Some topics in extending the C method to multilayer gratings of different profiles

In a recent Letter to the Editor (1995 Pure Appl. Opt. 4 1 - 5), the differential formalism of Chandezon et al (the C method) was extended to treat layered gratings in which the profiles of the medium interfaces within the same grating are different from each other. Numerical experiments have shown that a computer program based on the recipe given in the Letter gives excellent numerical results for diffraction efficiencies. However, a crucial assumption was implicitly used without justification. In this paper, we examine this assumption and comment on its validity. In addition, we suggest two alternative ways to extend the C method, and show that one of them is as effective as the recipe given in the Letter.