Frequency comb

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An ultrashort pulse of light in the time domain. In this figure, the amplitude and intensity are Gaussian functions. Note how the author chooses to set the maximum of the function into the maximum of the envelope.

A Dirac comb is an infinite series of Dirac delta functions spaced at intervals of T.

A frequency comb allows a direct link from radio frequency standards to optical frequencies. Current frequency standards such as atomic clocks operate in the microwave region of the spectrum, and the frequency comb brings the accuracy of such clocks into the optical part of the electromagnetic spectrum.

Mode-locked 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 is a series of delta functions separated by the repetition rate (the inverse of the round trip time) of the laser. Each line is displaced from a harmonic of the repetition rate by the carrier-envelope offset frequency, which is the rate at which the phase of the pulse slips from one pulse to the next. This series of sharp spectral lines forms the basis for the frequency comb.

In the absence of active stabilization, the repetition rate and carrier-envelope offset frequency would be free to drift. They vary with changes in the cavity length, refractive index of laser optics, and nonlinear effects such as the Kerr effect. The repetition rate can be stabilized using a piezoelectric transducer, which moves a mirror to change the cavity length. A simple electronic feedback loop can lock the repetition rate to a frequency standard.

The breakthrough which led to a practical frequency comb was the development of technology for stabilizing the carrier-envelope offset frequency. This requires broadening of the laser spectrum so that it spans an octave. This is usually done using highly nonlinear photonic crystal fiber. However, it has been shown that an octave-spanning spectrum can be generated directly from a Ti:sapphire laser using intracavity self-phase modulation.

The femtosecond comb technique has recently been extended to the extreme ultraviolet range, which enables frequency metrology to that region of the spectrum.

Theodor W. Hänsch and John L. Hall shared the Nobel Prize in Physics 2005 for contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique.

Applications for the frequency comb technique include optical metrology, frequency chain generation, optical atomic clocks, high precision spectroscopy, and more precise GPS technology.

1 Carrier-envelope offset frequency measurement
2 Carrier-envelope offset frequency control
3 Applications
4 See also
5 External links

[edit] Carrier-envelope offset frequency measurement

Measurement of the carrier-envelope offset frequency is usually done with a self-referencing technique, in which the laser spectrum is broadened to be octave-spanning, and the phase of one part of the spectrum is compared to its harmonic. Broadening to an octave is typically achieved using supercontinuum generation by strong self-phase modulation in nonlinear photonic crystal fiber.

In the 'frequency - 2*frequency' technique, light at the lower energy side of the broadened spectrum is doubled using second harmonic generation 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 frequency, detectable with a photodiode, is the carrier-envelope offset frequency.

It has been shown that, with an optical pulse of sufficient peak power, sufficient broadening and second harmonic can be produced in a single nonlinear crystal. This greatly simplifies the technique.

[edit] Carrier-envelope offset frequency control

In Ti:sapphire lasers using prisms for dispersion control, the carrier-envelope offset frequency can be controlled by tilting the high reflector mirror at the end of the prism pair. This can be done using piezoelectric transducers.

In high repetition rate Ti:sapphire ring lasers, which often use double-chirped mirrors to control dispersion, modulation of the pump power using an acousto-optic modulator is often used to control the offset frequency. The phase slip depends strongly on the Kerr effect, and by changing the pump power one changes the peak intensity of the laser pulse and thus the size of the Kerr phase shift.