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Free Spectral Range

Definition: frequency spacing of the axial modes of an optical resonator

Alternative term: axial mode spacing

German: freier Spektralbereich

Category: optical resonators

Formula symbol: Δν

Units: Hz

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URL: https://www.rp-photonics.com/free_spectral_range.html

The free spectral range of an optical resonator (cavity) is the spacing of its axial (Gaussian-shaped) resonator modes in terms of optical frequency. It is also called axial mode spacing. For an empty standing-wave resonator of length L, it can be calculated as

free spectral range

For a standing-wave resonator filled with a dispersive medium, the free spectral range is determined by the group index, rather than by the ordinary refractive index:

free spectral range

Due to chromatic dispersion, the group index can deviate from the refractive index, and can be frequency-dependent.

For a waveguide resonator, one would have to calculate the group index using the frequency-dependent effective refractive index.

Calculator for the Free Spectral Range

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Free spectral range: calc

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

More generally, e.g. for an optical resonator containing different transparent media, the free spectral range is the inverse of the round-trip time (more precisely, the round-trip group delay) of a light pulse.

The free spectral range of a Fabry–Pérot interferometer (or a Lyot filter) often limits the optical frequency range in which it can be used as a spectrometer. A large free spectral range can thus be desirable. It can be obtained simply by making the resonator shorter – which, however, also leads to a larger bandwidth of the resonances, thus to poorer spectral resolution, as long as the same mirrors are used. For better resolution, one then needs to increase the finesse by minimizing the round-trip power losses of circulating light.

For a wavelength-tunable single-frequency laser, the free spectral range often (but not always) limits the achievable mode-hop-free tuning range.

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See also: cavities, resonator modes, etalons, group index, group delay
and other articles in the category optical resonators

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