Diffraction analysis of electromagnetic wave scattering from slab lamellar gratings
Abstract
Although a lot of experimental works have been demonstrated to either verify or suggest many applications of diffractional gratings, a lot more theoretical works still need to be explored in order to stimulate more applications of gratings on modern signal processing filed. This dissertation work is devoted to the diffraction analysis of the slab lamellar grating which is assumed to be perfectly conducting. We use the classical moment and mode matching method to solve our problem. In general, the performance of grating is determined by many parameters: incident wave polarization, incidence angle, ratios among grating period, aperture size, wavelength and so on. Combinations of the values of these parameters can attribute to various degrees of difficulties when numerical techniques are applied. A solution will be satisfactory it it meets fundamental energy criteria and boundary conditions. Many times a solution can not be obtained, depends on the values of parameters, because some numerical difficulties are involved. Under these situations, we use SVD(Singular Value Decomposition) to obtain the answer. The trade-off is to spend more computer time to obtain an otherwise incorrect solution. Both one dimensional and two dimensional problems have been studied. We also devise a pseudo-noise array signal pattern to address an application of the grating. The signal pattern we designed makes use of the polarization dependent characteristic of the diffraction grating when the period is small compared with the wavelength of the incident wave. By examining the autocorrelation function of two identical such gratings we are able to know whether two such patterns are aligned or not. As the result, the pseudo-noise array can be successfully implemented as an automatic alignment system without human intervention.
Degree
Ph.D.
Advisors
Gallagher, Purdue University.
Subject Area
Electrical engineering
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