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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
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Pyramid diffraction in parity-time-symmetric optical lattices.

Sean Nixon1, Jianke Yang

  • 1Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.

Optics Letters
|June 1, 2013
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Nonlinear wave packets in parity-time-symmetric optical lattices exhibit pyramid diffraction. Blow-up phenomena are possible in both focusing and defocusing nonlinearities near the phase transition point.

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Area of Science:

  • Nonlinear optics
  • Quantum physics
  • Condensed matter theory

Background:

  • Parity-time-symmetric (PT-symmetric) systems offer unique optical properties.
  • Optical lattices are crucial for simulating complex physical phenomena.
  • Understanding wave packet dynamics is key to controlling light propagation.

Purpose of the Study:

  • To analytically investigate nonlinear wave packet dynamics in 2D PT-symmetric optical lattices.
  • To explore the behavior near the phase transition point.
  • To identify potential phenomena like diffraction patterns and blow-up.

Main Methods:

  • Analytical study of nonlinear dynamics.
  • Derivation of a fourth-order equation for wave packet envelopes.
  • Analysis in both linear and nonlinear regimes.

Main Results:

  • A pyramid diffraction pattern was demonstrated for wave packets.
  • This pattern holds true in both linear and nonlinear propagation.
  • Wave packet blow-up was shown to be possible for both focusing and defocusing nonlinearities.

Conclusions:

  • The study provides analytical insights into complex wave packet behavior in PT-symmetric lattices.
  • Pyramid diffraction is a robust feature across different regimes.
  • The possibility of blow-up highlights the rich nonlinear dynamics and potential instabilities.