Fabry-Perot resonator: spectral line shapes, generic and related Airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity

We systematically characterize the Fabry-Perot resonator. We derive the generic Airy distribution of a Fabry-Perot resonator, which equals the internal resonance enhancement factor, and show that all related Airy distributions are obtained by simple scaling factors. We analyze the textbook approaches to the Fabry-Perot resonator and point out various misconceptions. We verify that the sum of the mode profiles of all longitudinal modes is the fundamental physical function that characterizes the Fabry-Perot resonator and generates the Airy distribution. Consequently, the resonator losses are quantified by the linewidths of the underlying Lorentzian lines and not by the measured Airy linewidth. Therefore, we introduce the Lorentzian finesse which provides the spectral resolution of the Lorentzian lines, whereas the usually considered Airy finesse only quantifies the performance of the Fabry-Perot resonator as a scanning spectrometer. We also point out that the concepts of linewidth and finesse of the Airy distribution of a Fabry-Perot resonator break down at low reflectivity. Furthermore, we show that a Fabry-Perot resonator has no cut-off resonance wavelength. Finally, we investigate the influence of frequency-dependent mirror reflectivities, allowing for the direct calculation of its deformed mode profiles. (C) 2016 Optical Society of America