16:45 〜 17:00
▲ [16p-A501-12] Zak phase of Three-Dimensional Photonic Crystals
キーワード：topological photonic crystals, zak phase, 3D photonic crystals
The topological properties of photonic crystals (PhCs) have been experimentally realized in many photonic systems. To explain for these robust properties, topological invariants such as Chern number, Berry curvature are successfully theoretically determined for two-dimensional PhCs. Besides, Zak phase is also a good quantum number to explain for the existence of topological states in these systems. Zak phase is defined as one-dimensional integral of Berry connection over the first Brillouin zone. While in one-dimensional systems, Zak phase is determined for each individual band, in two-dimensional systems, it is determined for each arbitrary direction.
To generalize this notation to three-dimensional systems, in this work, we will numerically calculate Zak phase for a three-dimensional photonic system. Fig. 1(a) is photonic band structure of simple cubic PhC. The two lowest bands have orthogonal polarization, where electric and magnetic field are well separated into in plane and out of plane modes. The dispersion of interface structure between two kinds of unit cell in the top panel of (c) and (d) is shown in Fig. 1(b). Two red lines indicate the states where electromagnetic wave are localized at the interface. Because of the similarities in polarization, the first (second) interface state is derived from the first (second) bulk states. These states are explained by the difference in Zak phase between two kinds of unit cell as shown in the middle and bottom panels of Figs. 1(c) and (d). Our numerical results are consistent with the parity of eigenstates at high symmetric points. Field profile of topological interface state at G point is shown in Fig. 1(e). Our description of three-dimensional Zak phase calculation is a priori not only restricted for photonic systems, but it is also applicable for other three-dimensional systems.
To generalize this notation to three-dimensional systems, in this work, we will numerically calculate Zak phase for a three-dimensional photonic system. Fig. 1(a) is photonic band structure of simple cubic PhC. The two lowest bands have orthogonal polarization, where electric and magnetic field are well separated into in plane and out of plane modes. The dispersion of interface structure between two kinds of unit cell in the top panel of (c) and (d) is shown in Fig. 1(b). Two red lines indicate the states where electromagnetic wave are localized at the interface. Because of the similarities in polarization, the first (second) interface state is derived from the first (second) bulk states. These states are explained by the difference in Zak phase between two kinds of unit cell as shown in the middle and bottom panels of Figs. 1(c) and (d). Our numerical results are consistent with the parity of eigenstates at high symmetric points. Field profile of topological interface state at G point is shown in Fig. 1(e). Our description of three-dimensional Zak phase calculation is a priori not only restricted for photonic systems, but it is also applicable for other three-dimensional systems.