Ray Tracing Theory in a Radially Uniaxial Sphere

Ray tracing theory for a radially uniaxial dielectric sphere is presented in this communication. Reflection and transmission of the plane waves obliquely incident on the spherical interface between air and uniaxial are briefly examined and the general formulations for phase velocities as well as the refractive indices of the ordinary and extraordinary waves propagating in a radially uniaxial medium are investigated. The ray tracing method is implemented for both ordinary and extraordinary rays and the results are applied to evaluate the propagation paths and arrival times of the shortcut wave returns appearing in the transient backscattering response of a uniaxial dielectric sphere. The effect of the variation in relative permittivity on the arrival times of shortcut waves is studied. The results of the ray tracing method are compared with those computed using the Mie and Debye series solutions with good agreement.