Kuen-Wey Shieh
Published: 2000
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In this thesis, the motivation was to study the applicability and test the limits of analytical formulations using surface equivalence, in dealing with the scattering problem of a thin dielectric slab of finite extent. In this application of the surface equivalence principle, the unknowns, equivalent surface electric and magnetic currents, are established using the method of moments. Described herein, in order to solve for the unknowns, are four new numerical techniques called LSM, CLSM, CLSM+RCA and CWLSM+RCA, employed to deal with the radar cross section (RCS) of electromagnetic wave scattering from thin dielectric slabs, for different thicknesses in three dimensions. The designations, LSM, CLSM, CLSM+RCA and CWLSM+RCA stand for least squares method, constrained least squares method, constrained least squares method plus ring current approximation and constrained weighted least squares method plus ring current approximation, respectively. The least squares method is utilized in the new numerical techniques, providing a better solution in the null region of the RCS than the combined field integral equation (CFIE). The new numerical techniques employ surface distributions of equivalent currents, thus in principle requiring less computer memory than those employing volume distributions of current density. Moreover, there is no need to worry about how nearly perfect should be the absorbing boundary condition (ABC) that is used in the finite difference time domain technique (FDTD). Further, in this work, the importance of the equivalent surface currents flowing on the edge of a thin slab (which are referred to as 'ring currents') has been identified. The new techniques also show fast convergence for the particularly challenging case of edge-on wave incidence, even when the slab is as thin as 0.001 [lambda]0 ([lambda]0 is wavelength in free space). In particular, the CLSM+RCA and CWLSM+RCA analyses have been validated by experiments for the case of backward RCS, these experiments showing good agreement with the analyses. For edge-on incidence, the bistatic RCS predicted by CLSM+RCA is also compared with a simulation from a simple approximation: the simulation shows qualitative similarity to CLSM+RCA, but the quantitative differences of up to 10 dB indicate that use of the new methods can be significantly beneficial.