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Hydrodynamic optical soliton tunneling.

P Sprenger1, M A Hoefer1, G A El2

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review. E
|May 20, 2018
PubMed
Summary
This summary is machine-generated.

Dark solitons can tunnel through evolving potential barriers in optical fibers. This phenomenon, described by nonlinear Schrödinger (NLS) equations, offers new methods for controlling dark solitons.

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Area of Science:

  • Nonlinear Optics
  • Soliton Dynamics
  • Dispersive Hydrodynamics

Background:

  • Solitons are stable, self-reinforcing solitary waves that maintain their shape while propagating at a constant velocity.
  • The nonlinear Schrödinger (NLS) equation describes various phenomena in optics, including soliton propagation.
  • Understanding soliton interactions with potential barriers is crucial for optical signal processing and communication.

Purpose of the Study:

  • To introduce and analyze the concept of hydrodynamic optical soliton tunneling.
  • To investigate the interaction of dark solitons with evolving potential barriers within the framework of the NLS equation.
  • To explore potential applications in controlling dark solitons in optical fibers.

Main Methods:

  • Utilized a dispersive hydrodynamic interpretation of the one-dimensional defocusing nonlinear Schrödinger (NLS) equation.
  • Applied nonlinear wave (Whitham) modulation theory under scale separation assumptions.
  • Employed self-similar, simple wave solutions from an asymptotic reduction of Whitham-NLS equations to describe soliton-barrier interactions.

Main Results:

  • Demonstrated soliton tunneling and trapping through smooth rarefaction waves and oscillatory dispersive shock waves.
  • Identified Riemann invariants that govern soliton interaction with mean flow, leading to tunneling or trapping.
  • Quantified the tunneled soliton's phase shift and observed phenomena like propagation direction reversal and soliton cavitation.

Conclusions:

  • Hydrodynamic optical soliton tunneling is a viable phenomenon governed by the NLS equation and Whitham modulation theory.
  • The interaction dynamics provide insights into soliton behavior in complex potential landscapes.
  • Observed effects suggest novel methods for manipulating and controlling dark solitons in optical fiber systems.