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

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Abstract

Spatial optical soliton propagation in a planar waveguide is often modelled by a Non-Linear Schrödinger (NLS) type equation. Such systems are paraxial in nature, and cannot describe accurately off-axis propagation at nontrivial angles. The NLS equation typically allows for a Kerr non-linearity, but real optical materials often possess a response that deviates from this idealization [1]. We report, for the first time, exact analytical soliton solutions to a generalized Non-Linear Helmholtz (gNLH) equation. Solutions, and accompanying simulations, thus account for both the inherent symmetries of propagation problems and more realistic (polynomial-type) non-linearities. Models based on the gNLH equation are suitable for describing accurately the angular aspects of wave propagation [2]. Since the assumption of beam paraxiality is omitted, such descriptions can support both travelling- and standing-wave solutions. We will present distinct novel families of solutions of the gNLH equation. These will include: sech-shaped and algebraic (e.g. Lorentzian) solitons, and also spatially-extended (transverse periodic) nonlinear waves. Thorough numerical investigations will demonstrate the role of gNLH solitons as attractors of the system. With few exceptions, we have found that dynamics exhibit limit-cycle qualities (perturbed initial conditions give rise to self-sustained oscillations in the long term). Departure from pure Kerr non-linearity will also be shown to result in much stricter conditions on how closely a launched beam needs to match the corresponding exact soliton solution.

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