Extremal transmission at the Dirac point of a photonic band structure

Abstract

We calculate the effect of a Dirac point ͑a conical singularity in the band structure͒ on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum near the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission T 0 = ⌫ 0 W / L is inversely proportional to the longitudinal dimension L of the crystal ͑for L larger than the lattice constant and smaller than the transverse dimension W͒. The interface transparencies affect the proportionality constant ⌫ 0 , and they determine whether the extremum is a minimum or a maximum, but they do not affect the "pseudodiffusive" 1 / L dependence of T 0 .

Artificial honeycomb lattices for electrons, atoms and photons

“…The authors of Ref. [52] have shown that the transmission through this crystal displays a pseudodiffusive [24] 1/L dependence on the thickness L of the crystal. In addition, they measured the eigenmode intensity distributions in a rectangular microwave billiard that contains a triangular photonic crystal.…”

“…In such crystals, the unusual transmission properties near a Dirac point [23][24][25] were predicted and observed experimentally.…”

“…Current methods of design and synthesis include i) nanopatterning of ultra-high-mobility 2D electron gases (EGs) [13][14][15][16][17][18], ii) molecule-by-molecule assembly on metal surfaces by scanning probe methods [19], iii) trapping ultracold fermionic and bosonic atoms in honeycomb optical lattices [20][21][22], and iv) confining photons in honeycomb photonic crystals [23][24][25][26]. Figure 1 summarizes these four different approaches and the relevant tunable parameters.…”

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

“…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.…”