Anatoliy A. Savchenkov, Andrey B. Matsko, Vladimir S. Ilchenko, Nan Yu, and Lute Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007)
We show theoretically that the absolute frequency stability of a solid-state millimeter-scale whispering gallery mode resonator can reach one part per per 1 s integration time if proper crystalline material as well as proper stabilization technique is selected. Both the fluctuations of the resonator temperature and the fluctuations of the temperature in the mode volume can be measured with the sensitivity better than the fundamental thermodynamic limit and actively compensated.
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The data are taken from manufacturer specifications if the reference is not provided. We should note that the values vary significantly depending on the published study and/or the specifications. The variation: reaches tens of percents. We use the following notations: ρ is the density, C is the specific heat capacity (we assume that ), n is the refractive index, is the thermorefractive coefficient. is the linear thermal expansion coefficient, κ is the thermal conductivity coefficient, is the compressibility of the resonator host material (we assume that the isothermal and adiabatic compressibilities are approximately equal).
Table 2
Thermorefractive, Thermal Expansion, and Thermoelastic of WGM Frequency Stability at Room Temperaturea
Material
(nK)
(nK)
(nK)
80
9
89
427
34
446
7
11
246
129
6
109
303
29
481
; determines the effective value of external temperature instability (quality of compensation of external technical temperature fluctuations) required to observe the limits.
Tables (2)
Table 1
Linear and Nonlinear Thermorefractive Coefficients of the Ca, Ba, , Sapphire, and Crystalline Quartz at and a
The data are taken from manufacturer specifications if the reference is not provided. We should note that the values vary significantly depending on the published study and/or the specifications. The variation: reaches tens of percents. We use the following notations: ρ is the density, C is the specific heat capacity (we assume that ), n is the refractive index, is the thermorefractive coefficient. is the linear thermal expansion coefficient, κ is the thermal conductivity coefficient, is the compressibility of the resonator host material (we assume that the isothermal and adiabatic compressibilities are approximately equal).
Table 2
Thermorefractive, Thermal Expansion, and Thermoelastic of WGM Frequency Stability at Room Temperaturea
Material
(nK)
(nK)
(nK)
80
9
89
427
34
446
7
11
246
129
6
109
303
29
481
; determines the effective value of external temperature instability (quality of compensation of external technical temperature fluctuations) required to observe the limits.