Helmholtz solitons in non-Kerr media

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

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.

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. Helmholtz solitons in non-Kerr media. Poster presented at 25th European Quantum Electronics Conference (CLEO Europe/EQEC), Munich, Germany

• Presentation Conference Type: Poster
• Conference Name: 25th European Quantum Electronics Conference (CLEO Europe/EQEC)
• Conference Location: Munich, Germany
• End Date: Jun 17, 2005
• Publication Date: Jun 16, 2005
• Deposit Date: Oct 17, 2011
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference; References : [1] R.W. Micallef, V.V. Afanasjev, Y.S. Kivshar and J.D. Love, “Optical Solitons with Power-Law Asymptotics,” Phys. Rev. E 54, 2936 (1996). [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).