Encyclopedia … combined with a great Buyer's Guide!


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

German: Finesse

Category: optical resonatorsoptical resonators

Units: (dimensionless)

Formula symbol: <$F$>


Cite the article using its DOI: https://doi.org/10.61835/hf3

Get citation code: Endnote (RIS) BibTex plain textHTML

The finesse of an optical resonator (cavity) is a measure for how narrow the resonances are in relation to their frequency distance: a high finesse means sharp resonances. It is defined as the free spectral range (i.e., the fundamental mode spacing) divided by the (full width at half-maximum) bandwidth of the resonances. It is fully determined by the resonator losses and is independent of the resonator length. It can be specified not only for Fabry–Pérot interferometers, but also for other types of optical resonators, and is often used in the context of resonators with sharp resonances, as used e.g. in optical frequency standards. It is not common to specify the finesse e.g. of a laser resonator.

transmission of an optical resonator
Figure 1: Frequency-dependent transmissivity 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 2: Same as in Figure 2, but with higher mirror reflectivities of 90%. The finesse is ≈ 29.8.

For the calculation of the finesse, we assume that some light is circulating in the resonator while there is no incident field from outside the resonator. Some of the optical energy will be lost after each resonator round-trip. If a fraction <$\rho$> of the circulating power is left after one round-trip (i.e., a fraction <$1 - \rho$> of the power is lost), the finesse is

$$F = \frac{\pi }{{2\arcsin \left( {\frac{{1 - \sqrt \rho }}{{2\sqrt[4]{\rho }}}} \right)}} \approx \frac{\pi }{{1 - \sqrt \rho }} \approx \frac{{2\pi }}{{1 - \rho }}$$

where the approximation holds for low round-trip losses (e.g., <10%), i.e., only for high finesse values. That is actually the regime in which the term finesse is mostly used.

Calculator for the Finesse

Round-trip losses:

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 3: Finesse of a symmetric resonator as a function of the mirror reflectivity.

High-finesse Resonators for Spectral Analysis

An optical resonator with variable length can be used as a tunable frequency filter for spectral analysis: by measuring the optical power throughput as a function of resonator length (which is scanned e.g. with a piezo actuator behind one of the mirrors), one can obtain the optical spectrum, provided that it is limited to a region which is smaller than the free spectral range. Otherwise, multiple frequency components could be transmitted at the same time.

One does not arbitrarily increase the frequency resolution of such an optical spectrometer by choosing a long resonator length because that would lead to a too narrow respectable range. Instead, one must increase the finesse of the resonator.

A very high finesse (above 106) of a Fabry–Pérot resonator can be achieved by using dielectric supermirrors, which have a reflectance very close to 1 and exhibit very weak phase distortions. There are also high-finesse resonators of other types, for example microcavities based on whispering gallery modes, a compact kind of ring resonators.

Apparently Reduced Finesse due to Higher-order Modes

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.

Relation of Finesse to the Q Factor

The finesse is related to the Q factor: the latter is the finesse times the resonance frequency divided by the free spectral range. Essentially, while the finesse relates the resonance bandwidth to the free spectral range, the Q factor relates it to the average optical frequency.

If one increases the resonator's round-trip length while keeping the power losses per round trip constant, the finesse will stay constant, while the Q factor will increase. The latter reflects that it will take more time for the internal optical energy to decay.

More to Learn

Encyclopedia articles:


[1]E. D. Palik, H. Boukari, and R. W. Gammon, “Experimental study of the effect of surface defects on the finesse and contrast of a Fabry–Perot interferometer”, Appl. Opt. 35 (1), 38 (1996); https://doi.org/10.1364/AO.35.000038
[2]M. Suter and P. Dietiker, “Calculation of the finesse of an ideal Fabry–Perot resonator”, Appl. Opt. 53 (30), 7004 (2014); https://doi.org/10.1364/AO.53.007004
[3]N. Ismail et al., “Fabry-Pérot resonator: spectral line shapes, generic and related Airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity”, Opt. Express 24 (15), 16366 (2016); https://doi.org/10.1364/OE.24.016366

(Suggest additional literature!)

Questions and Comments from Users


What exactly is the physical explanation for increasing the width of these resonances with increasing optical losses?

The author's answer:

Increased losses lead to faster damping of the intracavity field. A consequence of that is that the exact optical frequency of an incident beam is less important: there is less memory for the oscillation phase in the past.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

Spam check:

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.


Share this with your network:

Follow our specific LinkedIn pages for more insights and updates: