Birefringence in a Silicon Beamsplitter at 2um for Future Gravitational Wave Detectors

The next generation of gravitational wave detectors will move to cryogenic operation in order to reduce thermal noise and thermal distortion. This necessitates a change in mirror substrate with silicon being a good candidate. Birefringence is an effect that will degrade the sensitivity of a detector and is of greater concern in silicon due to its crystalline nature. We measure the birefringence in a <100> float zone silicon beamsplitter since we expect there to be a large inherent birefringence due to the spatial dispersion effect. We observe that the birefringence varied between $3.44\pm 0.12\times {10}^{-7}$ and $1.63\pm 0.05\times {10}^{-7}$ and estimate the birefringence along the <110> axis to be $1.64\pm 0.5\times {10}^{-6}$ at 2um. We demonstrate this effect and argue that it strengthens the case for 2um and <100> silicon.