Numerical Computation of High Frequency Wave Propagation in Complex Media

The link communication from/to satellite, re-entry or space vehicles is often subject to degradation known as black-out. To assess this issue, radio frequency (RF) wave propagation through complex media (such ionosphere, plasmas and complex gas mixtures) must be considered. Asymptotic techniques such as ray or beam tracing can be used to predict EM propagation in these inhomogeneous media where the radiation can be refracted, reflected and/or absorbed compared to free-space propagation. Coupled with integral equations for the free-space part of the simulation domain, the model provides a powerful numerical tool to design antennas for critical applications and for calculating the Radar Cross Section (RCS) of objects surrounded by complex media such as hypersonic plasma. The ray tracing method effectively decompose the wavefront with plane wave represented by one or more rays and follow the propagation using the Eikonal approximation valid for short wavelength. Contrary to ray tracing in homogeneous media, where the ray trajectories are straight lines, here a ray can be curved due to the continuous variation of the refractive index (inhomogeneity). A numerical code capable of simulating the behavior of rays and following their trajectory within complex media has been developed at LINKS Foundation. One of the limitations of this model and consequently of the numerical code is the fact that in order to have reliable results, a sufficiently dense grid of rays must be generated which interacts with objects in the "scene" while traversing it (ray traversal); this involves an enormous amount of computational time. The first part of this thesis work focused precisely on this problem: speeding up the ray traversal process; this was done by using special data structures such as K-D Trees or Octrees that can subdivide the physical space (the scene) into boxes and then through an appropriate traversal algorithm identify which boxes were hit by the ray in such a way as to follow its trajectory. In the second part, on the contrary, improvements were made to the physical model, thus enabling the simulation of electromagnetic scattering situations not present in the original code, that were limited to the calculation of the Radar Cross Section considering only perfectly reflective and impenetrable surfaces (PEC); in particular the equations for boundary surfaces between different and possibly lossy dielectrics have been introduced, enabling the simulation of scattering with penetrable dielectrics bodies with sharp boundaries. Due to the secondary rays generated at the discontinuities the bookkeeping of rays is more complicated and has to be implemented efficiently. As initial test cases, the Radar Cross Section of dielectric spheres was calculated and compared with the results obtained with exact solutions derived from Mie's series.