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.
multiple scales analysis bragg gratings coupled-mode theory optical waveguide filters chirped periodic structures