Refraction law for self-collimated light beams at material interfaces

McCoy, EA; Christian, JM; McDonald, GS; Sanchez-Curto, J; Chamorro-Posada, P

Abstract

Perhaps the most fundamental electromagnetic phenomenon is the behaviour of light at the interface between dissimilar materials. In fact, the entire field of Optics follows from this single key concept. The reflection and refraction properties of a plane wave incident on the uniform boundary between two linear dielectric materials is an elementary configuration covered in standard textbooks on electromagnetism (see, e.g. Ref. [1]). In contrast,
the behaviour of a beam with a finite transverse cross-section is much more complicated affair, and one must
often resort to wholly-numerical calculations. Relatively little is known about light-interface interactions when
nonlinear components are thrown into the mix – for instance, where the refractive index (of one or both
materials) depends in some way on incident light intensity.

The problem of fully-nonlinear interfaces was first attacked in a pair of seminal papers some two decades ago by
Aceves and coworkers [2,3]. Their classic approach considered scalar spatial optical solitons (self-collimated,
self-stabilizing light beams with a stationary intensity profile) incident on the boundary between two dissimilar
Kerr-type media (i.e., materials whose refractive index varies proportionally with local light intensity I). While
highly instructive, these early analyses were based upon a governing equation whose central tenet was that angles of incidence, reflection and refraction (with respect to the interface) must be negligibly small.

In practice, the “small angles” approximation is not entirely satisfactory. In the laboratory, one generally has
complete freedom to choose any incidence angle; ideally, one would like any theoretical model to possess the same angular freedom. To this end, we have recently developed a theoretical framework that allows us to predict, for the first time, the refraction of soliton beams incident at any angle on a Kerr-type interface [4,5]. Our latest efforts have been to extend these preliminary analyses to much wider classes of power-law materials [6], whose refractive index varies with light intensity according to Ip (where 0 < p < 2 – the Kerr nonlinearity thus corresponds to the particular case of p = 1). By a curious twist of fate, it turns out that the full nonlinear beams configuration can be described by a simple generalization of the trivially-familiar Snell’s law for plane waves.

Citation

McCoy, E., Christian, J., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2010, November). Refraction law for self-collimated light beams at material interfaces. Presented at 1st CSE Doctoral School Postgraduate Research Conference, University of Salford, Greater Manchester, UK

• Presentation Conference Type: Lecture
• Conference Name: 1st CSE Doctoral School Postgraduate Research Conference
• Conference Location: University of Salford, Greater Manchester, UK
• Start Date: Nov 17, 2010
• Publication Date: Nov 17, 2010
• Deposit Date: Oct 17, 2011
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference; References : [1] J. D. Jackson, Classical Electrodynamics 3rd Ed., 1999 John Wiley & Sons (New York). [2] A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989). [3] A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1828 (1989). [4] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 35, 1347 (2010). [5] J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 32, 1126 (2007). [6] J. M. Christian, G.S. McDonald, R. J. Potton, and P. Chamorro-Posada, Phys. Rev. A 76, 033834 (2007).