We present an optimization-based synthesis algorithm for the design of diffractive optical elements (DOE's) that are finite in extent, have subwavelength features, and are aperiodic. The subwavelength nature of the DOE's precludes the use of scalar diffraction theory, and their finite extent and aperiodic nature prevents the use of coupled-wave analysis. To overcome these limitations, we apply the boundary element method (BEM) as the propagation model in the synthesis algorithm. However, the computational costs associated with the conventional implementation of the BEM prevent the design of realistic DOE's in reasonable time frames. Consequently, an alternative formulation of the BEM that exploits DOE symmetry is developed and implemented on a parallel computer. Designs of finite extent, subwavelength, and aperiodic DOE's, such as a lens and a focusing beam splitter, are presented. # 1998 Optical Society of America [S0740-3232(98)00306-8] OCIS codes: 0.50.1970,050.1940,050.1960.
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