In Chapter 2, the basis for the electromagnetic behavior of DOEs was introduced. To this end, scalar diffraction theory was presented and formulated from an intuitive point of view. As pointed out in the course of the derivation, there are several approximations inherent in the scalar formulation. For this reason, in certain applications, scalar theory becomes invalid and consequently in these cases a modeling technique that more rigorously accounts for the interaction between the incident optical field and the DOE must be used. In this chapter, we present two such techniques, namely, the modal and the finite-difference time-domain methods (FDTD). Results from these techniques are given, along with a discussion of effective medium theory, a simplified approach to modeling the performance of DOEs with subwavelength features. However, before we introduce these techniques we first present a discussion on the limitations of scalar diffraction theory.
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