Transmission properties near Dirac-like point in two-dimensional dielectric photonic crystals

Abstract

We study the wave transport properties near the Dirac-like point at the Brillouin zone center in two-dimensional dielectric photonic crystals with finite thickness. Both simulations and microwave experiments confirm that the transmittance is nearly inversely proportional to the length (L) of the samples in the propagation direction near the Dirac-like point. This transmittance law comes from the conically shaped dispersion. Since the conical singularity at the Brillouin zone center corresponds to zero refractive index, the field at the Dirac-like point contains a basic component of nearly uniform field. In contrast, the field at the Dirac point in the corner of the hexagonal Brillouin zone contains a basic component of inhomogeneous standing-wave–like field.

Relativistic quantum chaos

“…[216], references therein). Due to the wave nature of the electron motion in the honeycomb graphene lattice, the relativistic pseudo-particles can also be created using microwave photonic crystals [217][218][219][220][221][222][223][224][225][226][227][228][229][230] or mechanical vibrations and phononic crystals [231][232][233][234][235][236], where the propagation of the electromagnetic or acoustic wave follows the same honeycomb lattice structure, as shown in the left panel of Fig. 2.…”

“…The effective boundary displacement can be determined as δ 1 = ∆l − ∆ l − and δ 2 = ∆ l + − ∆l. (220,222,223)]. The parameters are u 0 = 2.045/a, ∆l = 2a, m 0 = 0.2/a, and the resulting boundary shift is δ = 0.032a.…”

Precise identification of Dirac-like point through a finite photonic crystal square matrix

“…The dispersion properties obeying the 1/L scaling law near the DP or DLP in the normal propagation direction have been verified theoretically and experimentally212627 through the dielectric PhC ribbons with the finite thicknesses, which come from the conically shaped dispersion and the transmission as a function of frequency with an extremum near the conical singularity826. Although the transmission properties can be used to demonstrate the existence of Dirac cone, it is difficult to distinguish the precise crossing point from the wide extremum range just relying on the transmittance spectrum.…”

“…By proper design and fabrication, photonic crystals (PhCs) can also exhibit Dirac cones at the corners of the Brillouin zone of the triangular and honeycomb lattices891011121314, leading to many unusual transmission properties, such as the classical analogs of Zitterbewegung15, pseudodiffusion816 and extinction of coherent backscattering17. Since the accidental degeneracy of two dipolar modes and a single monopole mode generates at the Dirac-like point (DLP), the linear dispersions of Dirac cone can also occur at the Brillouin zone center of PhCs181920212223. The PhC can mimic the zero-index medium (ZIM) with the characteristics of uniform field distribution, which can be understood from the effective medium perspective18.…”

“…The PhC can mimic the zero-index medium (ZIM) with the characteristics of uniform field distribution, which can be understood from the effective medium perspective18. Compared with the DP induced by double degeneracy near the corner points of the triangular/honeycomb lattice, linear dispersions near the center point induced by the triple degeneracy display many unique scattering properties, such as conical diffraction212223, wave shaping and cloaking181920. Different from the conventional metamaterials2425 comprising metallic components whose high inherent losses may actually reduce the functionality of any proposed device, PhCs can be made entirely of dielectric or semiconductor materials which have the evident benefits in terms of low loss.…”