Ultra-low dissipation resonators for improving the sensitivity of gravitational wave detectors

Broadband enhancement of the sensitivity of gravitational wave detectors can be achieved by the use of negative dispersion filters to create white light signal recycling cavities. This filter should have mechanical frequency of 300 kHz or higher and $T/Q_{\mathrm{m}}～6\times {10}^{?10}$ K, in order to achieve appreciable sensitivity enhancement in the range of 1–2 kHz. This paper investigates the possibility of using optical dilution of GaAs/AlGaAs-coated Si and GaAs “cat-flap” micro-resonators to achieve such performance. We analyse the loss contributions to such resonators, particularly thermoelastic loss, suspension loss and acceleration loss. Sufficient reduction of thermoelastic loss is possible when operating near the zero thermal expansion point with temperature control of ～1 K for both materials. Acceleration loss and suspension losses can be minimised in the frequency range ${10}^4\text{–}{10}^5\text{Hz}$, allowing Q-factors in the range ${10}^{11}\text{–}{10}^{12}$, but these are reduced at the target 400 kHz frequency. Results are subject to assumptions regarding material losses. Fabrication techniques for creating GaAs and SiN_x suspended silicon cat-flap resonators are presented.