| In recent years, with the development of microphotolithography technology, so-phisticated micro-optical elements have been fabricated with a very small featuresize. Compared with conventional bulk optical elements, diffractive optical elements(DOEs) offer a number of advantages, such as the smaller size, lighter weight andlower cost. DOEs have many potential applications in laser-beam focusing, opticalcoupling, wavelength division multiplexing, information storage, optical interconnec-tion, and so on. DOEs have also attracted great research interest owing their meritsin application and fabrication. For DOEs with characteristic scale comparable to orsmaller than the incident wavelength, scalar diffraction theory cannot be employedto analyze their focal performance. Therefore, accurate analysis of the focal perfor-mance of DOEs with subwavelength characteristic scale requires a fully rigorous so-lution to the electromagnetic equations. Among the numerous numerical methods, theboundary element method (BEM) takes great advantage in solving a two-dimensionalfinite-size scattering problem, especially for the performance analysis of cylindricalmicrolenses. As the most common components in DOEs, focusing diffractive ele-ments have an extensive history and can be used to focus, collimate, or redirect beamsof light. When the light is incident upon the closed-boundary cylindrical microlens(CBCM), owing to the strong scattering and diffraction effects of light fields in theclosed region, it is quite different from the case of the open-boundary cylindricallenses.Main achievements in this thesis are summarized as follows.(1) Focusing performance of CBCMs is analyzed based on rigorous electromag-netic theory and the BEM. For the refractive CBCMs, our numerical results indicatethat the real focal position deviates greatly from the preset focal plane and the focalspot size is very large, which is due to a very large thickness of the refractive CBCMs.For the multilevel CBCMs, the real focal position is much closer to the preset focalplane and the focal spot size is much smaller. When the quantization-level numberis increased, the diffraction efficiency is steadily increased in that the scattering anddiffraction effects of fields on microlens boundary are weakened. For the f/1.0 8-level CBCMs, when the microlens diameter is less than 15.0μm, scalar theory brings large errors in the performance analysis and vectorial theoretical methods should beemployed. The diffraction efficiency and the normalized transmitted power for TMpolarization are usually a little larger than those for TE polarization. It provides veryuseful information in designing the CBCMs in micro optical systems.(2) Focal performance of the dual-closed-surface microlens arrays (DCSMAs) isstudied based on rigorous electromagnetic theory and the BEM in the case of TEpolarization. The DCSMAs are designed with different substrate thicknesses anddifferent distances between microlenses. DCSMAs designed according to differentwavelengths are also surveyed. Several focusing performance measures, such as thefocal spot size, the focal position on the preset focal plane, the diffraction efficiencyand the normalized transmitted power, are presented. Numerical results indicate theDCSMAs with different parameters can implement focusing beams. With the increaseof spacing, the DCSMAs can be considered as two independent closed-boundary mi-crolenses. The focal performance of DCSMAs is easily in?uenced by the substrate-thickness and the incident wavelength. Furthermore, the substrate thickness for themaximal diffraction efficiency of the DCSMAs is given. We believe that the researchcan offer useful information in design of array elements.(3) Instead of the existing zero-thickness model (ZTM), the finite-thicknessmodel (FTM) is employed to designs of CBCMs with small f-numbers based on thewave-front interference principle. Focal performance of all the designed microlensesis investigated by the rigorous electromagnetic theory and BEM. For CBCMs withsmall f-numbers, numerical results by the BEM reveal that the designed CBCMsby using the FTM possess better focal performance than the designed CBCMs byusing the ZTM, such as a more exact real focal position, a smaller focal spot size,and a higher diffraction efficiency. In designs of multilevel CBCMs, the FTM alsotakes slight advantages over the ZTM. The performance improvement for multilevelCBCMs is not so prominent as that for refractive CBCMs only because the largestthickness of diffractive CBCMs is limited. The proposed strategy is useful in vecto-rial designs in that it can provide a better initial point in iterations.(4) Focal performance of CBCMs made of anisotropic uniaxial crystal is inves-tigated. For both TE and TM polarizations, focal performances of the anisotropicCBCMs with different f-numbers are studied in detail. The in?uence of illuminationtype on focal performances of CBCMs are also considered. Several focal perfor- mance quantities, such as the real focal position, the focal spot size, the diffractionefficiency and the normalized transmitted power, are presented. Numerical resultsindicate that the focal performance of anisotropic CBCMs made of uniaxial crystaldiffers greatly in the case of different polarizations. Especially, there exists a largefocal shift, which is due to the birefringence effect of a uniaxial crystal. In contrast,for conventional isotropic CBCMs, the focal characteristics for different polarizationsare similar. Comparing with planar surface illuminated, the focal performances ofCBCMs in the case of curved surface illuminated are studied in detail. Numericalresults indicate that the focal performances of CBCMs with small f-number are sen-sitive to illumination type.(5) A general focal length function is proposed to design microlenses with longextended focal depth and high lateral resolution. The focal performance of the de-signed microlenses, including the actual focal depth, the focal spot size and the diffrac-tion efficiency, is calculated by rigorous electromagnetic theory and BEM for severalf?numbers. Numerical results indicate that the designed microlenses can exhibit longextended focal depth and good focal performance. The general focal length expres-sion extends the parameter space in designing microlenses with long extended focaldepth. It means that such microlenses are comparatively convenient to design.
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