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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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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

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

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.

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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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