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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 14076–14094

Interband resonant transitions in two-dimensional hexagonal lattices: Rabi oscillations, Zener tunnelling, and tunnelling of phase dislocations

Valery S. Shchesnovich, Anton S. Desyatnikov, and Yuri S. Kivshar  »View Author Affiliations

Optics Express, Vol. 16, Issue 18, pp. 14076-14094 (2008)

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We study, analytically and numerically, the dynamics of interband transitions in two-dimensional hexagonal periodic photonic lattices. We develop an analytical approach employing the Bragg resonances of different types and derive the effective multi-level models of the Landau-Zener-Majorana type. For two-dimensional periodic potentials without a tilt, we demonstrate the possibility of the Rabi oscillations between the resonant Fourier amplitudes. In a biased lattice, i.e., for a two-dimensional periodic potential with an additional linear tilt, we identify three basic types of the interband transitions or Zener tunnelling. First, this is a quasi-one-dimensional tunnelling that involves only two Bloch bands and occurs when the Bloch index crosses the Bragg planes away from one of the high-symmetry points. In contrast, at the high-symmetry points (i.e., at the M and Γ points), the Zener tunnelling is essentially two-dimensional, and it involves either three or six Bloch bands being described by the corresponding multi-level Landau-Zener-Majorana systems. We verify our analytical results by numerical simulations and observe an excellent agreement. Finally, we show that phase dislocations, or optical vortices, can tunnel between the spectral bands preserving their topological charge. Our theory describes the propagation of light beams in fabricated or optically-induced two-dimensional photonic lattices, but it can also be applied to the physics of cold atoms and Bose-Einstein condensates tunnelling in tilted two-dimensional optical potentials and other types of resonant wave propagation in periodic media.

© 2008 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Diffraction and Gratings

Original Manuscript: May 19, 2008
Revised Manuscript: August 19, 2008
Manuscript Accepted: August 20, 2008
Published: August 26, 2008

Valery S. Shchesnovich, Anton S. Desyatnikov, and Yuri S. Kivshar, "Interband resonant transitions in two-dimensional hexagonal lattices: Rabi oscillations, Zener tunnelling, and tunnelling of phase dislocations," Opt. Express 16, 14076-14094 (2008)

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