Figure 1

(Color online) A zigzag ribbon with 10 zigzag chains. The arrows indicate the translational (periodic) directions of the ribbon and the rectangle indicates the unit cell of the ribbon. The right panel shows the first Brillouin zone. The band structure of the ribbon will be projected along the $\Gamma -\text{K}$ direction.Reuse & Permissions

Figure 2

(Color online) (a) Band structure for a 2D honeycomb lattice of dielectric rods with ${ϵ}_m=15$ and $r=0.2a$. (b) The corresponding projected band structure (of a supercell containing 10 primitive unit cells) onto a zigzag axis $\left(\Gamma -\text{K}\right)$. (c) The band structure of the ribbon shown in Fig. 1 along the $\Gamma -\text{K}$ direction. The light cone is shaded and the edge states are shown in red (dark gray).Reuse & Permissions

Figure 3

(Color online) (a) Band structure for a 2D triangular lattice of dielectric rods with ${ϵ}_m=40$ and $r=0.35a$. (b) The corresponding projected band structure (of a supercell containing 20 primitive unit cells) onto the $\Gamma -\text{K}$ direction. (c) The band structure along the $\Gamma -\text{K}$ direction for a finite slab of 20 layers. The light cone is shaded and the edge states are shown in red (dark gray).Reuse & Permissions

Figure 4

(Color online) (a) Band structure for a honeycomb lattice of ferrite rods with ${ϵ}_m=15$, $H_0=500\text{Oe}$, $4\pi M_s=1750\text{G}$, $r=0.2a$, and $a=10\text{mm}$. (b) The corresponding projected band structure of a supercell containing 10 unit cells onto a zigzag axis $\left(\Gamma -\text{K}\right)$. (c) Band structure of the ribbon along the $\Gamma -\text{K}$ direction. The light cone is shaded and the edge states are shown in red (dark gray) and green (light gray). (d) Squared amplitude of the $E_z$ field for one-way edge mode at one edge of the zigzag ribbon with 10 zigzag chains excited by a line source at $fa/c=0.254$ with green (light gray) and red (dark gray) representing zero and positive values. The line source is at $\left(-10,-4\right)$ (marked with “$+$” in the figure). The excited edge mode propagates to the right.Reuse & Permissions

Figure 5

(Color online) (a) $E_z$ field distribution for a hexagonal cavity consisting of ferrite rods excited by a line source at $fa/c=0.254673$ (near the resonant frequency of the cavity) located at $\left(0.5,-7.5\right)$ (marked with “$+$” in the figure). There are nine rods at the outermost edge of the hexagon. The rods are the same as in Fig. 4. (b) Same as in (a) but with an obstacle inserted on the upper edge (black rectangle; a metal plate with thickness $0.15a$). (c), (d) Distribution of Poynting vectors near the upper edge of the hexagon in (a) and (b), respectively. The power flow is cycling anticlockwise on the edges of the hexagon.Reuse & Permissions