ABSTRACT
Optical frequency combs [1-3] provide equidistant frequency markers in the infrared, visible and extreme ultra-violet [4,5]. Early work by T.W. Hänsch recognized that the periodic pulse train of a mode-locked laser [6,7], which intrinsically provides in Fourier domain an output spectrum that constitutes an optical frequency comb, can be used to measure unknown optical frequencies. An optical frequency comb is generally characterized by its two degrees of freedom, the mode spacing frep, which in a pulsed laser is given by the pulse repetition rate [8], as well as the carrier envelope offset frequency fceo, which determines the frequency offset of the comb teeth from integer multiples of the repetition rates.
In time domain, fceo describes the phase slippage of the pulse envelope with respect to the carrier. Thus, any comb line of the resulting output spectrum can be expressed by fm = fceo + mfrep, where m is an integer. Measurement and control of frep and fceo allows to phase-coherently link optical frequencies across the entire spectrum spanned by the comb [8,9]. In this case, every comb tooth is uniquely determined by the experimentally controlled quantities fceo and frep. Therefore, any arbitrary optical frequency within the spectrum of the comb may be synthesized, or, vice versa, any given optical frequency within this spectrum may be phase-coherently compared to the frequencies fceo and frep in the RF domain, which can be referenced to microwave time standard [10,11]. This unique ability has made the frequency comb a revolutionary tool in metrology and laser spectroscopy, and, serving as a clockwork mechanism, has enabled the development and practical use of time standards in the optical domain [2,3,12,13]. Beyond these advances in metrology and precision measurements, frequency combs have given new impetus to applications such as broadband laser-based gas sensing [14-16] or cavity ring down spectroscopy [17].
