  Optical frequency combs are one of the most remarkable inventions of the last
decades. Originally conceived as the spectral counterpart of the train of short
pulses emitted by mode-locked lasers, frequency combs have also been
subsequently generated in continuously pumped microresonators, through
third-order parametric processes. Quite recently, direct generation of optical
frequency combs has been demonstrated in continuous-wave laser-pumped optical
resonators with a second-order nonlinear medium inside. Here, we presents a
concise introduction to such quadratic combs and the physical mechanism that
underlies their formation. We mainly review our recent experimental and
theoretical work on formation and dynamics of such quadratic frequency combs.
We experimentally demonstrated comb generation in two configurations: a cavity
for second harmonic generation, where combs are generated both around the pump
frequency and its second harmonic, and a degenerate optical parametric
oscillator, where combs are generated around the pump frequency and its
sub-harmonic. The experiments have been supported by a thorough theoretical
analysis, aimed at modelling the dynamics of quadratic combs, both in frequency
and time domains, providing useful insights into the physics of this new class
of optical frequency comb synthesizers. Quadratic combs establish a new class
of efficient frequency comb synthesizers, with unique features, which could
enable straightforward access to new spectral regions and stimulate novel
applications.
