Helmholtz-Manakov solitons

Christian, JM; McDonald, GS; Chamorro-Posada, P

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).

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. Helmholtz-Manakov solitons. Presented at 25th European Quantum Electronics Conference (CLEO Europe/EQEC), Munich, Germany

• Presentation Conference Type: Lecture
• Conference Name: 25th European Quantum Electronics Conference (CLEO Europe/EQEC)
• Conference Location: Munich, Germany
• End Date: Jun 17, 2005
• Publication Date: Jun 12, 2005
• Deposit Date: Oct 17, 2011
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference