In order to consider the effects of birefringence or double refraction in a uniaxial crystal like sapphire or calcite, I personally wrote a document

http://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=3519

to follow the discussions in CQG 27 185015 (2010).

In short:

(1) The KAGRA ETM with 0.05-degree wedge at its AR side would not spilt optical beams due to birefringence or such splitting is ignorable even if the c-axis of the sapphire substrate is tilted in no more than 2 degrees to the HR surface; the effect is indeed small, as the difference between ordinary and extraordinary index of refractions of sapphire are small.

(2) I found the CQG paper mentioned above contained at least two typos in its eq. (7), as indicated in my document.

Be careful that I don't mention any effects from polarization mixture. A uniaxial crystal would be used as a wave plate, and that means, it will mix two electric-field vectors in a propagating light beam through the crystal if its c-axis is tilted. The phase modulation in the light could be converted to amplitude modulation and vise versa due to the effects...