Vector spatial solitons: off-axis nonparaxialityin coupled Helmholtz equations

Vector spatial solitons are complex optical beams with several distinct components. These components (which may be bright-like and/or dark-like) are localized in space and tend to overlap strongly in the propagation plane, thereby allowing the interplay between diffraction and nonlinear effects (e.g., self- and mutual-focusing) to result in stationary light structures. Our group has proposed a more complete and realistic model for describing two-colour vector phenomena, where each electric-field component is at a distinct optical frequency. A key feature of our approach is that one may access multi-colour geometries involving beam propagation at arbitrary angles and orientations with respect to the reference direction in the laboratory frame – such considerations are central to technological device architectures involving multiplexing and interface geometries, but lie far outside the reach of conventional theory [1,2]. We have recently solved the modulational instability problem (which is 4x4 in nature) exactly [3], and extensive computations have confirmed theoretical predictions (e.g., the instability of bright-dark solitons in a focusing Kerr medium). New families of exact analytical two-colour solitons have also been derived, each of which has co-propagation and counter-propagation classes that are related by geometrical transformation. References: [1] R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992). [2] M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992). [3] C. Bostock, MPhil thesis "Two-colour Helmholtz solitons with a defocusing Kerr nonlinearity," University of Salford (2011).