Integrated optical Dirac physics via inversion symmetry breaking

Graphene and boron nitride are two-dimensional materials whose atoms are arranged in a honeycomb lattice. Their unique properties arise because their electrons behave like relativistic particles (without and with mass, respectively)—namely, they obey the Dirac equation. Here, we use a photonic analog of boron nitride to observe Dirac physics in a silicon integrated optical platform. This will allow for photonic applications of Dirac dispersions (gapped and ungapped) to be realized in an on-chip, integrated nanophotonic platform.

Figure 1

(a) SEM image of honeycomb lattice photonic crystal slab structure (holes are 114 nm in radius, nearest-neighbor spacing 273 nm, lattice constant $a=473\mathrm{nm}$, slab height 220 nm), with corresponding photonic band structure shown in (b). (c) Same as (a), but with an inversion broken structure: The holes of the two triangular sublattices have different radii ($\mathrm{\Delta }r=27\mathrm{nm}$), with corresponding photonic band structure shown in (d). (e) is an SEM image of the entire device, including grating couplers.

Figure 2

(a) Dispersion diagram (band structure) for the inversion-symmetry-broken photonic crystal slab shown in Fig. 1 (difference in hole radius $\mathrm{\Delta }r=27\mathrm{nm}$, blue solid line), and that without inversion breaking, and thus still a Dirac cone (red dashed line). (b) Experimental results for the transmission through the inversion-broken structure. The band gap is clearly observed as a sharp decrease in transmission. The black dashed line indicates the second band shoulder, where an increase and then sharp decrease in density of states leads to a peak in transmission.

Figure 3

Plot of the band-gap size (blue) and frequency difference between the bottom of the band gap and the second band shoulder (red). Experimental results are shown as circles and numerical calculations are solid curves. Inset are SEM images of the photonic crystal structures at $\mathrm{\Delta }r=0$ (at left) and $\mathrm{\Delta }r=27\mathrm{nm}$ (at right).