Rigorous analysis and design of diffractive optical elements

Analysis and design of complex diffractive optical elements (DOE's) with rigorous electromagnetic diffraction models is very challenging because of the mathematical complexity of these models. In this dissertation, a novel rigorous analysis method for stacked rotated grating structures (SRGS's), the SRG-RCWA algorithm, is developed for the first time. It is based on a new implementation of the standard three-dimensional rigorous coupled-wave analysis (RCWA) algorithm that utilizes improved numerical techniques for better convergence and stability of the algorithm. The new concept of sampling frequency theory is developed to permit the 3-D RCWA algorithm to be applied to a particular class of SRGS's. The resultant SRG-RCWA algorithm has been successfully applied to the characterization of two fabricated SRGS's as circular polarization filters for an infrared imaging polarimetry system. The agreement between numerical SRG-RCWA results and experimental measurements demonstrates its validity and usefulness.; The second effort of this dissertation is to develop a rigorous design tool for finite aperture aperiodic DOE's (FADOE's) with feature size comparable to the optical wavelength. A micro-genetic algorithm (muGA) is used for global optimization with a 2-D finite-difference time-domain (FDTD) method as the rigorous electromagnetic diffraction computations. With some latest FDTD techniques such as the perfect matched layer absorbing boundary conditions (PML ABC's), an efficient 2-D FDTD algorithm is developed to rigorously analyze and evaluate the performance of FADOE's for both TE and TM illumination. In the implementation of muGA, novel genetic operators such as the deterministic rank selection method and combination of arithmetical and heuristic crossover methods are developed to fully exploit the advantages of muGA. In addition, a 'creeping' operator for FADOE's is introduced to enhance the local search capability of muGA. Some common FADOE elements and interesting multi-functional elements have been optimized with the rigorous muGA-FDTD design tool.