Multiple scales analysis of chirped Bragg gratings

In this paper, a second-order multiple scales expansion is used to derive coupled-mode equations for a linearly chirped Bragg grating. This eliminates the error in the spectral response introduced by large values of the grating strength when conventional first-order coupled-mode theory is used. The autonomous and nonautonomous formulations of these equations are considered and compared in terms of accuracy and speed of the numerical solution of the resulting two-point boundary-value problem for the reflectance of the grating. These solutions are compared with the characteristic matrix solution taken as a reference. By using the fundamental matrix method, the autonomous formulation is found to be as accurate as the characteristic matrix method but faster in terms of computer CPU time.