Experimental Observation of Strong Edge Effects on the Pseudodiffusive Transport of Light in Photonic Graphene

Abstract

Photonic graphene is a two-dimensional photonic crystal structure that is analogous to graphene. We use 5 mm diameter Al 2 O 3 rods placed on a triangular lattice with a lattice constant a ¼ 8 mm to create an isolated conical singularity in the photonic band structure at a microwave frequency of 17.6 GHz. At this frequency, the measured transmission of microwaves through a perfectly ordered structure enters a pseudodiffusive regime where the transmission scales inversely with the thickness L of the crystal (L=a * 5). The transmission depends critically on the configuration of the edges: distinct oscillations with an amplitude comparable to the transmission are observed for structures terminated with zigzag edges, while these oscillations are absent for samples with a straight edge configuration. DOI: 10.1103/PhysRevLett.104.043903 PACS numbers: 42.25.Gy, 42.25.Bs, 42.70.Qs The experimental realization of graphene [1], a single layer of carbon atoms arranged in a two-dimensional hexagonal structure, has attracted a lot of attention. The interest in this gapless semiconductor is due to the conical singularities in the electronic band structure [2] that create a linear dispersion for electrons, leading to interesting physical phenomena such as an anomalous quantum Hall effect and the absence of Anderson localization [3,4]. Since the dispersion around these points is linear, the motion of electrons resembles that of massless particles and can be described by the relativistic Dirac equation. These singularities have been aptly named ''Dirac points'' and are entirely due to the geometry of the underlying triangular lattice.As a consequence, similar conical singularities can be identified in the band structure of electromagnetic waves in two-dimensional photonic crystals with a triangular lattice [5][6][7], acoustic waves in a sonic crystal [8], and electrons in a two-dimensional electron gas [9]. Of these analogous systems, only the propagation of acoustic waves was studied experimentally, and an acoustic analogue to the Zitterbewegung of relativistic electrons was identified [8]. The analogy between graphene and these structures strengthens our understanding of the physics common to these two-dimensional structures. In particular, the analogy with optics has already inspired researchers to predict known optical effects, such as negative refraction [10] and a Goos-Hänchen shift for electrons in graphene [11].Despite the success of graphene, the observation of effects predicted by theory often require samples with perfect edges of a well-defined configuration that can only be obtained by atomic scale engineering. In this Letter, we experimentally investigate a photonic crystal structure for microwave frequencies that is analogous to graphene and realize samples with ideal edges on a much more accessible millimeter length scale. The transmission at the Dirac point of this perfectly ordered structure enters a pseudodiffusive transport regime and becomes inversely proportional to the thickness of the sample, as predic...

Conical intersections for light and matter waves

“…When a conical dispersion is restricted to a finite system, the intersection is replaced by a (small) band gap, due to the vanishing density of states. In contrast to regular Bragg gaps, the wave transmission T ∼ 1/L scales pseudo-diffusively with the lattice size L, for both "fermionic" and "bosonic" intersections [18,[77][78][79]. On the other hand, the reflected beam is sensitive to the type of intersection, displaying a suppression of coherent backscattering (weak antilocalization) due to the π Berry phase of "fermionic" intersections [80].…”

Fiber guiding at the Dirac frequency beyond photonic bandgaps

“…At this special point, the Maxwell equations can be replaced by the two-dimensional massless Dirac equation for relativistic particles: Thus, analogies with the electronic energy band structure of graphene can be sustained 18 . Pseudo-diffusive transmission in such lattices has been observed 15,16 . A localized mode has also recently been identified at the Dirac frequency 17 .…”

“…Photonic crystals have been studied extensively for their bandgap 1 and special in-band dispersion effects such as negative refraction 13 . However, another really interesting feature of photonic crystals is the Dirac points that appear at corners of the Brillouin zone [14][15][16][17] . A Dirac point, as illustrated in Figure 1, is a conical singularity surrounded by a region of linear dispersion in the band structure of triangular, hexagonal, or kagome lattices.…”

Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

“…Thus, Dirac points appear in the band structure of 2D photonic [6][7][8][9][10] and sonic [11][12][13] crystals, showing also extraordinary propagation properties, like Zitterbewegung, 14 a near-zero refraction index, 15 edge states, 16 extraordinary transmission, 11,17,18 or one-way propagation. [19][20][21][22] An elastic analog of graphene has not been fully analyzed, although the effort to create structures to control the propagation of elastic waves in 2D systems has been remarkable.…”