Fig. 1

Thermal-compensation MgF₂ resonator. a Measurement of the frequency shifts for the conventional MgF₂ WGM resonator (red) and thermal-compensation WGM resonator (blue), respectively. Inset: The MgF₂ resonator (radius: 3.45 mm and thickness: 0.1 mm) sandwiched by Zerodur layers (thickness: 0.5 mm each) in the packaged unit. The MgF₂ resonator (middle) is glued in between two Zerodur components (top and bottom). The thickness of Zerodur layers is determined by the thermo-mechanical properties of the resonator. b Thermorefractive noise limit (blue) and thermal expansion noise limit (red) of the WGM resonator. The simulations show that the thermal expansion noise of the compensated resonator (solid red line) is lower than the thermorefractive noise near the carrier frequency while the conventional one (dashed red line) is similar. Therefore, the fundamental thermorefractive noise fluctuation can be clearly reached with the compensated resonator in this experiment