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Hydrodynamic optical soliton tunneling

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journal contribution
posted on 2018-03-16, 09:50 authored by P. Sprenger, M.A. Hoefer, Gennady El
A conceptually new notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrodinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Under certain conditions, soliton interaction with hydrodynamic barriers gives rise to new effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.


This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and EPSRC grant EP/R00515X/1 (G.A.E.).



  • Science


  • Mathematical Sciences

Published in

Physical Review E


SPRENGER, P., HOEFER, M.A. and EL, G.A., 2018. Hydrodynamic optical soliton tunneling. Physical Review E, 97 (3), 032218.


American Physical Society


  • AM (Accepted Manuscript)

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper was published in the journal Physical Review E and the definitive published version is available at https://doi.org/10.1103/PhysRevE.97.032218.




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