Thermal Noise in Cubic Optical Cavities

Thermal noise in optical cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Numata et al. derived three equations based on strain energy and the fluctuation–dissipation theorem to estimate the thermal noise contributions of the spacer, substrates, and coating. These equations work well for cylindrical cavities. Extending from that, an expression for the thermal noise for a cubic spacer based on the fluctuation–dissipation theorem is derived, and the thermal noise in cubic optical cavities is investigated in detail by theoretical analysis and finite element simulation. The result shows that the thermal noise of the analytic estimate fits well with that of finite element analysis. Meanwhile, the influence of the compressive force Fp on the thermal noise in cubic optical cavities is analyzed for the first time. For a 50 mm long ultra-low expansion cubic cavity with fused silica substrates and GaAs/AlGaAs crystalline coating, the displacement noise contributed from every Fp of 100 N is about three times more than that of the substrate and coating.