Acousto-optic scattering in a single-mode optic fiber

Abstract

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 $|R_{max}|^2=hbox{rm tanh}^2,(pifrac{L}{c}Deltanu)$ for the maximal reflection coefficient ($c$ stands for the phase velocity of light and $Deltanu$ denotes the width of the reflection band in $Hz$).