02-Fundamentals of Optical Fiber Waveguides-I.pptx

optical and wave guide

1. Chapter Two Fundamentals of Optical Fiber Waveguides Addis Ababa Science and Technology University College of Electrical & Mechanical Engineering Electrical & Computer Engineering Department Optics and Optical Communication (EEEg-4302)

2. Fundamentals of Optical Fiber Waveguides Outline: Geometric Optics Total Internal Reflection Acceptance Angle Numerical Aperture Electromagnetic Mode Theory for Optical Propagation Optical Fiber Types and Modes Signal Degradation in Optical Fibers Chapter 2 –Fundamentals of Optical Fiber Waveguides 2

3. Refractive Index In any dielectric medium, the speed of light becomes The factor n is the index of refraction (or refractive index) of the medium. e.g. For air and gases, v ~ c , so that n ~ 1 . At optic frequencies, the refractive index of water is 1.33. e.g. Glass has many compositions, each with a slightly different n . Chapter 2 –Fundamentals of Optical Fiber Waveguides 3

4. Interference – Effects Interference in the voice channels causes crosstalk A s ubscriber hears interference in the background due to an undesired transmission Interference in the control channels causes e rror in digital signaling which causes Missed calls Blocked calls Dropped calls Interference is more severe in urban areas , due to the greater RF noise floor and the large number of base stations and mobiles Chapter 2 –Fundamentals of Optical Fiber Waveguides 4

5. Basic optical laws and definitions • A light ray is reflected and refracted when it encounters the boundary between two different transparent mediums. •Light reflects or refracts depending on the angle at which it strikes a surface and the difference in refractive index of the two materials. Reflection is the change in direction of a light wave at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. • Refraction is the change in direction of a light wave due to a change in its velocity. This is most commonly seen when a wave passes from one medium to another. •The phenomenon of total internal reflection, responsible for guiding of light in optical fibers. Chapter 2 –Fundamentals of Optical Fiber Waveguides 5

6. 6 Law of Reflection The angle of Incidence = The angle of reflection Law of Refraction - Light beam is bent towards the normal when passing into a medium of higher refractive index. Light beam is bent away from the normal when passing into a medium of lower refractive index. Index of Refraction – n = Speed of light in a vacuum / Speed of light in a medium Inverse square law - Light intensity diminishes with square of distance from source. Properties of Light

7. Snell’s Law When a ray is incident on the interface between two dielectrics of different refractive indices (e.g. glass-air), reflection and refraction occur. The angle of incidence θ 1 and the angle of refraction θ 2 are related to each other and to the refractive indices of the dielectrics by Snell’s law of refraction as: Chapter 2 –Fundamentals of Optical Fiber Waveguides 7

8. Critical Angle For n 1 > n 2 , the angle of refraction θ 2 is always greater than the angle of incidence θ 1 . When the angle of refraction θ 2 is 90 , the refracted ray emerges parallel to the interface between the media. This is the limiting case of refraction and the angle of incidence is known as the critical angle θ c . Chapter 2 –Fundamentals of Optical Fiber Waveguides 8

9. Total Internal Reflection At angles of incidence θ > θ c , the light is totally reflected back into the incidence higher refractive index medium. This is known as total internal reflection. Chapter 2 –Fundamentals of Optical Fiber Waveguides 9

10. 10 Reflection and Refraction of Light  1  1  2 n 1 n 2 n 1 < n 2 Using the Snell's law at the boundary we have: n 1 sin  1 = n 2 sin  2 or n 1 cos  1 = n 2 cos  2 Medium 1 Medium 2 Boundary  1 = The angle of incident  1  2  1 n 2 n 1 n 1 > n 2  1  1 Reflected ray Refracted ray Incident ray  2

11. 11 Total Internal Reflection As  1 increases (or  1 decreases) then there is no reflection  c n 2 n 1 n 1 > n 2  1 The incident angle  1 =  c = Critical Angle Beyond the critical angle, light ray becomes totally internally reflected  1 > c n 2 n 1 n 1 > n 2  1 < c  1 When  1 = 90 o (or  c = 0 o ) n 1 sin  1 = n 2 Thus the critical angle

