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Definition: the free spectral range divided by the FWHM width of the resonances of an optical resonator

German: Finesse

Category: optical resonators

Formula symbol: F

Units: (dimensionless)

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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) when there is no incident field from outside the resonator, the finesse is


where the approximation holds for low round-trip losses (e.g., <10%), i.e., only for high finesse values.

Calculator for the Finesse

Round-trip losses:
Finesse: calc

Enter input values with units, where appropriate. After you have modified some inputs, click the "calc" button to recalculate the output.

finesse versus mirror reflectivity
Figure 1: Finesse of a symmetric resonator as a function of the mirror reflectivity.

The finesse is related to the Q factor: the latter is the finesse times the resonance frequency divided by the free spectral range.

transmission of an optical resonator
Figure 2: Frequency-dependent transmission of a linear Fabry–Pérot interferometer with mirror reflectivities of 80%. The finesse is ≈ 14, and perfect mode matching is assumed.
transmission of an optical resonator
Figure 3: Same as in Figure 2, but with higher mirror reflectivities of 90%. The finesse is ≈ 29.8.

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.

A high finesse can be useful for optical spectrum analysis (→ spectrometers), 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.

See also: cavities, Fabry–Pérot interferometers, supermirrors, reference cavities, bandwidth, Q factor, free spectral range
and other articles in the category optical resonators

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