**Ray and Dispersion in Fibers** Feb. 15, 2018

+
Ray in fibers:
based on internal reflection.` `

zig-zap abruptly

gradual oscillation like sin and cos.` `

Note: Path lengths of rays are different.` `

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Numerical aperture (NA):
where is the index outside
the
fiber and is the maximum acceptance angle.` `

Working out the relation with critical angle and
,
where and
percentage change in index
.` `

Assuming a > w of the beam, fraction of power coupled into fiber .` `

Note: For coupling light into fiber, we need to consider core area and
.` `

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Dispersion:
difference in delays for signals originating from a source in reaching
a certain receiving point.` `

2 parameters affect dispersion -

aka - { multipath, intermode, modal } dispersion;
measured by (ns / km).` `

aka - { intramode, chromatic } dispersion;
measured by (ns / km-nm).` `

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Group velocity:
( or in text);
group index .` `

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Max. data rate:
, conservative estimate.` `

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Modal dispersion:
step index where is group index of
the core and
.` `

grade index

* Reduce dispersion - shortest path has slower speed than that of
longest path.` `

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:
2 phenomena determine it

Freq dep of - can be modeled by Sellmeier Eqn.;
measured by material dispersion .` `

Freq dep of - nonlinear relation between and which is
determined by the eigen-solution of Maxwell's eqn.;
measured by waveguide (wavelength) dispersion .` `

.` `

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Definition of :
where is the group delay and
( in the text pp. 731-733 2nd Ed, pp. 769-771 3rd Ed.).` `

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Zero dispersion wavelength:
at

at owing to the the
negative cancelling .` `

Using this idea, special single mode fibers like
dispersion-shifted fiber and dispersion-flattened fiber are designed.` `

where is the zero dispersion slope.` `

Last Modified: February 11, 2018

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