Differential Methods

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From a mathematical point of view, the rigorous computation of the electromagnetic field diffracted by a grating reduces to the resolution of partial derivative equations with suitable boundary conditions. It is shown in Chap. 3 how this problem is equivalent to the resolution of Fredholm integral equations, but, as outlined in Chap. 1, it is possible to solve directly these differential equations. The method related in this chapter is equivalent to, but slightly different from, the scheme previously described in Chap. 1. It takes a place among the so-called differential methods that we shall classify into three categories: