PMID: 11308966Apr 20, 2001Paper

Nonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M J AblowitzSteve Blair

Abstract

We derive the asymptotic equations governing the evolution of a quasi-monochromatic optical pulse in a nonresonant quadratic material starting from Maxwell equations. Under rather general assumptions, equations of nonlinear Schrödinger (NLS) type with coupling to mean fields result (here called NLSM). In particular, if the incident pulse is polarized along one of the principal axes of the material, scalar NLSM equations are obtained. For a generic input, however, coupled vector NLSM systems result. Special reductions of these equations include the usual scalar and vector NLS equations. Based on results known for similar systems which arise in other physical contexts, we expect the behavior of the solutions to be characterized by a rather large variety of phenomena. In particular, we show that the presence of the coupling to the dc fields can have a dramatic effect on the dynamics of the optical pulse, and stable localized multidimensional pulses can arise through interaction with boundary terms associated to the mean fields.

References

Oct 1, 1984·Journal of the Optical Society of America. A, Optics and Image Science·B Crosignani, A Yariv
Jan 1, 1994·Physical Review. a·A G Kalocsai, J W Haus
Sep 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A G Kalocsai, J W Haus
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Citations

Sep 19, 2020·Physical Review. E·Mahmut Bağcı, J Nathan Kutz
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T KannaK Tamilselvan
Aug 11, 2005·Physical Review Letters·H Leblond
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Guoxiang HuangChao Hang
Aug 26, 2003·Physical Review Letters·Lucian-Cornel CrasovanLluis Torner

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