# Calculation of the finesse of a resonator is exact

Nov. 4, 2014
Optical resonators are widely used in photonics, for example as a wavelength locker, a sawtooth-spectrum generator, or a displacement-measuring tool. One of the most important qualities of an optical resonator is its finesse F.

Optical resonators are widely used in photonics, for example as a wavelength locker, a sawtooth-spectrum generator, or a displacement-measuring tool. One of the most important qualities of an optical resonator is its finesse F. (To understand F intuitively, consider that the spectral transmission of a Fabry–Perot resonator consists of an evenly spaced series of peaks at the resonances. Raising F by raising the reflectivity of the resonator’s two flat optical surfaces causes the peaks to become narrower while leaving the peak-to-peak spacing undisturbed. A higher F generally give a resonator finer spectral resolution.) Accurately knowing F is essential for experimentation using a resonator; for the case of no optical absorption, F can be approximately calculated using the Airy equation: F = 4R/(1 − R)2, where R is the intensity reflectivity. However, when optical absorption is added, or when an exact solution is needed, things get more complicated.

Martin Suter and Peter Dietiker of ETH Zürich (Zürich, Switzerland) have developed an exact calculation of F for an ideal resonator (one with no surface-figure errors) as a function of R including absorption; for the case of no absorption, the calculation defaults to an equivalent of the Airy equation. Their solution also eliminates the errors arising from numerous approximate calculations for F developed over the years. Reference: Martin Suter and Peter Dietiker, Appl. Opt. (2014); http://dx.doi.org/10.1364/AO.53.007004.

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