| In this thesis I apply numerical electromagnetic models to the analysis and synthesis of diffractive optical elements (DOEs) that are finite in extent, have subwavelength features, and are aperiodic. The integration of such elements with active components, such as emitters and detectors, is critical to the widespread use of optoelectronics in interconnects and sensors applications. However, DOE synthesis is made difficult by the micron scale of the active components and the micron scale of their operating wavelength. The subwavelength nature of the DOEs 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, I have applied the boundary element method and a hybrid finite element-boundary element method to the analysis and synthesis of micron-scale DOEs. However, the computational costs associated with their conventional implementation prevent the synthesis of realistic DOEs in reasonable time frames. Consequently, I develop a semi-infinite and symmetric boundary element model of diffraction and implement it on a parallel processor. Synthesis algorithms using this model are applied to the design of DOEs for application to infrared photodetectors and optical interconnects. Designs of finite extent, subwavelength, and aperiodic DOEs are presented. |
