  Media with symmetric inhomogeneity have been of great interest due to
numerous effects which occur when electromagnetic waves propagate through such
media. In general, the inhomogeneity of a certain medium means that the
refraction index of the medium is not constant and has some sort of spatial
dependency. These types of media are called gradient index (GRIN) media.
Different optical effects related to GRIN media are described by GRIN optics.
GRIN optics examines different phenomena related to the gradient of the
refractive index of the medium and/or the material. Electromagnetic waves
propagating in such materials result in many effects that are being exploited
to produce lenses, optical fibers, and other devices. By symmetric
inhomogeneity, we refer to the case when the inhomogeneity of the medium or
material is not an arbitrary function of position but has some sort of
symmetry. In this dissertation, our primary focus is on two types of
inhomogeneous media. Firstly, we examine photonic crystals which are optical
structures where the refractive index changes periodically. The other type of
inhomogeneity, that is examined, is the case when the refractive index of a
medium is a continuous function of position. Moreover, the central focus is
given to profiles possessing different symmetries. Specifically, we investigate
the effects occurring in Maxwell Fish eye profile which has spherical symmetry
as well as an extended symmetry which will be thoroughly studied in Chapters 3
and 4.
