A High-Finesse Fabry-Perot Cavity Displacement Sensor Sized by Shot Noise and Coating Thermal Noise

This paper presents a computed design for a 0.40 m Fabry-Perot cavity displacement sensor with dielectric supermirrors, intended for picometre-scale length sensing. The sizing follows from applying the relevant intensity, thermal, nonlinear and geometric bounds at a single stated operating point, with every number produced by a deposited computation. The headline result is a free spectral range of 375 MHz, a cavity linewidth of 1874 Hz at a finesse of 200,000, a shot-noise displacement floor near 7.7e-21 m per root hertz, a coating thermal noise floor of 2e-18 m per root hertz that dominates at low frequency, and a shot-noise-limited displacement of 2.4e-19 m in a 1 kHz band. The binding constraint is identified explicitly: coating Brownian thermal noise, which no increase in circulating power can reduce, and spacer drift with temperature. The design is SIMULATED, NOT MEASURED: no hardware was built for this study, and all performance figures are predictions from stated assumptions, offered as a basis for a build decision and a measurement plan.