a purposive
natural force, had at some time created these fundamental laws of
the mechanism of the universe with a definite design, and causes
them to work daily in accordance with his rational will. The
anthropomorphic notion of a deliberate architect and ruler of the
world has gone forever from this field; the “eternal, iron laws of
nature” have taken his place.

But the idea of design has a very great significance and application
in the organic world. We do undeniably perceive a purpose in the
structure and in the life of an organism. The plant and the animal
seem to be controlled by a definite design in the combination of
their several parts, just as clearly as we see in the machines which
man invents and constructs; as long as life continues the functions
of the several organs are directed to definite ends, just as is the
operation of the various parts of a machine. Hence it was quite
natural that the older naïve study of nature, in explaining the origin
and activity of the living being, should postulate a creator who had
“arranged all things with wisdom and understanding,” and had
constructed each plant and animal according to the special purpose
of its life. The conception of this “almighty creator of heaven and
earth” was usually quite anthropomorphic; he created “everything
after its kind.” As long as the creator seemed to man to be of human
shape, to think with his brain, see with his eyes, and fashion with his
hands, it was possible to form a definite picture of this “divine
engineer” and his artistic work in the great workshop of creation.
This was not so easy when the idea of God became refined, and
man saw in his “invisible God” a creator without organs—a gaseous
being. Still more unintelligible did these anthropomorphic ideas
become when physiology substituted for the conscious, divine
architect an unconscious, creative “vital force”—a mysterious,
purposive, natural force, which differed from the familiar forces of
physics and chemistry, and only took these in part, during life, into
its service. This vitalism prevailed until about the middle of the
nineteenth century. Johannes Müller, the great Berlin physiologist,
was the first to menace it with a destructive dose of facts. It is true
that the distinguished biologist had himself (like all others in the first
half of the century) been educated in a belief in this vital force, and
deemed it indispensable for an elucidation of the ultimate sources of
life; nevertheless, in his classical and still unrivalled Manual of
Physiology (1833) he gave a demonstrative proof that there is really
nothing to be said for this vital force. Müller himself, in a long series
of remarkable observations and experiments, showed that most of
the vital processes in the human organism (and in the other

animals) take place according to physical and chemical laws, and
that many of them are capable of mathematical determination. That
was no less true of the animal functions of the muscles and nerves,
and of both the higher and the lower sense-organs, than of the
vegetal functions of digestion, assimilation, and circulation. Only two
branches of the life of the organism, mental action and reproduction,
retained any element of mystery, and seemed inexplicable without
assuming a vital force. But immediately after Müller’s death such
important discoveries and advances were made in these two
branches that the uneasy “phantom of vital force” was driven from
its last refuge. By a very remarkable coincidence Johannes Müller
died in the year 1858, which saw the publication of Darwin’s first
communication concerning his famous theory. The theory of
selection solved the great problem that had mastered Müller—the
question of the origin of orderly arrangements from purely
mechanical causes.
Darwin, as we have often said, had a twofold immortal merit in the
field of philosophy—firstly, the reform of Lamarck’s theory of
descent, and its establishment on the mass of facts accumulated in
the course of the half-century; secondly, the conception of the
theory of selection, which first revealed to us the true causes of the
gradual formation of species. Darwin was the first to point out that
the “struggle for life” is the unconscious regulator which controls the
reciprocal action of heredity and adaptation in the gradual
transformation of species; it is the great “selective divinity” which, by
a purely “natural choice,” without preconceived design, creates new
forms, just as selective man creates new types by an “artificial
choice” with a definite design. That gave us the solution of the great
philosophic problem: “How can purposive contrivances be produced
by purely mechanical processes without design?” Kant held the
problem to be insoluble, although Empedocles had pointed out the
direction of the solution two thousand years before. His principle of
“teleological mechanism” has become more and more accepted of
late years, and has furnished a mechanical explanation even of the
finest and most recondite processes of organic life by “the functional

self-production of the purposive structure.” Thus have we got rid of
the transcendental “design” of the ideological philosophy of the
schools, which was the greatest obstacle to the growth of a rational
and monistic conception of nature.
Very recently, however, this ancient phantom of a mystic vital force,
which seemed to be effectually banished, has put in a fresh
appearance; a number of distinguished biologists have attempted to
reintroduce it under another name. The clearest presentation of it is
to be found in the Welt als That, of the Kiel botanist, J. Reinke. He
takes upon himself the defence of the notion of miracle, of theism,
of the Mosaic story of creation, and of the constancy of species; he
calls “vital forces,” in opposition to physical forces, the directive or
dominant forces. Other neovitalists prefer, in the good old
anthropomorphic style, a “supreme” engineer, who has endowed
organic substance with a purposive structure, directed to the
realization of a definite plan. These curious teleological hypotheses,
and the objections to Darwinism which generally accompany them,
do not call for serious scientific refutation to-day.
Thirty-three years ago I gave the title of “dysteleology” to the
science of those extremely interesting and significant biological facts,
which, in the most striking fashion, give a direct contradiction to the
teleological idea “of the purposive arrangement of the living
organism.”
[30]
This “science of rudimentary, abortive, arrested,
distorted, atrophied, and cataplastic individuals” is based on an
immense quantity of remarkable phenomena, which were long
familiar to zoologists and botanists, but were not properly
interpreted, and their great philosophic significance appreciated,
until Darwin.
All the higher animals and plants, or, in general, all organisms which
are not entirely simple in structure, but are made up of a number of
organs in orderly co-operation, are found, on close examination, to
possess a number of useless or inoperative members, sometimes,
indeed, hurtful and dangerous. In the flowers of most plants we

