Abstract
Recently, the simplified modal method (SMM) has proved to be very successful to facilitate grating design by reducing the diffraction problem to the interference (and reflection at interfaces) of a very small number of grating modes In this work, an intuitive and fully-analytical matrix formalism is developed to evaluate and improve the SMM. The present method focuses on the coupling between the grating modes and the influence of evanescent modes, which have not been touched on in detail in previous formulations of the SMM. In particular, we show that when there are only two grating modes, their coupling is exactly zero only for Littrow mounting and the reflection coefficients also reduce to the familiar Fresnel's form as is commonly used by previous formulations. For other incidence angles, mode coupling can be significant, and our model shows greatly improved accuracy over the common SMM when compared with numerical results. A new parameter measuring the boundary condition mismatch and reflecting the accuracy of the method is proposed, which can serve as a criterion for choosing the number of evanescent modes in the model. The improved model will be of great value for grating designs.
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