Optical Fibers Feb. 8, 2018

+ Effect of microcracks, microbending and temperature: Microcracks and microbending cause abrupted change in refractive index at certain locations [equation] 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 [equation], index of core is [equation] and core radius is [equation].

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

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

+ Common fibers: Grade index fiber - dispersion is medium [equation] data rate [equation] 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
[equation] require laser as source for single mode.

Last Modified: February 5, 2018
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