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Abstract
Two methods for grating synthesis which have appeared in the literature recently are compared directly. In particular, we point out the similarity between the two; both algorithms are based on propagation of the fields through the structure with simultaneous evaluation of the coupling coefficient according to simple causality arguments (layer-peeling algorithms). The first published method (the discrete layer-peeling algorithm) is reformulated in a simpler, more efficient way, and it is shown that its implementation can be made exact. For mathematical comparison, a derivation of the second method (the continuous layer-peeling algorithm) is presented. The methods are compared both mathematically and numerically. We find that the discrete layer-peeling algorithm is significantly faster and can be more stable than its continuous counterpart, whereas the continuous algorithm offers some advantages in flexibility.
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