Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials

Abstract

A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.

Conical intersections for light and matter waves

“…This approach is especially useful for metamaterials and photonic crystals, as it opens up new lattice geometries hosting conical intersections for beams at normal incidence [18,33,34] and intersections based on degeneracies of transverse electric (TE) and transverse magnetic (TM) modes [35]. Typically the degeneracy is achieved by tuning parameters such as dielectric rod radius or filling factor in photonic crystals [36][37][38], refractive index contrast of nanoparticles [18], lattice period [39], or coupling strength between resonators [31,40].…”

Terahertz Metamaterial Modulators Based on Absorption

“…Metamaterials have produced many exotic effects such as negative refraction [1][2][3][4], zero refractive index [5][6][7][8], sub-wavelength imaging superlens [9], electromagnetic cloaking [10][11][12][13]. The novel properties of metamaterials come from the artificial atoms which can flexibly tailor the electric and magnetic response.…”

Accidental degeneracy of double Dirac cones in a phononic crystal

“…1 as our focus. Different from the triply degenerate case11, there is no flat branch intersection in our model. Four cones are formed by the linear branches and touches at one point at the frequency of ω 0 = 892.77  Hz with tolerance of 10 −6 .These four eigen degenerate states are shown in Figs.…”

“…The defects in this system cannot be detected at the frequencies near ω 0 [shown in Fig. 6(b2)], which can be regarded as a type of cloaking1112. The negative refraction also can be realized in Fig.…”

“…Under certain circumstances, those Dirac cones can be mapped into a zero-refractive-index material, whose parameters (e.g. permittivity and permeability in electromagnetics, effective mass density and reciprocal of bulk modulus in acoustics) are both vanishing1112131415. It provides a new method to achieve zero-index materials with simple photonic and phononic crystals so that many interesting properties such as wave shaping and cloaking are easily demonstrated12131617.…”