Finite Bragg grating synthesis by numerical solution of Hermitian Gel'fand-Levitan-Marchenko equations

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel'fand-Levitan-Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectance homogeneous and hyperbolic secant profiles. The proposed method is shown to concede the popular discrete layer peeling technique in efficiency but surpasses it in accuracy and stability at high reflectance. (c) 2006 Optical Society of America.