find, besides the actual sex-leaves that effect reproduction, a
number of other leaf-organs which have no use or meaning
(arrested or “miscarried” pistils, fruit, corona, and calix-leaves, etc.).
In the two large and variegated classes of flying animals, birds and
insects, there are, besides the forms which make constant use of
their wings, a number of species which have undeveloped wings and
cannot fly. In nearly every class of the higher animals which have
eyes there are certain types that live in the dark; they have eyes, as
a rule, but undeveloped and useless for vision. In our own human
organism we have similar useless rudimentary structures in the
muscles of the ear, in the eye-lid, in the nipple and milk-gland of the
male, and in other parts of the body; indeed, the vermiform
appendix of our cæcum is not only useless, but extremely
dangerous, and inflammation of it is responsible for a number of
deaths every year.
Neither the old mystic vitalism nor the new, equally irrational,
neovitalism can give any explanation of these and many other
purposeless contrivances in the structure of the plant and the
animal; but they are very simple in the light of the theory of
descent. It shows that these rudimentary organs are atrophied,
owing to disuse. Just as our muscles, nerves, and organs of sense
are strengthened by exercise and frequent use, so, on the other
hand, they are liable to degenerate more or less by disuse or
suspended exercise. But, although the development of the organs is
promoted by exercise and adaptation, they by no means disappear
without leaving a trace after neglect; the force of heredity retains
them for many generations, and only permits their gradual
disappearance after the lapse of a considerable time. The blind
“struggle for existence between the organs” determines their
historical disappearance, just as it effected their first origin and
development. There is no internal “purpose” whatever in the drama.
The life of the animal and the plant bears the same universal
character of incompleteness as the life of man. This is directly
attributable to the circumstance that nature—organic as well as

inorganic—is in a perennial state of evolution, change, and
transformation. This evolution seems on the whole—at least as far
as we can survey the development of organic life on our planet—to
be a progressive improvement, an historical advance from the simple
to the complex, the lower to the higher, the imperfect to the perfect.
I have proved in my General Morphology that this historical progress
—or gradual perfecting (teleosis)—is the inevitable result of
selection, and not the outcome of a preconceived design. That is
clear from the fact that no organism is perfect; even if it does
perfectly adapt itself to its environment at a given moment, this
condition would not last very long; the conditions of existence of the
environment are themselves subject to perpetual change and they
thus necessitate a continuous adaptation on the part of the
organism.
Under the title of Design in the Living Organism, the famous
embryologist, Karl Ernst Baer, published a work in 1876 which,
together with the article on Darwinism which accompanied it, proved
very acceptable to our opponents, and is still much quoted in
opposition to evolution. It was a revival of the old teleological
system under a new name, and we must devote a line of criticism to
it. We must premise that, though Baer was a scientist of the highest
order, his original monistic views were gradually marred by a tinge of
mysticism with the advance of age, and he eventually became a
thorough dualist. In his profound work on “the evolution of animals”
(1828), which he himself entitled Observation and Experiment, these
two methods of investigation are equally applied. By careful
observation of the various phenomena of the development of the
animal ovum Baer succeeded in giving the first consistent
presentation of the remarkable changes which take place in the
growth of the vertebrate from a simple egg-cell. At the same time he
endeavored, by far-seeing comparison and keen reflection, to learn
the causes of the transformation, and to reduce them to general
constructive laws. He expressed the general result of his research in
the following thesis: “The evolution of the individual is the story of
the growth of individuality in every respect.” He meant that “the one

great thought that controls all the different aspects of animal
evolution is the same that gathered the scattered fragments of space
into spheres and linked them into solar systems. This thought is no
other than life itself, and the words and syllables in which it finds
utterance are the varied forms of living things.”
Baer, however, did not attain to a deeper knowledge of this great
genetic truth and a clearer insight into the real efficient causes of
organic evolution, because his attention was exclusively given to one
half of evolutionary science, the science of the evolution of the
individual, embryology, or, in a wider sense, ontogeny. The other
half, the science of the evolution of species, phylogeny, was not yet
in existence, although Lamarck had already pointed out the way to it
in 1809. When it was established by Darwin in 1859, the aged Baer
was no longer in a position to appreciate it; the fruitless struggle
which he led against the theory of selection clearly proved that he
understood neither its real meaning nor its philosophic importance.
Teleological and, subsequently, theological speculations had
incapacitated the ageing scientist from appreciating this greatest
reform of biology. The teleological observations which he published
against it in his Species and Studies in his eighty-fourth year are
mere repetitions of errors which the teleology of the dualists has
opposed to the mechanical or monistic system for more than two
thousand years. The “telic idea” which, according to Baer, controls
the entire evolution of the animal from the ovum, is only another
expression for the eternal “idea” of Plato and the entelecheia of his
pupil Aristotle.
Our modern biogeny gives a purely physiological explanation of the
facts of embryology, in assigning the functions of heredity and
adaptation as their causes. The great biogenetic law, which Baer
failed to appreciate, reveals the intimate causal connection between
the ontogenesis of the individual and the phylogenesis of its
ancestors; the former seems to be a recapitulation of the latter.
Nowhere, however, in the evolution of animals and plants do we find
any trace of design, but merely the inevitable outcome of the

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