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Two-dimensional solitons in PT linear lattice potentials.

Jianhua Zeng1, Yueheng Lan

  • 1State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China. zengjianhua1981@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary

We studied solitons in parity-time (PT) lattices, finding that 2D gap solitons can exist but are unstable. This research explores soliton stability in complex PT potentials.

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Area of Science:

  • Nonlinear optics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Solitons are self-reinforcing wave packets that maintain their shape.
  • Parity-time (PT) symmetric potentials offer unique properties for wave propagation.
  • Lattice potentials create periodic structures influencing wave behavior.

Purpose of the Study:

  • To investigate the existence and stability of two-dimensional (2D) ordinary and gap solitons.
  • To analyze these solitons within both 2D and quasi-one-dimensional parity-time (PT) linear lattice potentials.
  • To determine the stability diagrams for the investigated PT potentials.

Main Methods:

  • Numerical simulations to analyze soliton dynamics.
  • Stability analysis of soliton solutions.
  • Exploration of different PT lattice configurations.

Main Results:

  • Existence of 2D gap solitons in PT lattices was identified.
  • Stability diagrams for both 2D and quasi-1D PT potentials were computed.
  • 2D gap solitons with self-attractive nonlinearity were found to be unstable due to collapse.

Conclusions:

  • Parity-time lattices can support 2D gap solitons.
  • Collapse instability limits the practical existence of these self-attractive gap solitons in PT lattices.
  • The study provides insights into soliton behavior in complex optical potentials.