A numerical method is developed for solution of the Gel’fand–Levitan–Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz–Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.
© 2007 Optical Society of America
Fiber Optics and Optical Communications
Original Manuscript: November 14, 2006
Revised Manuscript: March 12, 2007
Manuscript Accepted: March 18, 2007
Published: June 15, 2007
O. V. Belai, L. L. Frumin, E. V. Podivilov, and D. A. Shapiro, "Efficient numerical method of the fiber Bragg grating synthesis," J. Opt. Soc. Am. B 24, 1451-1457 (2007)