Antiresonant Fabry-Pérot cavity with ultralow finesse

Abstract

The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-P\'erot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity $R\ensuremath{\rightarrow}0$, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse $\mathcal{F}$ approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at $R=0$. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of ``$\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\ensuremath{\pi}}\phantom{\rule{0.0pt}{0ex}}\ensuremath{\pi}$,'' which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when $R\ensuremath{\rightarrow}0$. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.