Frequency comb

In optics, a frequency comb is a laser source whose spectrum consists of a series of discrete, equally spaced frequency lines. Frequency combs can be generated by a number of mechanisms, 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 the latter 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. In optics, a frequency comb is a laser source whose spectrum consists of a series of discrete, equally spaced frequency lines. Frequency combs can be generated by a number of mechanisms, 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 the latter 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 a series of delta functions spaced according to where n {displaystyle n} is an integer, f r {displaystyle f_{r}} is the comb tooth spacing (equal to the mode-locked laser's repetition rate or, alternatively, the modulation frequency), and f 0 {displaystyle f_{0}} is the carrier offset frequency, which is less than f r {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) f 0 {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 ( f r {displaystyle f_{r}} and f 0 {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. 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 f 1 , f 2 , f 3 {displaystyle f_{1},f_{2},f_{3}} interact to produce light at a fourth frequency f 4 = f 1 + f 2 − f 3 {displaystyle f_{4}=f_{1}+f_{2}-f_{3}} . 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. Starting with intense light at two or more equally spaced frequencies, this process can generate light at more and more different equally spaced frequencies. For example, if there are a lot of photons at two frequencies f 1 , f 2 {displaystyle f_{1},f_{2}} , four-wave mixing could generate light at the new frequency 2 f 1 − f 2 {displaystyle 2f_{1}-f_{2}} . This new frequency would get gradually more intense, and light can subsequently cascade to more and more new frequencies on the same comb. Therefore, a conceptually simple way to make an optical frequency comb is to take two high-power lasers of slightly different frequency and shine them simultaneously through a photonic-crystal fiber. This creates a frequency comb by four-wave mixing as described above.