Effects of mirror birefringence and its fluctuations to laser interferometric gravitational wave detectors

Crystalline materials are promising candidates as substrates or high -reflective coatings of mirrors to reduce thermal noises in future laser interferometric gravitational wave detectors. However, birefringence of such materials could degrade the sensitivity of gravitational wave detectors, not only because it can introduce optical losses, but also because its fluctuations create extra phase noise in the arm cavity reflected beam. In this paper, we analytically estimate the effects of birefringence and its fluctuations in the mirror substrate and coating for gravitational wave detectors. Our calculations show that the requirements for the birefringence fluctuations in silicon substrate and AlGaAs coating will be on the order of 10-8 and 10-10 rad/ pat 100 Hz, respectively, for future gravitational wave detectors. We also point out that ffiffiffiffiffiHz optical cavity response needs to be carefully taken into account to estimate optical losses from depolarization.