Simulation of force-insensitive optical cavities in cubic spacers
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We analyze the properties of optical cavities contained in spacers with approximate octahedral symmetry and made of different materials, following the design of Webster and Gill (Opt Lett 36:3572, 2011). We show that, for isotropic materials with Young’s modulus less than 200 GPa, the Poisson’s ratio \(\nu\) must lie in a “magic” range \(0.13<\nu <0.23\) to null the influence of the forces supporting the spacer. This restriction can be overcome with the use of anisotropic materials such as silicon. A detailed study aiming at identification of all suitable crystal orientations of silicon with respect to the resonator body is performed, and the relation to the Poisson’s ratio and the Young’s modulus along these orientations is discussed. We also perform an analysis of the sensitivity of the cavity performance to errors in spacer manufacturing. We find that the orientation of the  or  crystallographic directions oriented along one of the three optical axes of the resonator provides low sensitivities to imprecise manufacturing and interesting options for fundamental physics experiments.
We thank T. Legero (PTB) for providing us with the design of the biconical Si resonator allowing us to test our simulations, A. Nevsky for stimulating discussions, and D. Sutyrin for his help with the simulations. This work was performed in the framework of project SCHI 431/21-1 of the Deutsche Forschungsgemeinschaft.
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