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

TL;DR

This work directly measures spatial-dispersion–induced birefringence in a $\langle 100 \rangle$ float-zone silicon beamsplitter at $2\,\mu\mathrm{m}$ to assess its suitability for future cryogenic gravitational-wave detectors. Using a PEM-based polarimetric setup and exhaustive 100×100 spatial scans across nine roll angles, the authors extract the birefringence and its dependence on crystal orientation, demonstrating a maximum along $\langle 110 \rangle$ of $1.64 \pm 0.05 \times 10^{-6}$ and pointwise values between $3.44 \pm 0.12 \times 10^{-7}$ and $1.63 \pm 0.05 \times 10^{-7}$. The results, consistent with the expected $1/\\lambda^2$ scaling from previous measurements, indicate that while birefringence is non-negligible, silicon can serve as a beamsplitter material provided precise crystal-axis alignment (within about $4^{\circ}$) and possibly compensation optics. The study reinforces the case for using $2\,\mu\mathrm{m}$ light with $\\langle 100 \\rangle$ silicon in future detectors, while highlighting manufacturing and alignment constraints that must be addressed to minimize spatial-dispersion–driven optical losses.

Abstract

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.

Figures (15)

• Figure 1: Optical loss from depolarisation in a silicon beamsplitter 6 cm thick at 2000. The cyan contour shows 0.1% loss and the red shows 1% loss. This does not take account of other birefringence related effects and therefore should be viewed as an indicative upper limit. The thickness of the beamsplitter is based on the parameters for the aLIGO beamsplitter Abbott2015.
• Figure 2: 3D plot of the direction dependence of the birefringence introduced by considering spatial dispersion. Note the maxima at the 〈110.0〉 axes and the minima at the 〈100.0〉 and 〈111.0〉 axes. There are also saddle points present at the 〈211.0〉 axes. The birefringence has been normalised to a maximum of 1.
• Figure 3: Change in Birefringence as a 〈100.0〉 and 〈111.0〉 silicon beamsplitter is rolled around its central axis. The birefringence has been normalised so that birefringence along the 〈110.0〉 axis is 1. The arm-transmitted beam and the antisymmetric (AS) transmitted beam in the case of 〈100.0〉 experience the same birefringence due to the 4-fold symmetry. Note that the birefringence is lowest at roll angle of 45. The two beams in a〈111.0〉 beamsplitter experience different birefringence levels due to the 3-fold symmetry. Inset shows the 〈100.0〉 axis as a green arrow and the 〈111.0〉 axis as a grey arrow
• Figure 4: Birefringence as a function of roll angle in a beamsplitter that has been cut so that the one of the transmitted beams will experience no spatial dispersion contribution to the birefringence. The cuts have been made at 12 from the specified crystal axis. There are two cases for each zero-birefringence axis: for a 〈111.0〉 beamsplitter the cut can be made towards the 〈001〉 axis or towards the 〈110.0〉 axis and for a 〈100.0〉 beamsplitter the cut can be made towards the 〈111.0〉 axis or towards the 〈110.0〉 axis. The incoming beam and outgoing beam will be separated by a roll angle of 180 in this figure. The axis that the cuts have been made on has been shown in the insets with the arrows representing the optics central axis. The colour of line on the plot corresponds to the colour of the arrow with the green and grey arrows representing the 〈100.0〉 and 〈111.0〉 axes respectively
• Figure 5: Experimental set up showing the difference between the measuring the birefringence in a beamsplitter and the background birefringence caused by internal and external stresses.