A widely celebrated feature of nonlinear optical materials is their support of optical solitons鈥攍ocalized, propagating pulses that maintain their shape over large distances. Light propagating in an optical fiber can be modeled effectively by the nonlinear Schr枚dinger equation (NLS), which can be cast into a hydrodynamic (fluid-like) system by a standard variable transformation. Consequently, optical materials admit both solitons and slowly varying, hydrodynamic solutions such as shock waves and rarefaction waves, analogous to those found in dissipationless fluids. This research explores the behavior of a soliton incident upon a hydrodynamic wave that evolves from an initial jump. 聽Appealing to the notion of classical, linear wave scattering, this research demonstrates when a soliton transmits (鈥渢unnels鈥�) through or gets trapped by a dispersive shock wave or a rarefaction wave.
In "Hydrodynamic optical soliton tunneling", recently published by Patrick Sprenger, Mark Hoefer, and Gennady El in Physical Review E, the soliton-hydrodynamic wave interaction is described mathematically. Utilizing a nonlinear wave modulation approach, this work presents conditions for soliton tunneling/trapping by a temporally evolving hydrodynamic wave.聽 Additionally, the modulation theory predicts the soliton trajectory and amplitude from the initial amplitude, phase, and size of the hydrodynamic jump. The results presented in this article may have utility in the engineering control of optical solitons in optical fibers and, more broadly, in other nonlinear wave systems modeled by the NLS equation such as Bose-Einstein condensates and deep water ocean waves.聽