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Wave dynamics in optically modulated waveguide arrays.

Mark J Ablowitz1, Keith Julien, Ziad H Musslimani

  • 1Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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We propose a new model for light wave propagation in optical waveguide arrays. This model predicts stable, localized light modes, similar to those seen in Bose-Einstein condensates.

Area of Science:

  • Physics
  • Optics
  • Nonlinear Dynamics

Background:

  • Wave propagation in optical waveguide arrays is crucial for photonic devices.
  • Understanding nonlinear effects is key to controlling light behavior.

Purpose of the Study:

  • To develop a robust model for wave propagation in optically modulated waveguide arrays.
  • To investigate the existence and stability of localized nonlinear modes.

Main Methods:

  • Derivation of a 2D semidiscrete nonlinear Schrödinger equation from Maxwell equations.
  • Numerical construction of unstaggered localized modes for defocusing nonlinearity.
  • Analysis of the well-posedness and stability of the derived nonlinear modes.

Main Results:

Related Experiment Videos

  • A Gross-Pitaevskii type model was derived, incorporating diffraction and an optical trap.
  • Dynamically stable, localized nonlinear modes were numerically identified.
  • The model demonstrates well-posedness for induced potentials.

Conclusions:

  • The proposed model accurately describes wave propagation in modulated waveguide arrays.
  • The findings support the potential for stable light localization in such systems.
  • The model's similarity to Bose-Einstein condensate equations suggests broader applicability.