RCWA Algorithm In Anisotropic Medium Of Periodic Structure And Optimized By Parallel Computing

Rigorous Coupled Wave Analysis is a non-iterative, deterministic technique utilizing a state-variable method that converges to the proper solution. It is a method widely used in diffraction of periodic structures in frequency domain. This method is natural suitable for modeling the different kinds of grating with the scale of wavelength. But it will may still coverage slowly when it is used to analyze the gratings with high contrast refractive index.Revealed by the Rigorous Coupled Wave Analysis in diffraction grating theory, a thorough and systematic research has been accomplished to cover the diffraction properties of periodic structures made of anisotropic medium. Firstly, the electromagnetic field is expressed as a Fourier expansion and the permittivity tensor of the grating region is expanded into a series of Fourier harmonics. Then boundary condition and condition of transversality of electromagnetic are applied. The problems solving the Maxwell’s equations are transformed to the Algebraic problems of Matrices’ Eigen solutions. We can get the diffraction properties what we want such as transmission, reflection and field distribution. The processes of the establishment of the rigorous coupled wave method are demonstrated. For the case that the optical axis coinciding with a coordinate in Cartesian Coordinate System,Staircase approximation and multilayer boundary condition are used to study the rectangular surface-relief and multilevel anisotropic gratings.Convergence and effective are hot topics in rigorous coupled wave method.High Performance Computing is exploited to implement rigorous coupled wave method, which achieve improvement in the numerical efficiency. Programmer encounter many problems in the design, optimization and debug of High performance computing. In this thesis, the history of the processors development is reviewed. The rules of high performance computing and algorithm design principles are presented. And development of the best performance from NVIDIA CUDA GPUs is taken into consideration. The programmable Graphic Processor Unit or GPU has evolved into a highly parallel, multi-thread, multi-core processor with tremendous computational horsepower and very high memory bandwidth. Several methods are used to establish parallelization and optimization and simplify programming for CUDA-capable GPU architectures, such as memory optimizations, execution configuration optimizations.Combining with CUDA GPUs technique, the LU decomposition and QR decomposition which are used frequency and time-consuming are investigated. We design appropriate CUDA-enable algorithms for LU decomposition and QR decomposition, taking the CUDA architecture into account. Computing resources and storage resources of GPU are exploitation. This makes it possible to greatly enhance the computational efficiency.In the end of the thesis, the applications of RCWA in photorefractive effect and periodically poled lithium niobate are demonstrated.