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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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 . 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 . 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.
|Item Type:||Conference or Workshop Item (Poster)|
Media, Digital Technology and the Creative Economy
Subjects outside of the University Themes
|Schools:||Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)|
|Depositing User:||JM Christian|
|Date Deposited:||17 Oct 2011 11:38|
|Last Modified:||29 Oct 2015 00:12|
|References:|| 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).  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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