Simple relations between a uniaxial medium and an isotropic medium

In this article, in a simple way, simple relations are derived between the electric field components of an electrically uniaxial medium and those of an isotropic medium. The permittivity of the isotropic medium is the same as the permittivity of the uniaxial medium that is common to the axes transverse to the optic axis. Using the spectral representation, the vector wave equation for the electric field intensity vector of the uniaxial medium is solved for the x directed, y directed and z directed point sources. For the x directed and y directed point sources, the electric field components transverse to the optic axis are written in terms of the corresponding components of the isotropic medium plus some other terms. Part of these terms are closed forms expressions, and the rest are Sommerfeld type integrals. Elements of each group are related to each other by coordinate transformations. The electric field components parallel to the optic axis are shown to be obtained from the isotropic medium components using coordinate transformations. The relations between the uniaxial medium and isotropic medium field components are verified by comparing the results of a previous study in the literature to the results obtained using the relations in this study. Good agreement is achieved between these results.