Colloquium: Femtosecond optical frequency combs

Recently there has been a remarkable synergy between the technologies of precision laser stabilization and mode-locked ultrafast lasers. This has resulted in control of the frequency spectrum produced by mode-locked lasers, which consists of a regular comb of sharp lines. Thus such a controlled mode-locked laser is a ``femtosecond optical frequency comb generator.'' For a sufficiently broad comb, it is possible to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical frequency metrology and synthesis. It has also served as the basis for the recent demonstrations of atomic clocks that utilize an optical frequency transition. In addition, it is having an impact on time-domain applications, including synthesis of a single pulse from two independent lasers. In this Colloquium, we first review the frequency-domain description of a mode-locked laser and the connection between the pulse phase and the frequency spectrum in order to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by a brief overview of how the comb technology is affecting and will affect time-domain experiments.