Interband resonant transitions in two-dimensional hexagonal lattices: Rabi oscillations, Zener tunnelling, and tunnelling of phase dislocations
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Shchesnovich, Valery; Desyatnikov, Anton S; Kivshar, Yuri
Description
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...[Show more]
dc.contributor.author | Shchesnovich, Valery | |
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dc.contributor.author | Desyatnikov, Anton S | |
dc.contributor.author | Kivshar, Yuri | |
dc.date.accessioned | 2009-06-02T05:34:58Z | |
dc.date.accessioned | 2010-12-20T06:05:38Z | |
dc.date.available | 2009-06-02T05:34:58Z | |
dc.date.available | 2010-12-20T06:05:38Z | |
dc.identifier.citation | Optics Express 16.18 (2008): 14076-14094 | |
dc.identifier.issn | 1094-4087 | |
dc.identifier.uri | http://hdl.handle.net/10440/376 | |
dc.identifier.uri | http://digitalcollections.anu.edu.au/handle/10440/376 | |
dc.description.abstract | 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 opticallyinduced 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. | |
dc.format | 19 pages | |
dc.publisher | Optical Society of America | |
dc.rights | "OSA will grant the authors permission to deposit the publisher’s pdf from their Optics Express articles into the repository with the proper citation (reference number or journal /volume/page/year citation)." - from email received from Authorized Agent, The Optical Society, 27/05/10 | |
dc.source | Optics Express | |
dc.source.uri | http://www.opticsinfobase.org/DirectPDFAccess/9F6BB1A1-BDB9-137E-CBF1B3E773BEFB8D_171316.pdf?da=1&id=171316&seq=0&CFID=39997365&CFTOKEN=32868506 | |
dc.subject | Diffraction and gratings | |
dc.subject | Photonic crystals | |
dc.subject | Optical vortices | |
dc.title | Interband resonant transitions in two-dimensional hexagonal lattices: Rabi oscillations, Zener tunnelling, and tunnelling of phase dislocations | |
dc.type | Journal article | |
local.identifier.citationvolume | 16 | |
dcterms.dateAccepted | 2008-08-20 | |
dc.date.issued | 2008-08-26 | |
local.identifier.absfor | 020501 | |
local.identifier.ariespublication | u9201385xPUB105 | |
local.type.status | Published Version | |
local.contributor.affiliation | Shchesnovich, Valery, Universidade Federal de Alagoas, Brazil | |
local.contributor.affiliation | Desyatnikov, Anton S, Research School of Physical Sciences and Engineering, Non-Linear Physics Centre | |
local.contributor.affiliation | Kivshar, Yuri S, Research School of Physical Sciences and Engineering, Non-Linear Physics Centre | |
local.bibliographicCitation.issue | 18 | |
local.bibliographicCitation.startpage | 14076 | |
local.bibliographicCitation.lastpage | 14094 | |
local.identifier.doi | 10.1364/OE.16.014076 | |
dc.date.updated | 2015-12-08T09:14:19Z | |
local.identifier.scopusID | 2-s2.0-51149119065 | |
local.identifier.thomsonID | 000259270600062 | |
Collections | ANU Research Publications |
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