Propagation of Gaussian beams through inhomogeneous cylinders with shock-like profiles of refractive index: Grazing incidence case

Wave propagation in inhomogeneous media has been studied for such diverse applications as propagation of radiowaves in the atmosphere, light propagation through thin films and in inhomogeneous waveguides, flow visualization, and others. In recent years an increased interest has been developed in the wave propagation through shocks generated in supersonic flows. Historically these shocks have been treated as discontinuities in refractive index profiles. However, a profile of the refractive index across the shock possesses a finite thickness and gradient. Geometry of the inhomogeneity also had an impact.; This dissertation reports on modeling and numerical analysis of wave propagation through inhomogeneous media with shock-like profiles of refractive indexes. In particular, effects of geometry of inhomogeneities and the refractive index profile are addressed.; The subject of study is a dielectric penetrable circular cylinder with a cylindrically symmetric profile of the refractive index illuminated by a two dimensional Gaussian beam. The propagation vector of the beam is normal to the long axis of the cylinder. The beam is a sheet of light with Gaussian profile along a direction normal to both, the propagation vector and the long axis of the cylinder. The incident electromagnetic field is a TM wave with the electric field vector being parallel to the long axis of the cylinder. The refractive index of the cylinder has a shock-like profile. In the dissertation, the refractive index profile of such a medium is described and the wave propagation phenomena through a such medium is formulated.; The wavefront that emerges after passing through the inhomogeneous cylinder described above is propagated to a remotely located screen using the Fresnel diffraction equation. The resultant pattern is evaluated. Thus the method is a hybrid one. The first part of the method is to propagate the incident Gaussian beam through an inhomogeneous medium of a given profile. The second part is to propagate the resultant field using the Fresnel diffraction integral.; The problem of a Gaussian beam propagation through a homogeneous medium containing an inhomogeneous cylinder described is solved numerically using the finite-difference time-domain (FD-TD) method and a "phase object" approach.; The FD-TD method is formulated for TM waves using the Yee algorithm in Cartesian coordinates and a "stair-case" approximation is used in the discretization process. The problem is solved numerically for different parameters of the refractive index profile. The same problem is also formulated and solved numerically by applying the FD-TD method to a similar homogeneous cylinder placed in a homogeneous medium with a different refractive index.; In the "phase object" approach the wavefront that emerges after passing through the inhomogeneous cylinder is presented as a result of the phase difference accumulation. Examples presented are similar to those evaluated by the FD-TD method.; Data from the numerical calculations are compiled, explained, and conclusions are made on the effects of various parameters on the wave propagation in inhomogeneous media with shock-like profiles. The computed data are also compared with the experimental results.