Giant topological magnetoelectric and optical Hall effects for a topological insulator as a defect in photonic crystals

A system with a topological insulator slab sandwiched by two one-dimensional photonic crystals as a defect is investigated. A giant topological magnetoelectric effect is proposed which is characterized by two resonant peaks with half-unit transmissions and rich polarization behaviors in the photonic band gap. We also predict a giant optical Hall effect in our system, in which the transverse shift of the transmitted light could be 1000 times larger than the wavelength. These effects are purely from the $\Theta$-domain walls at the topological insulator interfaces and could be observed easily.

Figure 1

Schematic show of our model with a TI slab as defect sandwiched by two 1D PhCs.

Figure 2

(a) Transmission $I_t/I_i$ and reflection $I_r/I_i$ spectra with incidence as a linearly polarized plane wave. (b) Evolution of transmission peaks with cell number $N$. The solid lines are numerical results, while the dash dots are from our theoretical resonant conditions. (c) Angle $\varphi$ (blue line) between the long axis of polarization and $x$ axis, and the intensity ratio (green line) between the short and long axis $l=I_b/I_a$ as a function of frequency. The insets are schematic polarization of transmitted wave at five typical frequencies, where the long axis is shown in red.

Figure 3

(a) Schematic show of OHE with transverse shift of transmitted beam. (b) Transverse shift versus incident angle at frequency ${\omega }_2$. (c) The spatial distribution intensity $I(x,y)$ and the energy current direction of transmitted light when the incidence is a linearly- polarized Gaussian beam with width $D_b=100\lambda$ and frequency as ${\omega }_2$ in Fig. (2).