Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

Hairun Guo, Xianglong Zeng, Binbin Zhou, Morten Bache

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    Abstract

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due to competition between self-steepening, Raman effects, and self-steepening-like effects from cascading originating in the group-velocity mismatch between the pump and the second harmonic. We analyze the first-order contributions, and show that this balance can be broken to create fast or slow pulses. Through further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena, such as blue/red shifting, nonstationary radiation in accordance with the nonlocal phase-matching condition, and dispersive-wave generation are observed and marked, which helps improve the experimental knowledge of cascading nonlinear soliton pulse compression.
    Original languageEnglish
    JournalOptical Society of America. Journal B: Optical Physics
    Volume30
    Issue number3
    Pages (from-to)494-504
    ISSN0740-3224
    DOIs
    Publication statusPublished - 1 Mar 2013

    Bibliographical note

    This paper was published in JOSA B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-3-494. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

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