Frequency-based temperature determination for a passively insulated cryogenic sapphire cavity via thermal transfer...

In high-precision cryogenic systems, accurate temperature determination with minimal thermal and mechanical influence is essential. This work demonstrates an accurate, non-contact temperature determination method for a passively insulated sapphire Fabry-Perot cavity operated in the liquid-helium regime. A thermal transfer model that incorporates a temperature-dependent attenuation factor and thermal time constant is established. These dynamics are experimentally identified through in-situ step-response measurements and incorporated into a finite-element-model to account for the system's thermal behavior. Furthermore, the dominant thermo-refractive contribution from the mirror coatings is quantitatively separated and corrected. By combining the optical frequency readout with a rigorously calibrated thermal model, the derived cavity temperature achieves a residual deviation of approximately 50 mK relative to the reference contact sensor. This approach provides a reliable non-contact temperature evaluation strategy for cryogenic cavity ultra-stable lasers. The demonstrated thermal modeling framework is applicable to temperature determination across broader precision cryogenic applications.