Families of two-colour Helmholtz spatial solitons

Bostock, C; Christian, JM; McDonald, GS

Abstract

Multi-colour spatial solitons comprise localized optical components at distinct temporal frequencies [1]. The
components (which may be bright-like and dark-like) tend to overlap in space, thereby allowing the interplay
between linear spreading (diffraction) and nonlinear effects (self- and mutual-focusing) to result in an
electromagnetic structure with a stationary intensity pattern. Two-colour spatial solitons for a Kerr-type medium
were proposed by De La Fuenete and Barthelemy [2] within the context of an intuitive nonlinear Schrödinger model. Subsequent experiments, using continuous-wave (CW) laser light at red and green wavelengths, demonstrated that such mutually-trapped light beams could be generated in CS2 waveguides [3]. This opened up the possibility of multi-colour photonic device applications and architectures [4].
Here, we introduce a novel Helmholtz model for two-colour CW optical fields whose temporal frequency separation is similarly large. A key advantage of our approach is that it allows one full access to multicomponent geometries involving propagation at arbitrary angles and orientations with respect to the reference direction [5] – such considerations are central to off-axis configurations involving, for instance, beam multiplexing [6] and interface [7] scenarios. In contrast, classic paraxial models [2,3] capture angles (in the laboratory frame) that are negligibly, or near-negligibly, small [4]. The two-colour modulational instability problem can be solved in a range of physically relevant regimes. Bright-bright and bright-dark solitons are also reported, each of which having co-propagation and counter-propagation solution classes that are connected by geometrical transformation. Extensive computations [8] have confirmed the validity of analyses.

Citation

Bostock, C., Christian, J., & McDonald, G. Families of two-colour Helmholtz spatial solitons. Poster presented at Salford Postgraduate Annual Research Conference (SPARC 11), University of Salford, Greater Manchester, UK

• Presentation Conference Type: Poster
• Conference Name: Salford Postgraduate Annual Research Conference (SPARC 11)
• Conference Location: University of Salford, Greater Manchester, UK
• End Date: Jun 9, 2011
• Publication Date: Jun 8, 2011
• Deposit Date: Oct 17, 2011
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference; References : [1] P. B. Lindquist, D. R. Andersen, and Y. S. Kivshar, “Multicolor solitons due to four-wave mixing,” Phys. Rev. E 57, 3551 (1998). [2] R. De La Fuente and A. Barthelemy, “Spatial solitons pairing by cross phase modulation,”Opt. Commun. 88, 419 (1992). [3] M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron.28, 2736 (1992). [4] H. T. Tran, R. A. Sammut, and W. Samir, “Interaction of self-guided beams of different frequencies,” Opt. Lett. 19, 945 (1994). [5] J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Helmholtz-Manakov solitons,” Phys. Rev. E 74, art. no. 066612 (2006). [6] P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E 74, art. no. 036609 (2006). [7] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, “Helmholtz solitons at nonlinear interfaces,” Opt. Lett. 32, 1126 (2007). [8] P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Nonparaxial beam propagation methods,” Opt. Commun. 192, 1 (2001).