Calculation of Light Scattering on a Bragg Grating by Recursion of Transfer Matrices on a Nonuniform Grid

The direct problem of light scattering for a fiber optic Bragg grating is considered. The formulation and solution of the problem based on the transfer-matrix method are discussed. A modification of the method is proposed which reduces it to a computationally convenient universal recursive algorithm similar to the Thomas algorithm. Using the finite volume method in the coupled-mode approximation, the elements of transfer matrices were calculated with local third-order accuracy in coordinate on a nonuniform computational grid. Numerical calculations for the direct scattering problem for a Bragg grating with apodization and nonlinear chirp were performed using the recursive algorithm. Numerical simulations confirmed the significant increase in the accuracy of calculations when solving the scattering problem on a nonuniform grid.