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.
© 2006 Optical Society of America
Fiber Optics and Optical Communications
Original Manuscript: March 22, 2006
Revised Manuscript: June 24, 2006
Manuscript Accepted: June 28, 2006
Oleg V. Belai, Evgeny V. Podivilov, Osip Ya. Schwarz, David A. Shapiro, and Leonid L. Frumin, "Finite Bragg grating synthesis by numerical solution of Hermitian Gel'fand-Levitan-Marchenko equations," J. Opt. Soc. Am. B 23, 2040-2045 (2006)