Optical Frequency Combs and their Applications

Recently there has been a remarkable synergy between the technology of precision laser stabilization and mode-locked ultrafast lasers. This has resulted in control of the frequency spectrum, which consists of a regular ``comb'' of sharp lines, produced by mode-locked lasers. 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 phase-sensitive extreme nonlinear optics and pulse manipulation and control. In this chapter, we first review the frequency-domain description of a mode-locked laser and the connection between the pulse phase and the frequency spectrum to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical frequency metrology, optical atomic clocks, and precision spectroscopy are discussed. Next, we discuss applications of the carrier-envelope phase coherence in time-domain experiments. This chapter serves as a broad introduction and summary for all subsequent chapters that present detailed discussions of specific topics.