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Thermal lensing in resonant optical interferometers such as those used forgravitational wave detection is a concern due to the negative impact on controlsignals and instrument sensitivity. In this paper we describe a method formonitoring the thermal state of such interferometers by probing thehigher-order spatial mode resonances of the cavities within them. Wedemonstrate the use of this technique to measure changes in the Advanced LIGOinput mode cleaner cavity geometry as a function of input power, andsubsequently infer the optical absorption at the mirror surfaces at the levelof 1 ppm per mirror. We also demonstrate the generation of a useful errorsignal for thermal state of the Advanced LIGO power recycling cavity bycontinuously tracking the first order spatial mode resonance frequency. Such anerror signal could be used as an input to thermal compensation systems tomaintain the interferometer cavity geometries in the presence of transients incirculating light power levels, thereby maintaining optimal sensitivity andmaximizing the duty-cycle of the detectors.

In-situ characterization of the thermal state of resonant optical interferometers via tracking of their higher-order mode resonances