  Cavity-enhanced direct frequency comb spectroscopy combines broad spectral
bandwidth, high spectral resolution, precise frequency calibration, and
ultrahigh detection sensitivity, all in one experimental platform based on an
optical frequency comb interacting with a high-finesse optical cavity. Precise
control of the optical frequency comb allows highly efficient, coherent
coupling of individual comb components with corresponding resonant modes of the
high-finesse cavity. The long cavity lifetime dramatically enhances the
effective interaction between the light field and intracavity matter,
increasing the sensitivity for measurement of optical losses by a factor that
is on the order of the cavity finesse. The use of low-dispersion mirrors
permits almost the entire spectral bandwidth of the frequency comb to be
employed for detection, covering a range of ~10% of the actual optical
frequency. The light transmitted from the cavity is spectrally resolved to
provide a multitude of detection channels with spectral resolutions ranging
from a several gigahertz to hundreds of kilohertz. In this review we will
discuss the principle of cavity-enhanced direct frequency comb spectroscopy and
the various implementations of such systems. In particular, we discuss several
types of UV, optical, and IR frequency comb sources and optical cavity designs
that can be used for specific spectroscopic applications. We present several
cavity-comb coupling methods to take advantage of the broad spectral bandwidth
and narrow spectral components of a frequency comb. Finally, we present a
series of experimental measurements on trace gas detections, human breath
analysis, and characterization of cold molecular beams.
