Electromagnetic scattering by lossy plasmonic and non-plasmonic half-spaces from vertically polarized incident waves

Eslami Nazari, Mohsen (2023) Electromagnetic scattering by lossy plasmonic and non-plasmonic half-spaces from vertically polarized incident waves. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

In this research, approximate analytical solutions for the scattered electromagnetic (EM) fields radiated by a vertical electric dipole (VED) antenna in the presence of a lossy half-space for ordinary and plasmonic media are investigated. First, an approximate analytical solution for the wave scattering above a lossy half-space with a smooth interface is proposed for frequencies below the very high frequency (VHF) band. The solution to the problem is given in terms of two-dimensional Fourier transforms, which leads to Sommerfeld-type integrals. The solution is decomposed into three terms. Two terms are expressed with hyperbolic functions and the third term is presented using the Gauss error function. A numerical evaluation of the integrals validates the accuracy and efficiency of the proposed solution at various frequencies and distances from the source. Second, an approximate analytical solution of the problem with a smooth interface is proposed for frequencies below 10 GHz. The solution for the intermediate Hertz potential is decomposed into two integrals and a rigorous approximate closed-form solution in the near and far field regions is presented for each term. Then, the scattered electric field (E-field) components are calculated from the intermediate Hertz potential. A numerical evaluation of the solution for different lossy half-spaces, i.e., seawater, wet earth, dry earth and lake water, validates the accuracy of the proposed solution at various frequencies and distances from the antenna. Following this work, a new asymptotic solution for the scattered EM fields above a lossy half-space with a smooth interface for ordinary and plasmonic media is proposed using the modified saddle point method. The new formulations are applied to calculate radiation patterns of different impedance half- planes for both ordinary media (e.g., seawater, silty clay soil, silty loam soil and lake water) and plasmonic media (e.g., silver and gold). A numerical evaluation of the proposed solution at various frequencies and comparisons with two alternative state- of-the-art solutions show that the proposed solution has higher accuracy for plasmonic and non-plasmonic structures. Lastly, random roughness is added to the interface, and a solution for EM scattering over a two-dimensional random rough surface with large roughness height using the generalized functions approach is proposed. The EM field derivation incorporates an arbitrary rough surface profile with small slope, a radiation source and involves all scattering orders of the scattered E-field for high and moderate contrast media. Subsequently, the first-order scattered E-field is calculated using the Neumann series solution for transverse magnetic (TM) polarization. By considering a pulsed dipole antenna and a two-dimensional Gaussian rough surface distribution with different root mean square heights and correlation lengths, the scattered E-field along with the radar cross-section is calculated. Using the result of the method of moments (MoM) as reference, a numerical evaluation of the solution for different roughness heights and contrast media demonstrates that the proposed solution is better than those of the small perturbation method (SPM), Kirchhoff approximation (KA) and small-slope approximation (SSA).

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