Rigorous Vector Analysis Of Subwavelength Diffractive Microlens

This dissertation is about the rigorous vector analysis and design of subwavelength diffractive microlenes. Because the feature size of subwavelength diffractive microlens is smaller than the incident wavelength, scalar diffractive theory cannot be used to the analysis. It also precludes rigorous vector coupled-wave theory for its finite and aperiod structure. In this dissertation an electromagnetic computational method is employed as rigorous vector diffractive theory for the analysis of subwavelength diffractive microlens. The design methods of subwavelength diffractive microlens are presented. The design examples are analyzed by the theory in the dissertation.In the first section, analysis methods are developed. In the dissertation body-of-revolution finite-difference time-domain method (BOR FDTD) is employed as the theory mode for the analysis of axially symmetric subwavelength diffractive microlens. Relative optical theory is considered in BOR FDTD algorithm. The major sub-algorithms in BOR FDTD are explained, the formulas in each sub-algorithm are given. As one important sub-algorithm of BOR FDTD, Perfect matched layer absorbing boundary conditions (PML ABCs) algorithm with split field components is presented for the first time, which greatly simplified computational process. The vector-based plane-wave spectrum method (VPWS) is improved, which can directly obtain the far field diffractive pattern depending on the output near field data in the BOR FDTD meshes by use of the deduced formulas in this dissertation. The above two algorithms of BOR FDTD and VPWS are used to the analysis of subwavelength diffractive microlenses, the analysis process and program flow chart are shown. The editing and debugging of the whole program of BOR FDTD and VPWS algorithms by Matlab code are finished successfully, in the program I used matrix to put values for variables instead of using cycle, which significantly increase the computing speed.The second section is to design diffractive microlenses. In the dissertation multilevel microlenses and binary subwavelength diffractive microlenses are designed, design methods and configuring formulas and design examples are illustrated. Two kinds method of design binary subwavelength diffractive microlenses are illustrated with emphasis. I obtained the result that the method of subwavelength pulse-width modulation is better than the method of linear approximation for continuous phase piece in designing binary subwavelength diffractive microlenses by comparing them. The effects of depth error and width error on diffractive microlenses are discussed. I find that there are little influences on diffractive microlenses when the relative fabrication error is small.The third section is to analyze the optical characteristic of diffractive microlenses. The influence of changing design parameters on diffractive microlens is investigated. The effects of changing design focal length and microlens material refractive index on diffractive efficiency and airy diffraction disc radius are presented. The numerical results are discussed by qualitative analysis. The dispersion property of subwavelength diffractive microlens is investigated. Numerical result illustrates that focal length becomes longer when incident wavelength becomes shorter, however the relationship between focal length and incident wavelength isn't absolute inverse ratio, it is that the increasing of focal length is faster than the decreasing of incident wavelength. At the same time the numerical result also show that scalar theory can't be used in the rigorous analysis of the dispersion property of subwavelength diffractive microlens.