Abstract

It is well known that an intense pulse sent through a medium with an intensity-dependent index will acquire a stationary shape (spatial soliton) while focusing and collapsing into a point. Many nonlinear phenomena, such as THz generation, require the simultaneous propagation and collapse at two wavelengths. It is shown here that the Kerr effect introduces a coupling between pulses sent co-propagating into a transparent medium with a nonlinear index. Because of this coupling, the pulses at the different wavelengths reshape towards a stationary pair that evolves towards a common focus in time and space. The effect of normal and anomalous dispersion on two-color pulse collapse is investigated numerically. The model to be considered here is an extension of ($ 2 + 1 $)-dimensional nonlinear Schrodinger equations (NLSEs) by inclusion of dispersion and for a beam consisting of two frequencies. As such, our study centers on a system of coupled ($ 3 + 1 $)-D NLSEs describing the co-propagation of two pulses in the non-resonant regime under self-focusing. We should emphasize that this model gives new insight on the initial dynamics of the two-color filament. While inclusion of the small normal dispersion tends to a temporal split of the beam, anomalous dispersion facilitates collapse. In considering initial “short” (fs) and “long” (ps–ns) temporal pulses, our results present different scenarios of the initial evolution that include the role dispersion may have.

© 2019 Optical Society of America

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