Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled-wave theory

We describe a local linear grating model that permits estimation of the diffraction efficiency of high-numerical-aperture two-dimensional circular lenses with one-dimensional rigorous coupled-wave analysis. The model is self-consistent and is consistent with the scalar theory that results for low-numerical-aperture lenses. The accuracy of the model increases with the number of Fresnel zones of the lens. On the basis of this model we optimize the discrete phase profile of the lens for the maximum diffraction efficiency, using the random search method. The TE and the TM modes are optimized simultaneously. Their phase variations as functions of local grating periods are removed by cyclic shifts of the grating profiles, resulting in constructive summation at the focus and high diffraction efficiency. (C) 1997 Optical Society of America.