Free spectral range

The free spectral range , FSB for short (English: free spectral range , FSR), symbol , is a term from optics and laser technology that characterizes optical devices such as resonators or Fabry-Pérot interferometers . It indicates the frequency spacing of various modes or interference orders supported by the device . ${\displaystyle \Delta \nu _{\mathrm {FSB} }}$

Definition and calculation

For a cavity resonator , the free spectral range is given by the frequency spacing of the axial (Gaussian) resonator modes.

A standing wave can form in a resonator of length if and only if an integral multiple of half the wavelength fits into the resonator: ${\displaystyle L}$ ${\displaystyle m}$ ${\displaystyle \lambda }$

${\displaystyle L=m{\frac {\lambda }{2}}}$   With   ${\displaystyle m=1,2,3,4,\dots }$

If you express this in frequencies , you get the free spectral range: ${\displaystyle \nu }$

${\displaystyle \Rightarrow \Delta \nu _{\mathrm {FSB} }={\frac {c}{2L}}}$

at the speed of light . ${\displaystyle c=\lambda \cdot \nu }$

If the resonator is filled with a dispersive medium , it must be replaced by the group velocity in the medium. ${\displaystyle c}$ ${\displaystyle v_{\mathrm {g} }}$

More generally defines the free spectral range than the inverse rotation period (English: inverse round-trip time ) of an optical pulse.

In a Fabry-Perot interferometer , the free spectral range (at a given wavelength) denotes the wavelength difference at which the -th order interference fringes overlap at the wavelength and -th order at the wavelength . ${\displaystyle \Delta \lambda }$ ${\displaystyle m+1}$ ${\displaystyle \lambda }$ ${\displaystyle m}$ ${\displaystyle \lambda +\Delta \lambda }$

The transmission wavelength of the Fabry-Pérot interferometer can be changed by tilting by the angle  α . The following then applies to the spectrometer obtained in this way :

${\displaystyle \Delta \nu _{\mathrm {FSB} }={\frac {c}{2\,n\,L\cos \alpha }}}$.

with the refractive index  n of the medium in the resonator.

swell

• Free Spectral Range in the Encyclopedia of Laser Physics and Technology (engl.)
• E. Hecht optics. Oldenbourg Verlag, 4th edition 2005, ISBN 3-486-27359-0