Frequency comb

A frequency comb or spectral comb is a spectrum made of discrete and regularly spaced spectral lines. In optics, a frequency comb can be generated by certain laser sources.

A number of mechanisms exist for obtaining an optical frequency comb, including periodic modulation (in amplitude and/or phase) of a continuous-wave laser, four-wave mixing in nonlinear media, or stabilization of the pulse train generated by a mode-locked laser. Much work has been devoted to this last mechanism, which was developed around the turn of the 21st century and ultimately led to one half of the Nobel Prize in Physics being shared by John L. Hall and Theodor W. Hänsch in 2005.^[1][2][3]

The frequency domain representation of a perfect frequency comb is like a Dirac comb, a series of delta functions spaced according to

${\displaystyle f_{n}=f_{0}+n\,f_{r},}$

where ${\displaystyle n}$ is an integer, ${\displaystyle f_{r}}$ is the comb tooth spacing (equal to the mode-locked laser's repetition rate or, alternatively, the modulation frequency), and ${\displaystyle f_{0}}$ is the carrier offset frequency, which is less than ${\displaystyle f_{r}}$.

Combs spanning an octave in frequency (i.e., a factor of two) can be used to directly measure (and correct for drifts in) ${\displaystyle f_{0}}$. Thus, octave-spanning combs can be used to steer a piezoelectric mirror within a carrier–envelope phase-correcting feedback loop. Any mechanism by which the combs' two degrees of freedom (${\displaystyle f_{r}}$ and ${\displaystyle f_{0}}$) are stabilized generates a comb that is useful for mapping optical frequencies into the radio frequency for the direct measurement of optical frequency.