Critical Angles for Reflectivity at an Isotropic-anisotropic Boundary

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Abstract
The angular dependent reflectivities, and in particular sharp, critical, edges in these have been analysed for the boundary between an isotropic and a uniaxial medium. For the general uniaxial case, it is shown that for measured reflectivities of the type transverse magnetic (TM) incident to TM reflected or transverse electric (TE) incident to TE reflected there is only one sharp critical angle, the other being rounded due to TM to TE conversion. On the other hand if the TM to TE conversion reflectivity is measured (or TE to TM) then a sharp cusp occurs at the otherwise rounded critical edge. This thereby allows, from some very simple reflectivity measurements the determination of the optical tensor for the anisotropic medium. A full analytic treatment of this behaviour is presented together with numerical evaluations of the electromagnetic field distributions which illustrate how this cusp arises. The possible application of the use of this TE to TM conversion cusp measurement in the case of obliquely oriented liquid crystals is also discussed.