McDonald, GS, Christian, JM, Hodgkinson, TF, Cowey, R and Lancaster, G 2012, Spatiotemporal pulse propagation: connections to special relativity theory , in: College of Science and Technology Research Showcase Day, 20th June 2012, University of Salford, Greater Manchester, UK.

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Abstract

We propose a more complete model for describing the evolution of scalar optical pulses in nonlinear waveguides. The electromagnetic wave envelope u satisfies a dimensionless spatiotemporal governing equation that is of a fully-second-order form. With few exceptions [1,2] throughout nearly 50 years of literature, the spatial disperion contribution has been routinely neglected. By retaining this otherwise-omitted term, we have found that pulse propagation problems are most transparently described with a frame-of-reference formulation. We have developed the mathematical and computational tools necessary for the full analysis of the spatiotemporal dispersion equation and its solutions. Intriguing parallels with Einstein’s special theory of relativity also emerge naturally (e.g., the velocity combination rule for pulses is akin to that for particles in relativistic kinematics) [3]. Exact bright and dark solitons have been derived for a range of classic nonlinearities, and their robustness has been tested through exhaustive numerical simulations. References: [1] Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, Opt. Quantum Electron. 11, 471 (1979). [2] F. Biancalana and C. Creatore, Opt. Exp. 16, 14882 (2008). [3] J. M. Christian et al., Phys. Rev. Lett. 108, art. no. 034101 (2012); Phys. Rev. A (accepted for publication, 2012).

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