Coupled spatiotemporal waves: New paradigms in vector soliton physics

Ashley, J T; Christian, JM; McDonald, GS

Abstract

In this presentation, we propose a novel spatiotemporal generalization of Menyuk’s classic equations [1] describing the propagation of two nonlinearly-coupled waves in a dispersive optical system (such as a fibre or planar waveguide). Our approach is similar in spirit to that recently introduced by Christian et al. [2] in a single-component context: both analyses are firmly rooted in special relativity-inspired frame-of-reference considerations, and are concerned with the universal properties of waves in fully second-order systems (where evolution is allowed to venture beyond the realms of the ubiquitous slowly-varying envelope approximation). Research highlights include the complete solution of the modulational instability (MI) problem for vectorized spatiotemporal continuous-wave solutions (the characteristic equation turns out to be an eighth-degree polynomial, rather than a quartic [1]). Predictions of the most-unstable frequency in the system, obtained from consultation of the MI spectrum, are in full agreement with extensive numerical calculations [see Figs. 1(a) & 1(b)]. We have also derived exact bright-bright solitons and investigated some of their key characteristics (e.g., robustness and the asymptotic recovery of Menyuk-type solutions). Future work will address spatiotemporal vector dark solitons [3,4] [see Fig. 1(c)].

References
[1] C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[2] J. M. Christian, G. S. McDonald, T. F. Hodgkinson, and P. Chamorro-Posada, Phys. Rev. Lett. 108, 034101 (2012).
[3] V. V Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, Opt. Lett. 14, 805 (1989).
[4] Y. S. Kivshar and S. K. Turitsyn, Opt. Lett. 18, 337 (1993).

Citation

Ashley, J. T., Christian, J., & McDonald, G. (2013, June). Coupled spatiotemporal waves: New paradigms in vector soliton physics. Presented at College of Science & Technology Research Showcase, University of Salford

• Presentation Conference Type: Other
• Conference Name: College of Science & Technology Research Showcase
• Conference Location: University of Salford
• Start Date: Jun 19, 2013
• Deposit Date: Jun 11, 2013
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference