|The analysis of |
acousto-optic scattering in a single-mode fiber in terms of the
effective equation with perturbation caused by variation of
the speed of light is done. Using an ansatz based on the Lorentz
transform we reduce the corresponding equation to Mathieu
equation with a non-canonical small (acousto-optic) parameter.
In the lowest order of perturbation theory we calculate
the positions and widths of spectral lacunae for the case when the
elastic wave is infinite. This result is applied for the estimation of
the reflection coefficient $R$ in the lacunae using methods
suggested earlier by authors for investigation of periodic nanostructures.
We calculate explicitly the reflection coefficient for
scattering by a segment of elastic wave of length $L$ and
derive the relation
for the maximal reflection coefficient ($c$ stands for the
phase velocity of light and $Deltanu$ denotes the width of the
reflection band in $Hz$).
optical waveguides, scattering, spectrum lacuna
Math Review Classification
Primary Mathematical Physics ; Secondary Scattering Theory
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