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Definition: free spectral range divided by FWHM width of resonances of an optical resonator
The finesse of an optical resonator (cavity) is defined as its free spectral range divided by the (full width at half-maximum) bandwidth of its resonances. It is fully determined by the resonator losses and is independent of the resonator length. If a fraction ρ of the circulating power is left after one round-trip (i.e., a fraction 1 - ρ of the power is lost), assuming that there is no incident field from outside the resonator, the finesse is
where the approximation holds for low losses (i.e. for high finesse).
Figure 1: Frequency-dependent transmission of a linear Fabry-Perot interferometer with mirror reflectivities of 90%. The finesse is ∼29.8, and perfect mode matching is assumed.
A high finesse can be useful for optical spectrum analysis, because it allows the combination of a large free spectral range with a small resonator bandwidth. Therefore, a high spectral resolution in a wide spectral range is possible.
A very high finesse (above 106) can be achieved either by using dielectric supermirrors or in certain microcavities based on whispering gallery modes.
The finesse is related to the Q factor: the latter is the finesse times the resonance frequency divided by the free spectral range.
Note that the apparent bandwidth of the resonances, observed e.g. by scanning the resonator length while observing the transmission with a single-frequency input wave, can appear to be increased due to the excitation of transverse modes with different orders. For a perfectly aligned confocal resonator, the frequencies of even higher-order modes are degenerate with frequencies of axial modes, so that this effect does not occur, but with some misalignment the modes are no longer perfectly degenerate. The apparent finesse can then be reduced.
See also: cavities, Fabry-Perot interferometers, supermirrors, reference cavities, bandwidth, Q factor, free spectral range
