Guiding Electromagnetic Waves around Sharp Corners: Topologically Protected Photonic Transport in Metawaveguides

The wave nature of radiation prevents its reflections-free propagation around sharp corners. We demonstrate that a simple photonic structure based on a periodic array of metallic cylinders attached to one of the two confining metal plates can emulate spin-orbit interaction through bianisotropy. Such a metawaveguide behaves as a photonic topological insulator with complete topological band gap. An interface between two such structures with opposite signs of the bianisotropy supports topologically protected surface waves, which can be guided without reflections along sharp bends of the interface.

Figure 1

BMW as a photonic topological insulator. (a) Schematic of the BMW. Part of the top metal plate is removed to reveal the “bed-of-nails” structure below. The enlarged regions on the right illustrate the origin of the bianisotropic response. Right inset: an equivalent way to produce bianisotropy by adding an asymmetrically placed metallic volume (washer) around the rod. (b) PBS of spin-degenerate metawaveguide ($g_1=0$) with TE and TM modes forming doubly degenerate Dirac cones at $K(K^{\prime })$ points. (c) Field profiles of the degenerate TE and TM mode at the $K$ point. Colors: energy density. Arrows: electric field for the TM mode and magnetic field for the TE mode. Yellow dashed line: metallic border. (d) PBS with the band gap induced by the bianisotropy of the metawaveguide ($g_1=g_0$). Dashed lines in (b) and (d): TE and TM bands of interest. BMW parameters: $h_0=a_0$, $d_0=0.345a_0$, $g_0=0.15a_0$.

Figure 2

Dirac dispersion of the dipolar TE and dipolar TM modes in the vicinity of the $K$ point. The in-plane magnetic field profiles ($|h_x|$ on the left and $|h_y|$ on the right) are overlaid atop the band structure to show the dominant component of the magnetic field. The positive- and negative-group-velocity bands are labeled with “$+$” and “$-$” signs.

Figure 3

Propagation of TPSWs along the interface between two topologically nontrivial BMWs (a) Side and top views of the topologically nontrivial interface (dashed line) between two BMWs introduced in Fig. 1. (b) 1D PBS of a supercell (single cell along the $x$ direction, 30 cells on each side of the interface) of the hybridized TE and TM modes. Black circles: bulk modes, blue lines: TPSW, arrows: spin state. (c) Color: energy density; arrows: Poynting flux of a TPSW at the frequency $\omega$ indicated by a black arrow in (d). (d) Transmission spectrum $T(\mathrm{\Delta }\omega )$ through the zigzag path, where $\mathrm{\Delta }\omega =\omega -{\omega }_G$ is the detuning from the band gap center at ${\omega }_G{a}_0/2\pi c=0.745$. Spin-down TPSWs are excited by placing an $L$-polarized electric dipole between the rod and metal plate in the upper right corner. Red line:$T=0.9$; BMW parameters: same as in Fig. 1.

Figure 4

Propagation of surface waves along the interface between two topologically trivial PhCs. (a) Side and top views of the two PhCs and their interface. Semicircular metal rods arranged in a hexagonal pattern connect the two metal plates. (b) 1D PBS of a supercell (a single unit cell along the $x$ axis, 30 unit cells on each side of the interface along $y$ axis) for TM modes. Black circles: bulk modes, blue lines: TTSWs. (c) Energy density of a TTSW with frequency indicated by the black arrow in (d). (d) Transmission spectrum $T(\omega )$ through the zigzag route, where $\omega$ spans the entire band gap and $\mathrm{\Delta }\omega =0$ corresponds to band gap center at $\omega a_0/2\pi c=0.86$. Red line: $T=0.9$. Structure parameters: $h_0=a_0$, $d=0.6a_0$.