Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Longhi, Stefano

doi:10.2478/s11534-010-0054-4

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…29 As compared to the photonic realization of the DKP with a real potential recently proposed in Ref. 7 and based on a superstructure FBG with a periodic sequence of π phase slips in the grating profile, in the PT symmetric DKP model considered in the present work the complex potential V (x) is realized by means of a periodic sequence of alternating regions of optical gain and absorption superimposed to the uniform modulation of the refractive index [see Fig. 1(b)].…”

Section: B Photonic Realizationmentioning

confidence: 99%

“…Photonic analogs of the DKP model, based on light scattering in superstructure optical Bragg gratings, 6 have been also recently proposed by one of the present authors in Ref. 7. In such previous works, the main aim was to provide experimentally accessible classical simulators of the physics of relativistic ordinary crystals, offering the possibility to observe, e.g., relativistic band shrinkage or relativistic Tamm surface states.…”

Section: Introductionmentioning

confidence: 96%

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SpontaneousPTsymmetry breaking in Dirac-Kronig-Penney crystals

2011

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We introduce a non-Hermitian PT invariant extension of the Dirac-Kronig-Penney model, describing the motion of a Dirac quasiparticle in a locally periodic sequence of imaginary δ-Dirac barriers and wells, and propose its optical realization using superstructure fiber Bragg gratings with alternating regions of optical gain and absorption. For the infinite crystal, we determine the band structure and show that the PT phase is always broken. For a finite crystal, we derive analytical expressions for reflection and transmission probabilities, and show that the PT phase is unbroken below a finite threshold of the δ-barrier area. In the proposed optical realization, the onset of PT symmetry breaking in the finite crystal corresponds to the lasing condition for the grating superstructures.

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Section: B Photonic Realizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

SpontaneousPTsymmetry breaking in Dirac-Kronig-Penney crystals

2011

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Classical simulation of relativistic quantum mechanics in periodic optical structures

Longhi

2011

Appl. Phys. B

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Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.

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Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Cited by 2 publications

References 35 publications

SpontaneousPTsymmetry breaking in Dirac-Kronig-Penney crystals

SpontaneousPTsymmetry breaking in Dirac-Kronig-Penney crystals

Classical simulation of relativistic quantum mechanics in periodic optical structures

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