Four-wave Mixing Instabilities Research Articles

Unusual scenarios in four-wave-mixing instability

A pump carrier wave in a nonlinear dispersive system may decay by giving birth to blue- and redshifted satellite waves due to modulation or four-wave mixing instability. We analyze situations where the satellites are so different from the carrier wave, that the redshifted satellite either changes its propagation direction $(k<0,$ $\ensuremath{\omega}>0)$ or even gets a negative frequency $(k,\ensuremath{\omega}<0)$. Both situations are beyond the envelope approach and require application of the Maxwell equations.

Four-wave mixing instabilities in photonic-crystal and tapered fibers.

Four-wave mixing instabilities are theoretically studied for continuous wave propagation in ultrasmall core photonic-crystal and tapered fibers. The waveguide, or geometrical, contribution to the overall dispersion of these structures is much stronger than in conventional fibers. This leads to the appearance of unstable frequency bands that are qualitatively and quantitatively different from those seen in conventional fibers. The four-wave mixing theory developed here is based on the full wave equation, which allows rigorous study of the unstable bands even when the detunings are of the order of the pump frequency itself. Solutions obtained using the generalized nonlinear Schrödinger equation, which is an approximate version of the full wave equation, reveal that it suffers from several deficiencies when used to describe four-wave mixing processes.

Modulation instability of ultrashort pulses via a generalized nonlinear Schrödinger equation with deviating argument

A modified nonlinear Schrödinger equation is proposed to describe the propagation of ultrashort optical pulses through a dispersive medium with inertial nonlinearity. From this equation we derive quite simply the initial growth rates of the sidebands corresponding to the modulational and four-wave mixing instabilities as well as the Raman interaction for modulational frequencies of the order of the Raman gain spectrum.