Femtosecond Optical Frequency Combs
The field of optical frequency metrology has recently been dramatically simplified by the development of optical frequency combs based on Kerr-lens mode-locked femtosecond lasers.
The output of a mode-locked laser in the time domain consists of a regular train of short pulses separated by time τ = 1 / frep where frep is the repetition rate of the laser. In the frequency domain, the output is a comb of frequencies with spacing equal to frep. However, in general, the comb modes are not at exact integer multiples of the repetition frequency. The difference between the phase and group velocities inside the laser cavity leads to a pulse-to-pulse phase shift Δφ of the carrier with respect to the peak of the pulse envelope. This leads to an offset f0 of the whole comb from the frequency origin.
Time domain:
Frequency domain:
The frequency spectrum of a mode-locked laser is therefore a comb with frequencies given by
fm = m frep + f0
where m is an integer. For Fourier-transform limited pulses, the full width at half maximum of the comb bandwidth is given by the inverse of the pulse duration. For example, 20 fs pulses give a full width at half maximum of 50 THz, although the useful bandwidth of the comb may extend well beyond this.
Nonetheless, it is desirable to further increase the bandwidth of the comb. Most obviously, this allows larger frequency intervals to be measured. However, if the bandwidth is increased enough, it becomes possible to determine the offset frequency f0, and hence the absolute frequency of all the comb modes, directly in terms of a microwave reference frequency without the need for any intermediate phase-locked oscillators. The simplest of these self-referencing techniques relies on being able to produce a comb that spans a complete optical octave, i.e. a factor of two in frequency. This spectral broadening may be achieved by coupling the output from the mode-locked laser into a short length of microstructured fibre.
Half the 2005 Nobel Prize in Physics was shared by John Hall (JILA and NIST) and Theodor Hänsch (Max-Planck Institute for Quantum Optics, Germany) for "their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique."