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The reduced Maxwell-Duffing description of extremely short pulses in non-resonant media

Elena V. Kazantseva·Andrei I. Maimistov·Jean-Guy Caputo
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Abstract

The propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of a model where the material medium is represented by anharmonic oscillators with cubic nonlinearities (Duffing model) and waves can propagate only in the right direction. The system of reduced Maxwell-Duffing equations admits two families of exact analytical solutions in the form of solitary waves. These are bright spikes propagating on a zero background, and bright and dark spikes, propagating on a nonzero background. Direct simulations demonstrate that these pulses are very robust against perturbations. We find that a high frequency modulated electromagnetic pulse evolves into a breather-like one. Conversely a low frequency pulse transforms into a quasi-harmonic wave.

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Elena V. Kazantseva, Andrei I. Maimistov, Jean-Guy Caputo. 2003-09-22. The reduced Maxwell-Duffing description of extremely short pulses in non-resonant media. https://arxiv.org/abs/nlin/0309057

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