Calculation of the finesse of an ideal Fabry-Perot resonator

A new derivation of an exact finesse F for the description of an optical resonator is reported. The finesse is derived using the superposition principle of plane waves in an ideal Fabry-Perot resonator in combination with the standard definition of the quality factor Q which relates the energy loss of a resonator cycle to the energy stored in the resonator. The derived exact expression of the finesse is compared to equations found in the literature, and it is shown that they are based on approximations. The exact finesse is then used to convert an infinite series of Lorentz functions into the well-known Airy equation in the case of neglected absorption. The derived expression provides a framework for the discussion of the finesse in terms of decay times, free spectral ranges, and resonator line widths. The provided expression for the finesse is valid for any value of the intensity reflectivity and gives insight into the underlying physical principles of resonators.