Optical Fibers |
Feb. 8, 2018 |
• Effect of microcracks, microbending and
temperature: Microcracks and microbending cause abrupted
change in refractive index at certain
locations$\text{\hspace{0.5em}}\to $
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.
• : Buffer coating > cladding >
core
index of cladding
is$\text{\hspace{0.5em}}{n}_{2}$
, index of core
is$\text{\hspace{0.5em}}{n}_{1}$
and core radius
is$\text{\hspace{0.5em}}a$
• Index profiles: Common ones -- step and with percentage change in refractive
index,$\text{\hspace{0.5em}}\Delta $
:
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`
Note:$\text{\hspace{0.5em}}{n}_{1}\text{\hspace{0.17em}}>\text{\hspace{0.17em}}{n}_{2}$
• 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
• :
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 beam.
`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.