摘要：

This dissertation is an investigation of electromagnetic wave interactions with fractal structures. Two major research areas are involved, the characterization of fractal structures and electromagnetic wave theory. This study, namely fractal electrodynamics, is a careful blend of both. This work provides increased understanding of electromagnetic wave scattering from rough objects through deeper physical insight and through a link between the object geometry and wave scattering parameters. From physical considerations, we know that finer and finer detail of scatterers can be remotely detected by electromagnetic waves with shorter and shorter wavelength. Here we use electromagnetic waves of varying wavelength as variable -size yardsticks to probe multi-scaled fractal structures. The variation in their scattering parameters characterize the fractal properties of these structures as the wavelength of the interrogating wave varies. In this work, band-limited multi-scaled fractal functions are designed to reflect the physical properties of natural rough surfaces. Fractal surfaces so specified can be exactly and easily controlled through several descriptors. Since fractal characteristics have been found in many naturally occurring rough surfaces, the fractal functions introduced here provide novel and accurate models to rough surfaces and their interactions with waves. Here we study both unbounded and bounded fractal structures, each with several different approaches. In the former case involving scattering from fractally corrugated surfaces, both the Kirchhoff and the generalized Rayleigh methods are used. Both solutions provide consistent and physically interesting results. The angular scattering pattern on a logarithmic scale exhibits a predetermined slope characteristic of fractal dimension of the surface. This slope becomes less steep as the fractal dimension increases. As an example of scattering from bounded fractal structures, we examine electromagnetic wave scattering from fractal cylinders. The Rayleigh-Gans approximation and the perturbation technique are invoked. The logarithmically -scaled angular scattering patterns exhibit varying slopes characteristic of the fractal dimension of fractally corrugated dielectric cylinder surfaces. The amplitude of scattering cross section variation in near back-scattering direction increases as the fractal dimension increases for fractally fluted conducting cylinders. In all cases, the scattering cross section variation provides a measure of object roughness.

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