A Fast and Stabilized Method for Gratings

The widely used Rayleigh expansion is not generally bounded and causes the instability and some limitations in numerical process. We extend the radiation condition for diffraction grating problems and stress that the radiation field excited by a planar periodic current source satisfies the generalized radiation condition; hence, it can be used as a modified Rayleigh expansion to formulate an enhanced Rayleigh method. The proposed method can considerably extend the domain of validity. Invoking the internal regularization mechanism, it can work with success when amplitude/period ratio equals 0.5 or higher for a sinusoidal metal grating and s polarization with normal incidence. At the same time, the simplicity, efficiency, and ability to explicitly depict the interactions among diffracted orders are as good as, if not better than in the Rayleigh method.