Spatial soliton refraction at cubic-quintic material interfaces

McCoy, EA; Christian, JM; McDonald, GS

Abstract

In their most general form, wave–interface problems are inherently angular in nature. For instance, the interaction between light waves and material boundaries essentially defines the entire field of optics [1]. The seminal works of Aceves et al. [2,3] considered scalar bright spatial solitons impinging on the interface between two Kerr-type media with different dielectric parameters. While these classic analyses paved the way toward understanding how self-collimated light beams behave at medium discontinuities, they suffer from a fundamental limitation: the assumption of slowly-varying wave envelopes means that, in the laboratory frame, angles of incidence, reflection and refraction (relative to the interface) must be of vanishingly small magnitude.

Over the last few years, the angular restriction of conventional (paraxial) nonlinear-Schrödinger modelling
has been lifted by deploying a more flexible nonlinear-Helmholtz approach [4]. This mathematical platform is
ideally suited to capturing the oblique-propagation aspects of interface scenarios We will report our latest research involving arbitrary-angle soliton refraction in more general classes of cubic-quintic materials [8], for which exact analytical bright [9] and dark [10] Helmholtz solitons are now known. A novel Snell’s law will be detailed that allows for both finite-beam effects and
medium mismatches. Numerical computations test analytical predictions of soliton refraction and critical angles
over a wide range of parameter regimes. Qualitatively new phenomena are also uncovered by simulations in
both small- and large-angle regimes.

Citation

McCoy, E., Christian, J., & McDonald, G. Spatial soliton refraction at cubic-quintic material interfaces. 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 18, 2011
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference; References : [1] J. D. Jackson, Classical Electrodynamcs, 3rd ed. (John Wiley & Sons, New York, 1998). [2] A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface,” Phys. Rev. A 39, 1809 (1989). [3] A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light-beam propagation at nonlinear interfaces. II. Multiple-particle and multiple-interface extensions,” Phys. Rev. A 39, 1828 (1989). [4] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, “Helmholtz solitons at nonlinear interfaces,” Opt. Lett. 32, 1126 (2007). [5] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, “Nonlinear interfaces: intrinsically nonparaxial regimes and effects,” J. Opt. A 11, 054015 (2009). [6] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, “Dark solitons at nonlinear interfaces,” Opt. Lett. 35, 1347 (2010). [7] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, “Black and gray Helmholtz Kerr soliton refraction,” Phys. Rev. A (accepted 2010). [8] Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471 (1979). [9] J. M. Christian, G. S. McDonald, and P. Chamorro-Poada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007). [10] J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable dark solitons of a cubic-quintic Helmholtz equation,” Phys. Rev. A 81, 053831 (2010).