Relativistic & pseudo-relativistic connections in optical pulse propagation

We explore a more complete model for describing the evolution of scalar optical pulses in generic nonlinear waveguides. The electromagnetic wave envelope satisfies a dimensionless equation that is of the Helmholtz type. Our approach is to retain the double-longitudinal-space derivative in the linear wave operator, which is routinely neglected – with few exceptions [1] – throughout nearly 50 years of literature. Pulse propagation problems are firmly rooted in frame-of-reference considerations, and as such the mathematical structure of the governing equation allows us to draw intriguing parallels with Einstein’s special theory of relativity (e.g., the velocity combination rule for pulses is akin to that for particles in relativistic kinematics). Exact analytical bright solitons have been derived for a range of classic nonlinearities, and their robustness has been tested through exhaustive computations