Helmholtz dark spatial solitons in waveguides
with defocusing saturable materials

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

Abstract

Angular configurations play a fundamental role in essentially all nonlinear photonic architectures: from beam multiplexing applications, to scattering at a single interface, to evolution inside patterned optical structures. Equations of the nonlinear Helmholtz type are ideally suited to describing scalar oblique-propagation contexts. Knowledge of their exact solitons facilitates novel device designs, and the pursuit of these classes of solution is a key research objective of our collaboration.

Saturation under high-intensity illumination is a property of many photonic materials. Phenomenological descriptions of a saturable refractive index must go beyond polynomial-type expansions in the (local) light intensity [e.g., the cubic-quintic approximation (Pushkarov et al., Quantum Electron. 11, 471 (1979)], which eventually break down. However, such approaches almost always result in a governing equation that does not possess exact soliton solutions. A notable exception is the model proposed by Wood et al. [Opt. Commun. 69, 156 (1988)].

We will present, for the first time, exact dark spatial solitons for a Helmholtz equation with a self-defocusing saturable nonlinearity. These novel solutions have been obtained by deploying a unified combination of analytical techniques (symmetry reduction, coordinate transformations, and direct integration). Multi-parameter asymptotic analysis recovers the predictions of conventional (paraxial) theory [Krolikowski and Luther-Davies, Opt. Lett. 18, 188 (1993)], while convergence to its Kerr counterpart [Chamorro-Posada and McDonald, Opt. Lett. 28, 825 (2003)] has been found in the limit of low light intensities. Computations involving perturbed initial-value problems have demonstrated that Helmholtz saturable dark solitons are highly robust nonlinear waves surrounded by wide basins of attraction.

Citation

with defocusing saturable materials. Presented at National Photonics Conference, Photon12, University of Durham, UK

• Presentation Conference Type: Other
• Conference Name: National Photonics Conference, Photon12
• Conference Location: University of Durham, UK
• Publication Date: Jan 1, 2012
• Deposit Date: Jul 17, 2012
• Publicly Available Date: Apr 5, 2016
• Publisher URL: http://www.photon.org.uk/home
• Additional Information: Event Type : Conference