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 is , index of core is and core radius is .

+ Index profiles: Common ones -- step and grade index profiles with percentage change in refractive index, :
General expression - for
for .
Note: .

+ Type of fibers:
Materials -- glass fiber, 800nm, 1300nm and 1500nm, low losses (i.e. windows of transmission), used in long distance; plastic fiber, 580nm, high losses, short distance (computer applications).
Core size -- single mode, , only 1 mode, reduced dispersion; multimode, , 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 where normalized freq. parameter where is 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. or where and 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 and TM .
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 or . Its distribution matches Gaussian beam. Next mode appear when .

+ Common fibers: Grade index fiber - dispersion is medium data rate 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.