Thermal detuning of a bichromatic narrow linewidth optical cavity

In the Advanced $\mathrm{Virgo}+$ interferometric gravitational-wave detector, the length control of the Fabry-Pérot cavities in the arms and of the detuned filter cavity, used for generating frequency-dependent squeezing, uses an auxiliary green beam at half of the operation laser wavelength (1064 nm). While operating the filter cavity with such a bichromatic control scheme for tens of hours, we observed that the mirror reflection phase shift of the fields at the two wavelengths responds differently to temperature changes in the mirrors, causing a change in the relative resonance condition of the two beams. In this paper we show that this thermal detuning effect can be explained by considering the thermomechanical properties of the mirror coating. Our experimental measurements are in good agreement with the theoretical predictions and allow us to drive requirements on the bicolor coating design and mirror temperature stability for long-term stable cavity control.

Figure 1

Optical layout of the squeezing system showing two main environments: in-air benches and vacuum-suspended benches. The orange beam, known as a subcarrier (SC), is antiresonant in the OPA and copropagates with the squeezing beam. It is another candidate for controlling FC. PD1 provides the Pound-Drever-Hall error signal for the green FC longitudinal locking while the IR PDH signal on PD2 is used to drive the AOM for keeping the SC beam in resonance. PD3,4 are dc photodiodes in transmission of the FC for the green and the IR beams, respectively, and are used for diagnostic purposes or for triggering the locking system. The other acronyms are defined in the text.

Figure 2

Measurement of bichromatic thermal detuning by decreasing the filter cavity end mirror temperature.

Figure 3

Measurement of bichromatic thermal detuning by increasing the filter cavity input mirror temperature. There are some data not shown in the plot since the cavity was not properly locked at that moment.