A rigorous electromagnetic algorithm is presented for the analysis of electrically large diffractive optical elements (DOE's), i.e., those that contain small features and have large apertures compared with the wavelength of illumination. The technique uses a finite-sized analysis window within which a rigorous electromagnetic technique is used to solve the local boundary-value problem. To this end the boundary-element and finite-difference time-domain methods are used. The analysis window is translated over the entire surface of the DOE and stitches together the complete solution. We validate the techniques by comparing the stitched boundary fields with those of a complete analysis, in both magnitude and phase, for a binary lens. To illustrate the utility of our method we analyzed an eight-level diffractive lens with a 10,000-wavelength diameter sampled at 0.05 wavelength that required 8 Mbytes of memory on a desktop personal computer.
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