Christian, JM, McDonald, GS and Chamorro-Posada, P 2005, Helmholtz-Manakov solitons , in: 25th European Quantum Electronics Conference (CLEO Europe/EQEC), 12th - 17th June, 2005, Munich, Germany.

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Abstract

The propagation of a spatial vector soliton beam in a Kerr planar waveguide is typically described by the Manakov equation [1]. However, the assumption of beam paraxiality breaks the rotational symmetry of the wave propagation problem. Manakov-based descriptions are, for example, incapable of describing physical effects associated with off-axis propagation at non-trivial angles. We will report the first Helmholtz generalizations of the Manakov equation and its soliton solutions, along with a thorough investigation of the dynamical properties of the new solutions. We introduce the Helmholtz-Manakov (H-M) equation as a vector generalization of the scalar Non-Linear Helmholtz (NLH) equation [2], whereby the guided electric field has two transverse orthogonal components. Exact analytical soliton solutions of the H-M equation will be derived for both focusing and defocusing media; the classic Manakov solitons are a subset of these new results. H-M solitons are found to exhibit non-trivial features that are absent from the paraxial-based descriptions (these new features will be shown to influence propagation characteristics). Well-tested numerical perturbative techniques will be employed to demonstrate the role of H-M solitons as robust attractors (in a non-linear dynamical sense). Rich dynamical behaviour will be summarised, including evolution characteristics associated with both fixed-point and limit-cycle attractors. References [1] S.V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248 (1974). [2] P. Chamorro-Posada, G.S. McDonald and G.H.C. New, “Exact soliton solutions of the nonlinear Helmholtz equation: communication,” J. Opt. Soc. Am. B 19, 1216 (2002).

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