PMID: 15244961Jul 13, 2004Paper

Three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Min ChenBoris A Malomed

Abstract

We formulate a general model of three-wave optical interactions (in the spatial domain), which combines quadratic (chi(2)) and cubic (chi(3)) nonlinearities, the latter including four-wave mixing. The model can be realized in chi(2) materials where an effective chi(3) nonlinearity is engineered by means of the quasi-phase-matching technique. Both self-focusing and self-defocusing chi(3) nonlinearities are considered. The birefringence of the two fundamental-frequency (FF) waves is taken into regard. Several types of solitons in this system are found, by means of the variational approximation and numerical methods. These are exact single-component solitons and generic three-wave (3W) ones, which are classified by relative signs of their components. Stability of the solitons is investigated by means of the Vakhitov-Kolokolov (VK) criterion, and then tested by direct simulations. One type of the single-component FF solitons (the "fast" one, in terms of the known two-component birefringent chi(3) model) is, chiefly, unstable, as in that model, but nevertheless a stability interval is found for it, which provides for the first example of stable fast solitons. The other FF soliton (the "slow" one, in terms of the same chi(3) model, w...Continue Reading

References

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Jun 1, 1995·Optics Letters·L W Liou, G P Agrawal

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Citations

May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hervé LeblondDumitru Mihalache
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G T Adamashvili, D J Kaup
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhi-Yuan SunYing Liu

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