Ray theory of transmission.pptx

Mumbai University
Optical Communication & Networks Sem VIII

1. 1 Structure of Optical Fiber Presented By: Prof. Shailaja Udtewar Department of EXTC Xavier Institute of Engineering, Mumbai

2. 2 Structure of Optical Fiber

3. Structure of Optical Fiber Core - central tube of very thin size made up of optically transparent dielectric medium and carries the light form transmitter to receiver. The core diameter can vary from about 5 um-100 um. Cladding - outer optical material surrounding the core having reflecting index lower than core. It helps to keep the light within the core throughout the phenomena of total internal reflection. The typical diameter of fiber cladding is 125 um. Buffer Coating - plastic coating made of silicon rubber that protects the fiber from damage and moisture. The typical diameter of fiber after coating is 250-300 um. Jacket - Holds one or more fibers in a cable. 3 Structure of Optical Fiber

4. Structure of Optical Fiber 4 TOTAL INTERNAL REFLECTION

5. 5

6. Refractive Index (n) is defined as the ratio of the velocity of light in a vacuum to the velocity of light in a material It is a constant for a particular medium. 6 REFRACTIVE INDEX

7. Low refractive index is low-density medium High refractive index is a high-density medium 7 REFRACTIVE INDEX

8. REFRACTIVE INDEX 8

9. 9 Refraction is bending of light ray when it passes from one medium to another medium. When a ray of light goes from a rarer medium to a denser medium, its speed decreases or it slows down and bends towards the normal. On the other hand, when a ray of light goes from a denser medium to rarer medium, its speed increases or it speeds up and bends away from the normal. REFRACTION (Bending)

10. 10 A high-refractive index (n) bends light ray a lot more towards the normal line and a low refractive index (n) bends very little towards the normal line. REFRACTION (Bending)

11. 11 Refraction of Air to Water n=1.3

12. 12 Refraction of Air to Glass n=1.5

13. 13 Refraction of Air to Diamond n=2.4

14. Snell’s Law Snell's law  describes the relationship between the angles of incidence and refraction, when light or other waves passing through a boundary between two different isotropic media , such as water, glass, or air. An  isotropic medium  is one such that the permittivity, ε, and permeability, μ, of the medium  are uniform in all directions of the  medium 14

15. Snell’s Law 15    

16. Snell’s Law The amount light is bent by refraction is given by Snell’s Law: n 1 sin φ 1 = n 2 sin φ 2 Light is always refracted into a fiber (although there will be a certain amount of Fresnel reflection) Light can either bounce off the cladding (TIR) or refract into the cladding 16

17. Snell’s Law When a ray is incident on the interface between two dielectrics of differing refractive indices (e.g. glass – air) refraction occurs. The angle of incidence and angle of refraction is related by Snell's law of refraction   17    

18. Critical Angle > c   = c   < c  

19. Ray Theory of Transmission 19

20. Critical Angle As n 1  n 2 , the angle of refraction φ 1 is always greater than the angle of incidence φ 2. The minimum angle of incidence φ 1 at which a light ray strike interface of two media and result in φ 2 = 90° This angle of incidence is now known as the critical angle φ 1 = φ c Total internal reflection When φ 1  φ c then total internal relection occurs. 20

21. Critical Angle As n 1  n 2 , the angle of refraction φ 1 is always greater than the angle of incidence φ 2. The minimum angle of incidence φ 1 at which a light ray strike interface of two media and result in φ 2 = 90° This angle of incidence is now known as the critical angle φ 1 = φ c Total internal reflection When φ 1  φ c then total internal relection occurs. 21

22. Critical Angle 22

23. Critical Angle 23

24. Total Internal Reflection 25 1   > c  

25. Total Internal Reflection 26

26. Acceptance Angle θ a 27 Acceptance Cone n 2 cladding n 2 cladding q a n 1 core

27. Acceptance Angle θ a θ a is maximum angle to axis at which light may enter the fiber in order to be propagated in zigzag path with <10 dB loss. If all possible direction of θ a are considered at same time we get a cone known as acceptance cone. An acceptance angle defined by the conical half angle θ a . 28

28. Acceptance Angle ( θ a ) 29 If the angle too large  light will be lost in cladding

29. Numerical Aperture (NA) Numerical aperture of the fiber is the light gathering capacity of the fiber. It is the measure of the amount of light rays that can be accepted by the fiber. It is equal to the sine of acceptance. NA = n sin θ a = (n 1 2 – n 2 2 ) 1/2 n =1 (R.I of Air) Numerical aperture of step index fiber is given NA = n 1 √2∆ 30

