Numerical Algorithms For Inverse And Direct Diffraction Problems Of Rectangular Grating And Stepped Grating

Scattering theory has become a key research content in the field of physics, electromagnetic wave and sound wave scattering problems is also more and more important in the real life. So the scattering theory research make some mathematical physics research scholars pay more attention to it. When the spread of the wave field meet the inhomogeneous medium, the original propagation path is affected by the wave field, we call this process is scattering. Among them, the change of wave field propagation path of inhomogeneous medium is called a scatterer. Then, when the surface of the scatterer is the periodic structure, we call it is a diffraction grating. In real life, diffraction grating can be used in many ways, for example, optical holography, the design of the optical components, optical logic, optical fiber communication, signal processing, image recognition and so on.In this thesis, we have studied the physical and mathematical model of the diffraction problem of rectangular grating. We have fully understood the physical background and mathematical model of the diffraction problem. In this paper, we first solve the direct diffraction problems of rectangular grating. The direct problems are also used the finite element method and the difference method to solve it; Secondly, we should solve the inverse diffraction problems of the rectangular grating, the inverse problem also use a high degree of the total field u to reverse the performance of rectangular grating width l and the height h, for the inverse problem we will use the sequence of Monte Carlo (SMC) method in probability of statistical theory to slove it; SMC sampling method is used to obtain a series of sampling points, and the expected value of sampling points to approximate the width l and height h of the rectangular grating. Finally, we will use the MATLAB software to achieve the results, and the results are analyzed; In addition, based on the prediction of the two dimensional data, we will add a turning point to the original rectangular grating model, and then estimate the four-dimensional data using the above method.