Unifying the description of fiber-optic frequency conversion: From cascaded four-wave mixing to Cherenkov radiation

The emission of Cherenkov radiation (CR) by solitons propagating in optical fibers has been extensively studied and is known to play a central role in the generation of broadband supercontinua. This process is generally described in terms of a phase-matching condition between the soliton propagating in the anomalous dispersion regime and a dispersive wave in the region of normal dispersion. Although it may seem surprising, this is one of the very few nonlinear mechanisms that are yet to be described within the traditional formalism of nonlinear optics, i.e., in terms of a nonlinear polarization and associated energy conservation laws. Here, we resolve this long-standing problem, and show that cascaded four-wave mixing (FWM) of two CW fields can mimic a higherorder nonlinear process in a way that results in the amplification of a selected component in the cascade. This cascaded process is naturally phase-matched in waveguides with frequency-dependent group-velocity-dispersion, and we show that the frequency-shift of the amplified component coincides precisely with that of the Cherenkov radiation emitted by a soliton centered at the mean frequency of the CW pumps. This implies that cascaded FWM constitutes the frequency mixing mechanism responsible for CR.