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...
We show that Weyl points with topological charges 1 and 2 can be found in very simple chiral woodpile photonic crystals, which can be fabricated using current techniques down to the nano-scale. The sign of the topological charges can be tuned by changing the material parameters of the crystal, keeping the structure and the symmetry unchanged. The underlying physics can be understood using a tight binding model, which shows that the sign of the charge depends on the hopping range.Gapless surface states and their back-scattering immune properties are also demonstrated in these systems. 8 sink for the lower band and vice versa. Fig. 3(e) shows the source/sink distributions for the red band (the lower band), which shows that charge 1 flux sinks locate at the 0 z k plane and topological charges 2 flux sources locate at / z kp planes, generatingBerry flux between these planes. Fig. 3(f) and Fig. 3(g) shows respectively the source/sink distribution for the green band (the upper band) and the blue (middle) band, showing net Berry flux going through z k =constant planes for the green band while no net flux passes through z k =constant planes for the blue bands. As a consequence, the Chern number of the red and green band are -1 and +1 while it is 0 for the blue (middle) band when 0 z k , which in turn implies that the gaps in Fig.3 (b) are topological
Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect without longitudinal spherical aberration, when the size of zero-index lens is large enough. Here, we designed and fabricated a prototype of zero-refractive-index lens by comprising large-area silicon nanopillar array with plane-concave profile. Near-zero refractive index was quantitatively measured near 1.55 m through anomalous focusing effect, predictable by effective medium 2 theory. The zero-index lens was also demonstrated to perform ultralow longitudinal spherical aberration. Such IC compatible device provides a new route to integrate all-silicon zero-index materials into optical communication, sensing, and modulation, and to study fundamental physics on the emergent fields of topological photonics and valley photonics.Dirac cones in fermionic systems have attracted tremendous attention in the fields of topological insulator and graphene [1][2][3] . Following the pace of condensed matter, these conical dispersion bands have been extended to bosonic systems particularly for electromagnetic waves 4-12 . Bosonic Dirac cones at the zone boundary reveal many similar phenomena with fermionic particles. For example, bianisotropic metamaterials can access to modulate the spin flow of light with backscattering immune at the boundary of topological photonic crystals, after opening a nontrivial gap from Dirac cone 13,8,11 . An alternative method is proposed to implement photonic analogue of the integer quantum Hall effect by using periodic coupling resonators on a silicon-on-insulator platform in near-infared (NIR) wavelength scale 7,14,15 .Beyond those predominant behaviors, bosonic Dirac cones also present extra features other than femionic systems. Recently, another type of photonic Dirac cones induced by accidental degeneracy at the zone center has been found in a class of all-dielectric photonic crystals 16,17 , in which the optical response shows very different to the case at the zone boundary. One of the remarkable properties is zero-index behavior such that the effective permittivity and permeability are simultaneously to be zero at Dirac frequency. To date, nanorod-array structure is the exclusive way to realize all-dielectric zero-index photonic crystal in optical frequency regime. How to sufficiently confine the propagation wave in the plane of periodicity is a practical challenge for 3 rod-slab structures. The first implementation at near-infrared (NIR) wavelength has been fabricated by alternating silicon/silica layers ...
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Recently, the existence of multiple Weyl points was theoretically shown for chiral woodpile photonic crystals [1]. These Weyl points carry topological charges and thus lead to the emergence of backscattering-immune gapless surface states, making the photonic crystal a topological photonic insulator. The proposed photonic crystal structure consists of chirally stacked rods made of a perfect electric conductor (PEC), forming a hexagonal lattice. The structure parameters are designed to obtain isolated Weyl points in the THz regime. Polymer structures are fabricated using three-dimensional laser lithography and subsequently coated with silver via polymer sensitization and electroless deposition. For a silver film thickness well above the skin depth of the THz radiation, a material optically comparable to a bulk PEC can be realized. Measurements of the angle resolved transmission spectra using photoconductive antennas as THz sources and detectors will be carried out soon. From these spectra one can obtain the band structure and hence show the existence of the Weyl points.
In this article, we designed, fabricated, and characterized an electromagnetic metacrystal that topologically carries nontrivial nodal surface degeneracies. Compared with nodal surfaces observed in an acoustic system, the topological charge of the nodal surface in our system is compensated by charge-2 Weyl points, and we designed our system considering the rules of symmetry. To demonstrate the existence of the nodal surfaces and their topological properties, we have experimentally observed surface state arcs derived from helicoid sheets of surface states connecting the nodal surface with a charge-2 Weyl point. The surface states support the robust unidirectional transport on the surface, and the nodal surface provides more degrees of freedom to engineer the dispersion of surface states. Our system offers a platform to explore this new class of gapless topological electromagnetic wave systems.
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