Position measurement of a cavity mirror using polarization spectroscopy

A high-reflectivity coated mechanical silicon oscillator with high quality value of the mechanical resonance was employed as a planar rear mirror in a Fabry–Perot interferometer. Active stabilization of the interferometer improves the stability of the resonance and makes it possible to perform sensitive interferometric measurements. The frequency locking of lasers to optical cavities requires typically the generation of an error signal with a typical steep slope at resonance. The Hänsch–Couillaud locking method utilizes polarization spectroscopy by monitoring changes in the polarization of the light field reflected from the cavity. A polarization analyser detects dispersion shaped resonances which give the error signal for the electronic servo loop. The error signal contains information about the changes in the cavity length and thus the motion of the mechanical oscillator can be observed. The error signal was detected with the use of a spectrum analyser. The noise floor of the interferometer response indicates that the sensitivity of the optomechanical sensor or the minimum observable displacement in the mechanical oscillator position is xmin = 1.7 × 10−14 m. This gives high enough sensitivity to observe the Brownian motion of the oscillator at room temperature.