<title>Genetic algorithm for the inverse problem in synthesis of fiber gratings</title>

Abstract

A new method for synthesis of fiber gratings with advanced characteristic is proposed. The method is based on an optimizing genetic algorithm, and facilitates the task of weighting the different requirements to the filter spectrum. A classical problem in applied physics and engineering fields is the inverse problem. An example of such a problem is to determine a fiber grating index modulation profile corresponding to a given reflection spectrum. This is not a trivial problem, and a variety of synthesis algorithms has been proposed. For weak gratings, the synthesis problem of fiber gratings reduces to an inverse Fourier transform of the reflection coefficient. This is known as the first-order Born approximation, and applies only for gratings for which the reflectivity is small. Another solution to this problem was found by Song and Shin, who solved the coupled Gel'fand- Levitan-Marchenko (GLM) integral equations that appear in the inverse scattering theory of quantum mechanics. Their method is exact, but is restricted to reflection coefficients that can be expressed as a rational function. An iterative solution to the GLM equations was found by Peral et. al., yielding smoother coupling coefficients that the exact method. The algorithm is converging relatively fast, and gives satisfying results even for high reflectivity gratings. However, when specifying ideal, unachievable filter responses, it is desirable to have a weighting mechanisms, which makes it easier to weight the different requirements. For example, when synthesizing an optical bandpass filter, one may be interested in weighting linear phase more than sharp peaks. because the dispersion may be a more critical parameter. The iterative GLM method does not support such a mechanism in a satisfactory way.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.