Effective medium theory for a photonic pseudospin- 12 system

Abstract

Photonic pseudospin-1/2 systems, which exhibit Dirac cone dispersion at Brillouin zone corners in analogy to graphene, have been extensively studied in recent years.However, it is known that a linear band crossing of two bands cannot emerge at the center of Brillouin zone in a two-dimensional photonic system respecting time reversal symmetry. Using a square lattice of elliptical magneto-optical cylinders, we constructed an unpaired Dirac point at the Brillouin zone center as the intersection of the second and third bands corresponding to the monopole and dipole excitations.Effective medium theory can be applied to the two linearly crossed bands with the effective constitutive parameters numerically calculated using the boundary effective medium approach. It is shown that only the effective permittivity approaches zero while the determinant of the nonzero effective permeability vanishes at the Dirac point frequency, showing a different behavior from the double-zero index metamaterials obtained from the pseudospin-1 triply degenerate points for time reversal symmetric systems. Exotic phenomena, such as the Klein tunneling and Zitterbewegung, in the pseudospin-1/2 system can be well understood from the effective medium description. When the Dirac point is lifted, the edge state dispersion near the Γ point can be accurately predicted by the effective constitutive parameters.We also further realized magneto-optical complex conjugate metamaterials for a wide frequency range by introducing a particular type of non-Hermittian perturbations which make the two linear bands coalescence to form exceptional points at the real frequency.

Hermitian and Non-Hermitian Dirac-Like Cones in Photonic and Phononic Structures

“…It is reasonable, as the PhC are composed of low-loss dielectric materials. It is interesting to point out the band dispersion of the PhC could be drastically deformed if there exists loss/gain [24,80,136,[151][152][153][154][155]175]. In 2015, Zhen et al experimentally demonstrated that in a photonic crystal slab the radiative loss-induced non-Hermitian perturbation can deform the Dirac-like cone into a 2D flat band enclosed by a ring of EPs [136].…”

“…The PhC with a semi-Dirac cone behaves as an intriguing class of anisotropic ZIM with ε eff μ eff 0 along only one direction. The Dirac cone system has been extended from the original 2D to on-chip platform or the bound state in continuum (BIC) [22,[135][136][137][138][139][140][141][142][143][144][145][146][147] and three-dimension (3D) [148][149][150], and from the original Hermitian (lossless) to non-Hermitian (lossy or gain) ones [136,[151][152][153][154][155]. It was discovered that the Dirac degeneracy can be straightforwardly linked to exceptional points (EPs) through the introduction of non-Hermiticity, i.e., material loss, gain, or open boundaries.…”

Photonic Dirac nodal-line semimetals realized by a hypercrystal

“…Interestingly, nodal lines in topological semimetals can even form some complicated configurations, including helices [12], rings [13][14][15][16][17][18][19], links [20,21], chains [22][23][24], gyroscopes [18,[25][26][27], nexus [28][29][30][31][32], knots [33][34][35][36], nets [37][38][39][40], etc. So far, more and more topological semimetals have been proposed theoretically and verified experimentally in the electronic [7][8], optical [11,19,24,32], and acoustic systems [23,[39][40][41]. As a result, a finer classification of topological phases is supported by band structure of semimetals.…”

“…In the momentum k-space, topological semimetals possess robust nodal areas between conduction and valence bands. In particular, the co-dimension of nodal points [7][8][9][10][11], nodal lines and nodal surfaces [42][43][44] is 3, 2 and 1 respectively, which corresponding to the degrees of freedom of parameters that tuned to encounter a band degeneracy [45]. Interestingly, nodal lines in topological semimetals can even form some complicated configurations, including helices [12], rings [13][14][15][16][17][18][19], links [20,21], chains [22][23][24], gyroscopes [18,[25][26][27], nexus [28][29][30][31][32], knots [33][34][35][36], nets [37][38][39][40], etc.…”

“…As a result, a finer classification of topological phases is supported by band structure of semimetals. A rapidly growing frontier in this field is to emulate relativistic quasi-particles like two-fold Weyl fermions [8,41] and four-fold Dirac fermions [10,19], which have linear dispersion with novel transport properties like delocalization [46], Zitterbewegung [11,[47][48], and Klein tunneling [11,[49][50]. In addition, topological semimetal phases can be further divided into type-I [51][52], type-II [53][54], and type-III [55][56][57] based on the tilt angles of the Dirac/Weyl cones.…”