Physical Review A
Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance
Krishna Myneni, David D. Smith, Hongrok Chang, H. A. Luckay
Abstract
We derive analytic expressions for the on-resonant cavity scale factor enhancement dependence on temperature, ${S}_{0}(T)$, for an intracavity medium with a Gaussian absorption resonance. Results are expressed as functions of the cavity parameters and the two resonance parameters: ${\ensuremath{\alpha}}_{0}(T)$, the peak absorption coefficient, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\alpha}}^{R}(T)$, the resonance width. A semiempirical model is developed for the temperature-dependent absorption coefficient, ${\ensuremath{\alpha}}_{F}(\mathrm{\ensuremath{\Delta}},T)$, in an alkali-metal-atom vapor cell, and is used to compare the predicted behavior of ${\ensuremath{\alpha}}_{0}(T)$ and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\alpha}}^{R}(T)$ with the measured values for the $D{}_{2}\phantom{\rule{0.28em}{0ex}}F=2\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ resonance in $^{87}\mathrm{Rb}$, over the temperature range 298--325 K. Measurements of ${S}_{0}(T)$ in a low-finesse ring cavity, using the same vapor cell as the intracavity dispersive medium, were performed and found to be in agreement with the temperature-dependent behavior predicted by our theory, with quantitative agreement to 2 K for the critical temperature. The practical range of ${S}_{0}$ is found to be limited by the achievable temperature stability of the resonance parameters of the dispersive medium.