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Frequency comb

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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.

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

where is an integer, is the comb tooth spacing (equal to the mode-locked laser's repetition rate or, alternatively, the modulation frequency), and is the carrier offset frequency, which is less than .

Combs spanning an octave in frequency (i.e., a factor of two) can be used to directly measure (and correct for drifts in) . 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 ( and ) are stabilized generates a comb that is useful for mapping optical frequencies into the radio frequency for the direct measurement of optical frequency.

The most popular way of generating a frequency comb is with a mode-locked laser. Such lasers produce a series of optical pulses separated in time by the round-trip time of the laser cavity. The spectrum of such a pulse train approximates a series of Dirac delta functions separated by the repetition rate (the inverse of the round-trip time) of the laser. This series of sharp spectral lines is called a frequency comb or a frequency Dirac comb.

The most common lasers used for frequency-comb generation are Ti:sapphire solid-state lasers or Er:fiber lasers with repetition rates typically between 100 MHz and 1 GHz or even going as high as 10 GHz.

Four-wave mixing is a process where intense light at three frequencies interact to produce light at a fourth frequency . If the three frequencies are part of a perfectly spaced frequency comb, then the fourth frequency is mathematically required to be part of the same comb as well.

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