Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design

We have designed high-efficiency finite-aperture diffractive optical elements (DOE's) with features on the order of or smaller than the wave-length of the incident illumination. The use of scalar diffraction theory is generally not considered valid for the design of DOE's with such features. However, we have found several cases in which the use of a scalar-based design is, in fact, quite accurate. We also present a modified scalar-based iterative design method that incorporates the angular spectrum approach to design diffractive optical elements that operate in the near-field and have sub-wavelength features. We call this design method the iterative angular spectrum approach (IASA). Upon comparison with a rigorous electromag-netic analysis technique, specifically, the finite difference time-domain method (FDTD), we find that our scalar-based design method is surprisingly valid for DOE's having sub-wavelength features.