Casimir torque between two birefringent plates

The vacuum energy between two birefringent plates was calculated using the quantized surface mode technique. And an analytical approximate expression of Casimir torque was obtained in the retarded limit, which is found to vary as sin(2 phi) with phi, the angle between the two optical axes. This result is a supplement to the numerical calculation obtained by Munday, Iannuzzi, Barash, and Capasso [Phys. Rev. A. 71, 042102 (2005)].