Transfer matrix and full Maxwell time domain analysis of nonlinear gratings

In this paper we show that the transfer matrix method and the finite difference time domain technique applied to the full time-dependent Maxwell equations (in their one-dimensional form) permit to improve the description of nonlinear distributed feedback structures such as Bragg gratings. In fact, no simplifying hypothesis are introduced in the electromagnetic problem by these two numerical approaches. The two techniques validate qualitatively the results based on the standard coupled-mode theory for weakly nonlinear and shallow gratings, while significant quantitative deviations can appear in other cases.