Conical diffraction, pseudospin, and nonlinear wave dynamics in photonic Lieb lattices

Leykam, Daniel, Bahat-Treidel, Omri and Desyatnikov, Anton S. (2013). Conical diffraction, pseudospin, and nonlinear wave dynamics in photonic Lieb lattices. In: 2013 Conference on Lasers and Electro-Optics Europe and International Quantum Electronics Conference (CLEO EUROPE/IQEC). Proceedings. CLEO/EUROPE - IQEC 2013: Conference on Lasers and Electro-Optics - International Quantum Electronics Conference, Munich, Germany, (IG_5_6-IG_5_6). 13-16 May, 2013. doi:10.1109/CLEOE-IQEC.2013.6801833


Author Leykam, Daniel
Bahat-Treidel, Omri
Desyatnikov, Anton S.
Title of paper Conical diffraction, pseudospin, and nonlinear wave dynamics in photonic Lieb lattices
Conference name CLEO/EUROPE - IQEC 2013: Conference on Lasers and Electro-Optics - International Quantum Electronics Conference
Conference location Munich, Germany
Conference dates 13-16 May, 2013
Proceedings title 2013 Conference on Lasers and Electro-Optics Europe and International Quantum Electronics Conference (CLEO EUROPE/IQEC). Proceedings
Journal name Optics InfoBase Conference Papers
Place of Publication Piscataway, NJ, USA
Publisher IEEE
Publication Year 2013
Sub-type Other
DOI 10.1109/CLEOE-IQEC.2013.6801833
Open Access Status
ISBN 9781479905935
9781479905942
ISSN 2162-2701
Start page IG_5_6
End page IG_5_6
Total pages 1
Language eng
Formatted Abstract/Summary
This paper explores wave dynamics near a singularity which occurs in the Lieb lattice built with three square sublattices. The Lieb lattice band singularity consists of three intersecting bands - two with a conical shape, and a third flat band in between. This intersection is associated with pseudo-spin 1, rather than the pseudospin 1/2 of the honeycomb lattice. In analogy with earlier results in the honeycomb lattice, it is found that the angular momentum of waves propagating near the singularity is naturally divided into macroscopic (on the scale of many lattice periods) orbital angular momentum, and a microscopic (on the scale of a lattice period), pseudospin component. Their sum is a conserved quantity for waves near the singularity. Consequently, the pseudospin plays an important role in wave dynamics, which is demonstrated by studying the diffraction of different pseudospin eigenstates. The diffraction of pseudo-spin 0 waves closely resembles the conical diffraction that occurs in honeycomb lattices. In contrast, waves with pseudospin ±1 also excite the flat band, resulting in a nondiffracting central spot in addition to conically diffracting rings. Finally, the effect of nonlinearity on wave dynamics near the singularity is looked into by considering a photonic lattice with Kerr-type nonlinearity. Nonlinear effective field equation for the pseudo-spin 1 waves is derived and its dynamics is compared with numerical solutions to the full nonlinear SchroŐądinger equation, finding excellent agreement. The nonlinearity transforms the diffracting rings of conical diffraction into squares, whose orientation depends on the sign of the nonlinearity. This is explained by the nonlinearity-induced mixing of waves between the three intersecting bands.
Subjects 3105 Instrumentation
3107 Atomic and Molecular Physics, and Optics
Q-Index Code EX
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Conference Paper
Collection: School of Mathematics and Physics
 
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Created: Tue, 05 Aug 2014, 14:46:49 EST by Jon Swabey on behalf of School of Mathematics & Physics