Simple grating synthesis algorithm

Many authors (including this one) have suggested that the problem of synthesizing a grating from its reflection spectrum is significantly more difficult than the direct problem of obtaining the spectrum from the grating. Fortunately, this view is mistaken. One can synthesize a grating from any reflection spectrum by direct solution of the standard coupled-mode equations while simultaneously evaluating a simple integral to obtain the grating strength. This approach has the advantage of being based on a well-understood set of equations, making it amenable to physical interpretation, mathematical approximation, and generalization.