Bistable dark solitons of a cubic-quintic Helmholtz equation

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

Abstract

We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field, and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and non-degenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Bistable dark solitons of a cubic-quintic Helmholtz equation. Physical Review A, 81(5), https://doi.org/10.1103/PhysRevA.81.053831

• Journal Article Type: Article
• Publication Date: May 1, 2010
• Deposit Date: Apr 15, 2010
• Publicly Available Date: Apr 5, 2016
• Journal: Physical Review A (PRA)
• Print ISSN: 1050-2947
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 81
• Issue: 5
• DOI: https://doi.org/10.1103/PhysRevA.81.053831
• Publisher URL: http://dx.doi.org/ 10.1103/PhysRevA.81.053831