Abstract

An effective numerical technique for analyzing diffraction by a grating is presented with its mathematical foundations. The technique is based on the mode-matching method with a higher-order smoothing procedure; a higher-order indefinite integral of a truncated plane-wave expansion is fitted to that of the boundary condition through the least-squares method. The general algorithm for an arbitrarily shaped grating is described, and convergence of the solution is proven. The techniques with first-, second-, and third-order smoothing procedures are applied to the problem of a sinusoidal grating. Consequently it is made clear that a higher-order smoothing procedure provides a more effective means for evaluating the diffracted field than a lower-order procedure. Some numerical examples of efficiency are included.

© 1983 Optical Society of America

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