12. Light Ray Guiding Condition Light ray that satisfies total internal reflection at the interface of the higher refractive index core and the lower refractive index cladding can be guided along an optical fiber. Example: Under what condition will light be trapped inside the fiber core if n 1 = 1.46 and n 2 = 1.44? Chapter 2 –Fundamentals of Optical Fiber Waveguides 12

13. Optical Fiber Structures A typical bare fiber consists of a core, a cladding and a polymer jacket (buffer coating). The polymer coating is the first line of mechanical protection. The coating also reduces the internal reflection at the cladding, so light is only guided by the core. Chapter 2 –Fundamentals of Optical Fiber Waveguides 13

14. Optical Fiber Structures Chapter 2 –Fundamentals of Optical Fiber Waveguides 14 An optical fibre is a very thin strand of silica glass in geometry quite like a human hair. In reality it is a very narrow, very long glass cylinder with special characteristics. The basic structure of an optical fiber consists of three parts; the core, the cladding, and the coating or buffer as it is shown in figure. Core • It is a cylindrical rod of dielectric material which conducts no electricity. Light propagates mainly along the core of the fiber. •The core is mainly made of glass, in low-and medium-loss fibers.

15. Chapter 2 –Fundamentals of Optical Fiber Waveguides 15 Cladding •Made of a dielectric material with an index of refraction less than that of the core material. •The cladding is generally made of glass or plastic. The cladding performs the following functions: Reduces loss of light from the core into the surrounding air Reduces scattering loss at the surface of the core Protects the fiber from absorbing surface contaminants Adds mechanical strength Coating or buffer •The coating or buffer is a layer of material used to protect an optical fiber from physical damage. The material used for a buffer is a type of plastic. •The buffer is elastic in nature and prevents abrasions. •It also prevents the optical fiber from scattering losses caused by micro-bends. •Micro-bends occur when an optical fiber is placed on a rough and distorted surface.

16. Silica Optical Fibers Both the core and the cladding are made from a type of glass known as silica ( SiO 2 ) which is almost transparent in the visible and near-IR. In the case that the refractive index changes in a “step” between the core and the cladding, the fiber structure is known as step-index fiber. The higher core refractive index (~ 0.3% higher) is typically obtained by doping the silica core with germanium dioxide ( GeO 2 ). Chapter 2 –Fundamentals of Optical Fiber Waveguides 16

17. The maximum angle to the axis of the core at which light may enter the fiber in order to be propagated by total internal reflection is referred to as acceptance angle . Ray A incident at the critical angle θ c at the core-cladding interface enters the fiber core at an angle θ a to the fiber axis and is refracted at the air-core interface. Acceptance Angle Chapter 2 –Fundamentals of Optical Fiber Waveguides 17

18. Acceptance Angle……… Any rays which are incident into the fiber core at an angle θ> θ a have an incident angle less than θ c at the core-cladding interface. These rays will NOT be totally internal reflected, thus eventually loss to radiation (at the cladding-jacket interface). Chapter 2 –Fundamentals of Optical Fiber Waveguides 18

19. Numerical Aperture Fiber numerical aperture ( NA ) characterizes the fiber’s ability to gather light from a source and guide the light. The numerical aperture ( NA ) is defined as: Chapter 2 –Fundamentals of Optical Fiber Waveguides 19

20. Numerical Aperture……….. We can relate the acceptance angle θ a and the refractive indices of the core n 1 , cladding n 2 and air n a as follows: Chapter 2 –Fundamentals of Optical Fiber Waveguides 20

21. Numerical Aperture……….. The NA may also be given in terms of the relative refractive index difference Δ between the core and the cladding which is defined as: Chapter 2 –Fundamentals of Optical Fiber Waveguides 21

22. Numerical Aperture……….. The NA is then given by: The numerical aperture is a very useful measure of the light-collecting ability of a fiber. It is independent of the fiber core diameter and will hold for diameters as small as 8μm . However, for smaller diameters , it is inapplicable as the geometric optics approach is invalid. Chapter 2 –Fundamentals of Optical Fiber Waveguides 22

