Frequency comb

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.is the comb tooth spacing (equal to the mode-locked laser's repetition rate or, alternatively, the modulation frequency), andCombs spanning an octave in frequency (i.e., a factor of two) can be used to directly measure (and correct for drifts in)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.Here, a single laser is coupled into a microresonator (such as a microscopic glass disk that has whispering-gallery modes).This kind of structure naturally has a series of resonant modes with approximately equally spaced frequencies (similar to a Fabry–Pérot interferometer).Nevertheless, the four-wave mixing effect above can create and stabilize a perfect frequency comb in such a structure.In fact, nonlinear effects can shift the resonant modes to improve the overlap with the perfect comb even more.(The resonant mode frequencies depend on refractive index, which is altered by the optical Kerr effect.)In the time domain, while mode-locked lasers almost always emit a series of short pulses, Kerr frequency combs generally do not.[10] However, a special sub-type of Kerr frequency comb, in which a "cavity soliton" forms in the microresonator, does emit a series of pulses.The advantage of this method is that it can reach much higher repetition rates (>10 GHz) than with mode-locked lasers and the two degrees of freedom of the comb can be set independently.[13] The number of lines is lower than with a mode-locked laser (typically a few tens), but the bandwidth can be significantly broadened with nonlinear fibers.These are produced for electronic sampling oscilloscopes, but also used for frequency comparison of microwaves, because they reach up to 1 THz.Measurement of the carrier–envelope offset frequency is usually done with a self-referencing technique, in which the phase of one part of the spectrum is compared to its harmonic.In the "f − 2f" technique, light at the lower-energy side of the broadened spectrum is doubled using second-harmonic generation (SHG) in a nonlinear crystal, and a heterodyne beat is generated between that and light at the same wavelength on the upper-energy side of the spectrum.This beat signal, detectable with a photodiode,[18] includes a difference-frequency component, which is the carrier–envelope offset frequency.In the absence of active stabilization, the repetition rate and carrier–envelope offset frequency would be free to drift.The repetition rate can be stabilized using a piezoelectric transducer, which moves a mirror to change the cavity length.This was first proposed in 1999 [17] and demonstrated in 2011 using an erbium fiber frequency comb at the telecom wavelength.[20] This simple approach has the advantage that no electronic feedback loop is needed as in conventional stabilization techniques.A simple electronic feedback loop can lock the repetition rate to a frequency standard.A second photodiode can be added to the setup to gather phase and amplitude in a single shot, or difference-frequency generation can be used to even lock the offset on a single-shot basis, albeit with low power efficiency.In recent years, the frequency comb has been garnering interest for astro-comb applications, extending the use of the technique as a spectrographic observational tool in astronomy.[29] Optical frequency combs can also be utilized to measure greenhouse gas emissions with great precision.For instance, in 2019, scientists at NIST employed spectroscopy to quantify methane emissions from oil and gas fields [30].More recently, a greenhouse gas lidar based on electro-optic combs has been successfully demonstrated.[32] Theodor W. Hänsch and John L. Hall shared half of the 2005 Nobel Prize in Physics for contributions to the development of laser-based precision spectroscopy, including the optical frequency-comb technique.Also in 2005, the femtosecond comb technique was extended to the extreme ultraviolet range, enabling frequency metrology in that region of the spectrum.
An ultrashort pulse of light in the time domain. The electric field is a sinusoid with a Gaussian envelope. The pulse length is on the order of a few 100 fs
A Dirac comb is an infinite series of Dirac delta functions spaced at intervals of T ; the Fourier transform of a time-domain Dirac comb is a Dirac comb in the frequency domain .
Difference between group and phase velocity leading to carrier–envelope offset
Spectrum of the light from the two-laser frequency combs installed on the High Accuracy Radial Velocity Planet Searcher . [ 23 ]
Illustration showing how trace gases are detected in the field using a mobile dual-frequency comb laser spectrometer. The spectrometer sits in the center of a circle which is ringed with retroreflecting mirrors. Laser light from the spectrometer (yellow line) passes through a gas cloud, strikes the retroreflector and is returned directly to its point of origin. The data collected are used to identify leaking trace gases (including methane), as well leak locations and their emission rates.
spectrumspectral linesopticscontinuous-wave laserfour-wave mixingmode-locked laserNobel Prize in PhysicsJohn L. HallTheodor W. Hänschfrequency domainDirac combdelta functionsoctavepiezoelectric mirrorfeedback loopdegrees of freedomultrashort pulseMode-lockingDirac delta functionsFourier transformphotonic-crystal fiberKerr frequency combmicroresonatorwhispering-gallery modesFabry–Pérot interferometerdispersionnonlinearoptical Kerr effectsolitonoscilloscopessupercontinuumphotonic crystal fiberself-phase modulationwave envelopesecond-harmonic generationheterodynephotodiodephase is measured directlyKerr effectpiezoelectricprismsacousto-optic modulatorphase-locked loopHigh Accuracy Radial Velocity Planet Searcherradio frequencyatomic clocksmicrowaveoptical clockmetrologyfew-cycle pulsesabove-threshold ionizationattosecond pulsesnonlinear opticshigh-harmonics generationSpectral phase interferometry for direct electric-field reconstructionastro-combastronomyspectroscopyfrequency countersNobel PrizeRoy GlauberAtomic clockBandwidth-limited pulseMagneto-optical trapBibcodeCiteSeerXJournal of Lightwave TechnologyP. Del'HayeAppl. Phys. BLudwig Maximilian University of MunichOpt. Lett.Wayback MachinePhysical Review LettersNatureNathalie Picqué