Abstract
Previously ( Proc. R. Soc. Edinburgh122A, 317– 340, 1992) we established that solutions to problems of diffraction of light in a periodic structure behave analytically with respect to variations of the interface. We present an algorithm based on this observation for the numerical solution of the problem. The principal component of the algorithm is a simple recursive formula for the derivatives of the efficiencies with respect to the height of the grating. A conformal mapping mechanism is introduced to enhance the convergence of the series. This allows us to deal with the types of profile and wavelength usually considered in practice. To illustrate our method, we give numerical results for sinusoidal and echelette gratings.
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