Numerical 2D And 3D Simulations of a Spherical Fabry–Pérot Resonator for Application as a Reference Cavity for Laser Frequency Stabilisation

We report on the results of a numerical study of deformations of a spherical Fabry-Pérot cavity that can be used for laser frequency stabilisation. It is demonstrated that for a precise simulation of the cavity deformations a 3D model has to be used instead of a simpler 2D model, which employs simulation on the symmetry plane of the cavity. To lower the sensitivity to environmental perturbations, it is suggested to use a material with a low density and a high Young’s modulus. We also show that the mechanical resonance frequencies of the cavity are mainly determined by the size of the cavity.