23. 23 Ray Propagation in Fibre - Bound Rays 1 2 3 4 5 Cladding n 2 Core n1 Air (no =1)   c  >  c ,  >  max From Snell’s Law: n0 sin  = n1 sin (90 - )  = max when  = c Thus, n sin  max = n 1 cos  c a 2 2 At high frequencies f , s ince a > light wavelength , lightt launched into the fibre core would propagate as plane TEM wave with v p = / 1 At high frequencies f , since a < , light launched into the fibre will propagate within the cladding, thus unbounded and unguided plane TEM wave with v p = / 2 Therefore, we have n 2 k =  2 <  <  1 = n 1 k

24. 24 Ray Propagation in Fibre - contd. Since Then NA determines the light gathering capabilities of the fibre n sin  max = n 1 (1 - sin 2  c ) 0.5 Or

25. 25 Ray Propagation in Fibre - contd. Therefore n sin  max = NA Fiber acceptance angle Note Relative refractive index difference Thus 0.14< NA < 1

26. Lens Coupling to Fiber End Faces By measuring the output couple ray cone angle, we can measure the fiber acceptance angle. Chapter 2 –Fundamentals of Optical Fiber Waveguides 26

27. Large NA Fibers Developing ways for fiber to collect light efficiently was an important early step in developing practical fiber optic communications. It seems logical to have optical fibers with NA as large as possible with as large Δ as possible in order to couple maximum amount of light into the fiber. Soon, we will find out that such large NA fibers tend to be “multimode” and are unsuitable for high-speed communications because of a limitation known as modal dispersion. Relatively small NA fibers are therefore used for high-speed optical communication systems. Chapter 2 –Fundamentals of Optical Fiber Waveguides 27

28. Typical fiber NA Silica fibers for long range transmission are designed to have numerical apertures from about 0.1 to 0.3. The low NA makes coupling efficiency tend to be poor, but turns out to improve the fiber’s bandwidth. Plastic fibers are restricted to short lengths because of the relatively high attenuation in plastic materials. Plastic optical fibers ( POFs ) are designed to have high numerical apertures (typically, 0.4 – 0.5) to improve coupling efficiency and so partially offset the high propagation losses. Chapter 2 –Fundamentals of Optical Fiber Waveguides 28

29. Examples On Geometric Optics Example-1: What is the fiber acceptance angle when n 1 =1.46 and n 2 =1.44 ? Solution: Chapter 2 –Fundamentals of Optical Fiber Waveguides 29

30. Examples On Geometric Optics……... Example-2: A silica optical fiber with a core diameter large enough to be considered by ray theory analysis has a core refractive index of 1.50 and a cladding refractive index of 1.47 . Determine: the critical angle at the core–cladding interface the NA for the fiber the acceptance angle in air for the fiber. Chapter 2 –Fundamentals of Optical Fiber Waveguides 30

31. Examples On Geometric Optics……... Solution: Chapter 2 –Fundamentals of Optical Fiber Waveguides 31

32. Examples On Geometric Optics……... Example-3: A typical relative refractive index difference for an optical fiber designed for long distance transmission is 1% . When the core index is 1.46 , calculate: the numerical aperture ( NA ) for the fiber the critical angle at the core–cladding interface within the fiber Chapter 2 –Fundamentals of Optical Fiber Waveguides 32

33. Examples On Geometric Optics……... Solution: Chapter 2 –Fundamentals of Optical Fiber Waveguides 33

34. Exercises On Geometric Optics Exercise-1: Consider a multimode silica fiber that has a core refractive index n 1 =1.48 and a cladding refractive index n 2 =1.46 . Find: the critical angle the numerical aperture the acceptance angel Chapter 2 –Fundamentals of Optical Fiber Waveguides 34

35. Exercises On Geometric Optics……. Exercise-2: Consider a multimode fiber that has a core refractive index of and a core-cladding index difference of 2% . Find: the numerical aperture ( NA ) the acceptance angle the critical angle Chapter 2 –Fundamentals of Optical Fiber Waveguides 35

36. 36 Chapter 2 –Fundamentals of Optical Fiber Waveguides The End! Any Question?