Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium

Photonic topological insulators are an interesting class of materials whose photonic band structure can have a band gap in the bulk while supporting topologically protected unidirectional edge modes. Recent studies on bianisotropic metamaterials that emulate the electronic quantum spin Hall effect using its electromagnetic analog are examples of such systems with a relatively simple and elegant design. In this paper, we present a rotating magnetic dipole antenna, composed of two perpendicularly oriented coils, that can efficiently excite the unidirectional topologically protected surface waves in the bianisotropic metawaveguide (BMW) structure recently realized by T. Ma et al. [Phys. Rev. Lett. 114, 127401 (2015)] despite the fact that the BMW medium does not break time-reversal invariance. In addition to achieving a high directivity, the antenna can be tuned continuously to excite reflectionless edge modes in the two opposite directions at various amplitude ratios. We demonstrate its performance through experiments and compare the results to simulation results.

Figure 1

(a) Numerically calculated band structure of the waveguide, where four edge modes have been labeled. (b–e) Field profile $|H_x-i{H}_y|$ of the four edge modes at 6.13 GHz [shown in (a) as the dashed line]. It is clear that only the two spin-up states (from the two valleys), and none of the spin-down states, can be excited by a right circularly polarized magnetic dipole.

Figure 2

(a) Schematic of the experimental setup. ${\mathrm{\Delta }}_{\mathrm{em}}$ is the bianisotropy coefficient [19] and the interface is defined by the boundary of the two regions with ${\mathrm{\Delta }}_{\mathrm{em}}$ of opposite sign, denoted by the dashed red line. (b) Photograph of the top of the BMW structure showing the elements corresponding to (a). Inset: Arrangement of the two loop coils which are in the air gap of a cylinder at the interface.

Figure 3

Transmission amplitude on the (a) left side and (b) right side of the BMW interface as a function of the frequency while the phase difference $\varphi$ of the two driving loop antennas is varied. The probe is positioned at the center of the edge. The BMW bulk band gap extends from 5.80 to 6.47 GHz, as shown by the dashed vertical lines.

Figure 4

CST simulation results for transmission amplitude on the left and right sides of the BMW structure while both the phase difference $\varphi$ and the driving amplitude (parameterized by angle $\theta \in [0,\pi /2]$) of the two loop antennas are varied. Results are shown for (a) left and (b) right at 6.47 GHz and (c) left and (d) right at 6.08 GHz.

Figure 5

Transmission amplitude on the (a) left side and (b) right side while both the phase difference $\varphi$ and the input power (parameterized by $\theta$) of the two loop antennas, as deduced from the data at a frequency of 6.38 GHz, are varied. To examine the directivity, we plot the ratio of (c) the left- to right-side and (d) the right- to left-side transmission amplitude (in dB) as a function of $\theta$ and $\varphi$.