Direction cosines and vectorial relations for extraordinary-wave propagation in uniaxial media

Extraordinary-wave propagation within homogeneous uniaxial media is analyzed in the case of an arbitrary optic-axis orientation. Unit vectors along the electric- and magnetic-field directions are represented by direction cosines and vectorial relations. The extraordinary-ray path is determined simply by direction cosines. Numerical examples are given for extraordinary-ray tracings within a plane-parallel uniaxial plate. It is shown that a symmetrical convergent beam is asymmetrically imaged when it is incident normally and passes through the uniaxial plate with an arbitrary optic-axis orientation.