This paper presents a comprehensive analytical study of temporal modulation instabilities in a finite, nonlinear, dispersive medium in which two counterpropagating pump beams interact through a Kerr-type nonlinearity. The analysis includes selfand cross-phase modulations, group-velocity dispersion, four-wave mixing, and reflections occurring at the two facets of the dispersive Kerr medium. The ...

A fast, hybrid numerical–asymptotic algorithm for the calculation of the dynamical field evolution that is due to an arbitrary input pulse in any linear dispersive, attenuative medium is presented. The algorithm combines the numerical efficiency of the fast-Fourier-transform algorithm over a finite frequency domain that encompasses all the medium resonances with the accuracy and analytical effi...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...