Helmholtz solitons: fresh perspectives and new angles in photonics

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

Abstract

Spatial solitons are self-localizing optical beams that can evolve with a stationary intensity profile when diffraction is off-set by material nonlinearity. Classic descriptions of spatial solitons [1] involve the paraxial approximation, which can impose strong constraints on the experimental geometries that can be accurately modelled. For example, even very simple beam configurations, interaction or material-interface scenarios [2] have intrinsically angular characters that are outside the remit of paraxial theory.

Helmholtz soliton theory provides a full description of scalar optical beams in uniform two-dimensional planar waveguides [3]. Crucially, these two spatial dimensions are physically equivalent. By respecting this fundamental symmetry, the governing equation supports beam propagation arbitrary angles relative to the reference direction. In this way, one can exploit the full angular characters of interaction and interface geometries [3].

Here, we provide a complete account of the first exact analytical bistable soliton solutions that have been derived for nonlinear Helmholtz equations. These novel solitons provide the physical and mathematical basis for designing novel photonic devices that combine the phemonenon of non-degenerate bistability with arbitrary-angle interaction and oblique- incidence effects [4].

Both bright and dark solutions have been derived for a range of experimentally-important materials (e.g., cubic-quintic and saturable nonlinearities), and their geometry explored in detail. Extensive computer simulations have verified analytical predictions regarding the stability of the new solitons, which are generally robust entities.

References

[1] V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34 62 (1972); 37, 823 (1973).

[2] J. P. Gordon, Opt. Lett. 8, 596 (1983); O. Cohen et al., Opt. Lett. 27, 2013 (2002).

[3] P. Chamorro-Posada and G. S. McDonald, Phys. Rev. E 74, 036609 (2006); J. Sánchez- Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 32, 1126 (2007).

[4] S. Gatz and J. Herrmann, IEEE J. Quant. Electron. 28, 1732 (1992); J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, Phys. Rev. A 76, 033833 (2007).

Citation

Christian, J., Mcdonald, G., & Chamorro-Posada, P. (2008, August). Helmholtz solitons: fresh perspectives and new angles in photonics. Poster presented at National Photonics Conference, Photon 08, Heriot-Watt University, Edinburgh, UK

• Presentation Conference Type: Poster
• Conference Name: National Photonics Conference, Photon 08
• Conference Location: Heriot-Watt University, Edinburgh, UK
• Start Date: Aug 26, 2008
• End Date: Aug 29, 2008
• Publication Date: Aug 26, 2008
• Deposit Date: Oct 14, 2011
• Publicly Available Date: Apr 5, 2016
• Publisher URL: http://photon08.iopconfs.org/
• Additional Information: Event Type : Conference