Free spectral range

Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element.

The FSR is not always represented by $\Delta\nu$ or $\Delta\lambda$, but instead is sometimes represented by just the letters FSR. The reason is that these different terms often refer to the bandwidth or linewidth of an emitted source respectively.

In general

The free spectral range (FSR) of a cavity in general is given by
:$\left, \Delta\lambda_\text\ = \frac\left, \left(\frac\right)^ \$
or, equivalently,
:$\left, \Delta\nu_\text\ = \frac\left, \left(\frac\right)^\$
These expressions can be derived from the resonance condition $\Delta \beta L = 2\pi$ by expanding $\Delta \beta$ in Taylor series. Here, $\beta = k_0 n(\lambda) = \fracn(\lambda)$ is the wavevector of the light inside the cavity, $k_0$ and $\lambda$ are the wavevector and wavelength in vacuum, $n$ is the refractive index of the cavity and $L$ is the round trip length of the cavity (notice that for a standing-wave cavity, $L$ is equal to twice the physical length of the cavity).

Given that \left, \left(\frac\right) \ = \frac\left (\lambda)-\lambda \frac\right= \fracn_g, the FSR (in wavelength) is given by
:$\Delta\lambda_\text = \frac,$
being $n_\text$ is the group index of the media within the cavity.
or, equivalently,
:$\Delta\nu_\text = \frac,$
where $c$ is the speed of light in vacuum.

If the dispersion of the material is negligible, i.e. $\frac\approx 0$, then the two expressions above reduce to
:$\Delta\lambda_\text \approx \frac,<$