30. Numerical Aperture (NA) 31

31. Numerical Aperture (NA) It lies between 0 and 1. NA= 0 means fiber gathers no light (corresponding to θ a = 0 o ) NA= 1 means fiber gathers all light that falls on it (corresponding to θ a = 90 o ) High NA increases dispersion Hence low NA is desirable ( 0.13-0.5 ) 32

32. Numerical Aperture (NA) 33

33. Derivation of Numerical Aperture (NA) Consider a light ray incident on the fiber core at an angle θ1 to the fiber axis which is less than the acceptance angle for the fiber θa . The ray enters the fiber from a medium (air) of refractive index n 0, and the fiber core has a refractive index n 1, which is slightly greater than the cladding refractive index n 2. 34

34. Derivation of Numerical Aperture (NA) Assuming the entrance face at the fiber core to be normal to the axis, then considering the refraction at the air–core interface and using Snell’s law 35

35. Derivation of Numerical Aperture (NA) Considering the right-angled triangle ABC 36

36. Derivation of Numerical Aperture (NA) Considering the right-angled triangle ABC 37       But  

37. Derivation of Numerical Aperture (NA) Using the trigonometrical relationship sin 2 φ + cos 2 φ = 1 When the limiting case for total internal reflection is considered, φ becomes equal to critical angle φ c for the core–cladding interface and θ 1 becomes the acceptance angle for the fiber θ a . 38

38. Derivation of Numerical Aperture (NA) 39      

39. Derivation of Numerical Aperture (NA) 40      

40. Derivation of Numerical Aperture (NA) 41

41. NA =

42. V- Number (Normalized Frequency) No. of modes supported by optical fiber is obtained by cut-off condition known as normalized frequency or V-Number. NA = √n 1 2  – n 2 2  NA = Sin θ max NA = n1√2 Δ a=radius of core, λ=wavelength of light through core of fiber. V-number can be reduced either by reducing numerical aperture or by reducing diameter of fiber. 43

43. V- Number 44

44. V- Number 45

45. V- Number If V < 2.405 then the fiber is single mode. If V > 2.405 then fiber is multimode. V number is also related with number of modes in fiber Number of modes for step index fiber α = ∞ M = V 2 / 2 Number of modes for graded index fiber α = 2 M= V 2 / 4 46

46. Cutoff Wavelength ( λ C ) The cutoff wavelength is the minimum wavelength in which a particular fiber still acts as a single mode fiber. Above the cutoff wavelength, the fiber will only allow the LP01 mode to propagate through the fiber (fiber is a single mode fiber at this wavelength). Below the cutoff wavelength, higher order modes, i.e. LP11, LP21, LP02, etc will be able to propagate (fiber becomes a multimode fiber at this wavelength). 47

47. Cutoff Wavelength ( λ C ) Theoretical value for λ c For step index fiber , v c = 2.405 For practical system, λ c is = 1.3 μ m to avoid modal noise. For single mode fiber, λ c is = 1.1 to 1.28 μ m 48 

48. Cutoff Wavelength ( λ C ) 49

49. Cutoff Wavelength ( λ C ) 51

50. Cutoff Wavelength ( λ C ) 52

51. FORMULA SUMMARY Index of Refraction Snell’s Law Critical Angle Acceptance Angle Numerical Aperture 57

52. V- Number If V < 2.405 then the fiber is single mode. If V > 2.405 then fiber is multimode. V number is also related with number of modes in fiber Number of modes for step index fiber α = ∞ M = V 2 / 2 Number of modes for graded index fiber α = 2 M= V 2 / 4 64

53. 67 LP lm modes Fundamental mode l = 0, m = 1  LP 01 mode The field is maximum at the center of the core and penetrates somewhat into the cladding. The intensity distribution has a maximum along the fiber axis.

54. 68 LP lm modes Each mode has its own propagation vector  lm and its own electric filed pattern E lm ( r, ). Each mode has its own group velocity V g ( l , m ) that depends on the  vs.  lm dispersion behavior. When a pulse is fed into the fiber, it travels down the fiber through various modes. Output pulse is broadened.  I ntermodal dispersion

55. N UMBER OF MODES M IN MM F IBER A ray will be accepted by the fiber if it lies within angle θ defined by NA . The solid acceptance angle of fiber -

56. N UMBER OF MODES M IN MM F IBER For electromagnetic radiation of wavelength λ from a laser or fiber, number of modes per unit solid angle is 2A/ λ 2 . A = πa 2 2 is because plane wave can have 2 polarization orientations.