Dirac Dispersion in Two-Dimensional Photonic Crystals

Chan, Che Ting; Hang, Zhi Hong; Huang, Xueqin

doi:10.1155/2012/313984

Cited by 72 publications

(69 citation statements)

References 83 publications

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“…This "protection" can be understood in terms of the quantized π Berry phase accumulated when encircling a Dirac cone [31]. On the other hand, this property no longer holds for higher values of s: at a bosonic s = 1 intersection with Berry phase 0 (mod 2π) [61], symmetry only protects the degeneracy of two modes (eg. orthogonal dipolar modes in a metamaterial), while the third (typically a monopole mode) must be tuned to achieve an accidental degeneracy and conical intersection.…”

Section: Theorymentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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Section: Theorymentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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“…Engineering the photonic band gap to create a large and complete band gap was the goal of much early research in this area [1,2,4] . On the other hand, engineering the photonic bang gap to achieve a type of gapless band structure, namely the Dirac and Dirac-like cone dispersion relation, has been the focus of much recent work [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. This dispersion relation is analogues to the Dirac cones in electron systems, where two linear bands touch so that there is no band gap.…”

Section: Introductionmentioning

confidence: 99%

“…Various theoretical approaches, such as multiple scattering [18], tight binding [19], and perturbation [20][21][22], have also been developed to analyze the properties of Dirac cones in PhCs.…”

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confidence: 99%

A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

Wu¹

2014

Opt. Express

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A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the isofrequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction. Wave control, including beam splitting and directional beam shaping, is also demonstrated.

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“…Recently, a class of periodic dielectric photonic crystals [1][2][3] with conical dispersions at k ¼ 0 [4][5][6] have been demonstrated to behave as a zero-refractive-index material at Dirac frequency. Such dielectric photonic crystals [1][2][3][4][5][6][7][8][9][10] have the advantage of being nearly lossless as no metal resonators are needed, and have a finite group velocity while the phase velocity is infinite [2]. These designs have been realized and characterized from microwave [1] to optical frequencies [10].…”

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confidence: 99%

Conical Dispersion and Effective Zero Refractive Index in Photonic Quasicrystals

et al. 2015

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It is recognized that for a certain class of periodic photonic crystals, conical dispersion can be related to a zero-refractive index. It is not obvious whether such a notion can be extended to a noncrystalline system. We show that certain photonic quasicrystalline approximants have conical dispersions at the zone center with a triply degenerate state at the Dirac frequency, which is the necessary condition to qualify as a zerorefractive-index medium. The states in the conical dispersions are extended and have a nearly constant phase. Experimental characterizations of finite-sized samples show evidence that the photonic quasicrystals do behave as a near zero-refractive-index material around the Dirac frequency. [10]. However, the connection between conical dispersions at k ¼ 0 and zero-refractive index were built upon periodicity. The conical dispersion was obtained by tuning the system parameters of "one-atom-per-unit-cell" photonic crystals with a well-defined photonic band structure. Whether a conical dispersion can exist in a nonperiodic system is still an interesting and open question. Furthermore, the claim that a system behaves like a zero-index medium implicitly assumes that an effective medium description could be applied. While not explicitly stated, many coherent-potential-approximation-type effective medium theories, employed to map a Dirac cone to zero index [11], assume that each scatter resides in the same environment. Although this assumption of periodicity is not needed in the ω → 0, k → 0 limit, it is not immediately obvious that such effective medium description can be applied to nonperiodic systems if we consider effective parameters at k → 0 but at a finite frequency such as a Dirac point. Can a nonperiodic system behave operationally as if it has zero-refractive index?Photonic quasicrystal (PQC) is constructed by building blocks positioned on well-designed patterns but lacks translational symmetry [12][13][14][15][16][17][18][19][20][21][22][23]. Nonetheless, PQC can still have relatively sharp diffraction patterns due to longrange order. Such patterns confirm the existence of wave scattering and interference, providing similar functionalities as periodic counterparts, such as photonic band gaps [12][13][14][15], negative refraction [16], lasing [17][18][19], and nonlinear light propagations [20][21][22]. We will show theoretically and experimentally that some two-dimensional photonic quasicrystalline approximants can possess conical dispersion at k ¼ 0, and their finite-sized counterparts can behave like a zero-refractive-index medium as evidenced by different experimental measurements.In this Letter, we show the existence of conical dispersions and extended states with zero-refractive-index characteristics in some PQCs, and experimentally characterize these states. The extended states are close to the Dirac frequency, and form two cones intersecting at a "Dirac point." The eigenmodes have almost constant field intensity at each quasicrystalline site, regardless of the size and the bounda...

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Dirac Dispersion in Two-Dimensional Photonic Crystals

Cited by 72 publications

References 83 publications

Conical intersections for light and matter waves

Conical intersections for light and matter waves

A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

Conical Dispersion and Effective Zero Refractive Index in Photonic Quasicrystals

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