Research On A New Vector Method For Diffraction Gratings

With the development of manufacture, especially the emergence of micro-manufacture, the trend of integration and minisize become an inevitable process, micro-optics attach more and more attention and recognition. The vector diffraction methods to the sub wavelength gratings, including Fourier Model method, C method and Rayleigh method, which are the most comprehensive and popular ones, have been consummated, while the limitation of these methods are also obvious.Under the thorough research of above methods, we integrate Waterman-Rayleigh method (WRM), Fourier Model method (FMM), and C Method properly into our new method- Waterman-Fourier-Chandezon Method (WFCM for short), which assimilates their main advantages to operate multilayer-coated gratings so as to save the numerical computation time of eigenvalues and eigenvectors, simplify theoretical deductions and the boundary condition respectively; The Fourier factorization theory is applied to achieve the good numerical convergence of our method; The reflection and transmission coefficient matrix method (RTCM) is also used to save the computation time and overcome numerical values instability brought by the added layers.A set of comprehensive program, making a solid theoretical foundation and providing a new calculated tool, is compiled independently under the theoretical direction of WFCM, which is rapid in performance with good convergence and numerical stability.The reflection and transmission coefficient matrix method (RTCM), a widelyused propagation algorithm to theoretical calculations and designing, which simulates the real physical process with a model of "three-node-network of incidence, reflection and transmission" is clear in physical concept, compact in expression form and rapid in propagation. The band structures of one-dimensional (ID) photonic crystals are obtained with this method under the condition of different dielectric constants and geometric structures.