Optical Fibers

Feb. 8, 2018

• Effect of microcracks, microbending and temperature: Microcracks and microbending cause abrupted change in refractive index at certain locations leakage of signal, i.e. attenuation.
Temperature can cause gradual changes in refractive index along a fiber -- introduce phase distortion, dispersion, i.e. spreading of pulse and limiting speed.
Fiber structure: Buffer coating > cladding > core
index of cladding isn2 , index of core isn1 and core radius isa
• Index profiles: Common ones -- step and grade index profiles with percentage change in refractive index,Δ :
General expression `-` `n= n_1 [1 - 2 Delta ( r / a )^ alpha ] ^(1/2)` for `r < a`
and `n = n_2 = n_1 (1 - 2 Delta ) ^ (1/2)` for `r > a`

• Type of fibers:
Materials -- glass fiber, `lambda =` 800nm, 1300nm and 1500nm, low losses (i.e. windows of transmission), used in long distance; plastic fiber, `lambda =` 580nm, high losses, short distance (computer applications).
Core size -- single mode, `a = 5 mu m` , only 1 mode, reduced dispersion; multimode, `a = 50 - 85 mu m` , many modes, large dispersion

Mode description: can be thought as harmonics in space for a light pipe.
`-` Each mode corresponds to a ray along a certain path.
`-` only a finite number of incidence angles results in constructive interference and forms mode pattern.
`-` Number of mode `M = "Int" ( V^2 / 2)` where normalized freq. parameter `V = (2 pi) / lambda a sqrt ( n_1^2 - n_2^2 )` where `sqrt( n_1^2 - n_2^2 )` is the numerical aperture (NA) and Int(.) means integer part.
This formula is good when `M` is large.
`-` This formula explains that a fiber with very small a as single mode fiber.
`-` Mode designation, e.g. `TE_(mn)` or `TM_(mn)` where `m` and `n` are the mode indices (harmonic number), `TE` means transverse electric (i.e. s-polarized), `TM` transverse magnetic (i.e. p-polarized).
Assuming wave propagating along `z`, `TE -> E_z =0` and `TM -> H_z =0`
Each mode is a eigenfunction of the wave equation and its eigenvalue is the transverse wave number.
`-` Fundamental mode that cannot be cut-off is called `HE_{11}` or `LP_(01)` Its distribution matches Gaussian beam. Next mode appear when `V > 2.405`

• Common fibers: Grade index fiber `-` dispersion is medium `=>` data rate `times` distance = RL is medium; difficulty in coupling of light is medium.
Step index multimode `-` dispersion is large, RL small, difficulty in coupling low.
Step index single mode `-` dispersion is low, RL large, difficulty in coupling high `=>` require laser as source for single mode.

Last Modified: February 5, 2018
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