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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

Formula symbol: Δν

Units: Hz

Author:

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

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:

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

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

## Calculator for the Free Spectral Range

 Length: Group index: 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 (round-trip group delay) of an optical pulse.

The free spectral range of a Fabry–Pérot interferometer (or a Lyot filter) is the frequency spacing of its transmission peaks. It often limits the optical frequency range in which it can be used. A large free spectral range can thus be desirable. However, for a given finesse, a larger free spectral range also leads to a larger resonator bandwidth and thus a poor spectral resolution.

For a wavelength-tunable single-frequency laser, it 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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