Emerging chiral optics from chiral interfaces

Twisted atomic bilayers are emerging platforms for manipulating chiral light-matter interaction at the extreme nanoscale, due to their inherent magnetoelectric responses induced by the finite twist angle and quantum interlayer coupling between the atomic layers. Recent studies have reported the direct correspondence between twisted atomic bilayers and chiral metasurfaces, which features a chiral surface conductivity, in addition to the electric and magnetic surface conductivities. However, far-field chiral optics in light of these constitutive conductivities remains unexplored. Within the framework of the full Maxwell equations, we find that the chiral surface conductivity can be exploited to realize perfect polarization transformation between linearly polarized light. Remarkably, such an exotic chiral phenomenon can occur either for the reflected or transmitted light. Moreover, we reveal that all transmitted light through the judiciously designed chiral surface conductivity can always have the polarization different from the incident light, irrespective of the incident angle.

Figure 1

Schematic of the reflection and transmission from a chiral metasurface under the incidence of linearly polarized waves. The chiral metasurface is featured with an electric surface conductivity ${\overline{\overline{\sigma }}}_{\mathrm{e}}$, a magnetic surface conductivity ${\overline{\overline{\sigma }}}_{\mathrm{m}}$, and a chiral surface conductivity ${\overline{\overline{\sigma }}}_{\chi }$. The chiral metasurface is located at the boundary between region 1 ($z<0$) and region 2 ($z>0$). Due to the chiral response of metasurfaces, the reflected and transmitted waves generally contain both the transverse-electric (TE, or $s$ polarized) and transverse-magnetic (TM, or $p$ polarized) field components.

Figure 2

Perfect polarization transformation between TM (incident) and TE (transmitted) waves. Here the chiral metasurface has ${\sigma }_{\chi ,x}{\sigma }_{\chi ,y}=1$. Regions 1 and 2 are the same dielectric (e.g., vacuum used here). (a) Schematic illustration. (b) Reflection and transmission coefficients as a function of the incident angle ${\theta }_{\mathrm{i}}$. For conceptual demonstration, ${\sigma }_{\chi ,x}=2$ and ${\sigma }_{\chi ,y}=0.5$ are chosen. If ${\sigma }_{\chi ,x}{\sigma }_{\chi ,y}=1, R_{\mathrm{r},\mathrm{TE}}^{\mathrm{i},\mathrm{TM}}$ and $T_{\mathrm{t},\mathrm{TM}}^{\mathrm{i},\mathrm{TM}}$ are equal to zero, irrespective of the incident angle. The critical incident angle is denoted as ${\theta }_{\mathrm{c}}$, at which $R_{\mathrm{r},\mathrm{TM}}^{\mathrm{i},\mathrm{TM}}=0$ and $|T_{\mathrm{t},\mathrm{TE}}^{\mathrm{i},\mathrm{TM}}|=1$. (c) ${\theta }_{\mathrm{c}}$ as a function of ${\sigma }_{\chi ,y}/{\sigma }_{\chi ,x}$.

Figure 3

Perfect polarization transformation between TM (incident) and TE (reflected) waves. The basic structural setup is the same as Fig. 2, except for that the chiral metasurface has ${\sigma }_{\chi ,x}{\sigma }_{\chi ,y}=-1$. (a) Schematic illustration. (b) Reflection and transmission coefficients as a function of ${\theta }_{\mathrm{i}}$. Here ${\sigma }_{\chi ,x}=2$ and ${\sigma }_{\chi ,y}=-0.5$ are chosen for conceptual illustration. If ${\sigma }_{\chi ,x}{\sigma }_{\chi ,y}=-1, T_{\mathrm{t},\mathrm{TE}}^{\mathrm{i},\mathrm{TM}}$ and $T_{\mathrm{t},\mathrm{TM}}^{\mathrm{i},\mathrm{TM}}$ are equal to zero for arbitrary incident angle. The critical incident angle is denoted as ${\theta }_{\mathrm{c}}$, at which $R_{\mathrm{r},\mathrm{TM}}^{\mathrm{i},\mathrm{TM}}=0$ and $|R_{\mathrm{r},\mathrm{TE}}^{\mathrm{i},\mathrm{TM}}|=1$. (c) ${\theta }_{\mathrm{c}}$ as a function of ${\sigma }_{\chi ,y}/{\sigma }_{\chi ,x}$.

Figure 4

Schematic illustration of the hybrid chiral structure constructed by the twisted atomic bilayer and the uniaxial magnetic metasurface.

Figure 5

Influence of imperfections on the polarization transformation between the incident and transmitted light. All basic setup here are the same as Fig. 2, except for the value of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}$. As a typical example of imperfection, here we set ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}\ne 1$. (a) Reflection and transmission coefficients as a function of the incident angle under the scenario of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}=0.8$. (b) Proportion of TE waves among all transmitted waves as a function of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}$. Here the incident light is TM polarized (same as Fig. 2), and we set the incident angle to be 60 °, namely the critical incident angle at which the perfection polarization transformation happens in Fig. 2.

Figure 6

Influence of imperfections on the polarization transformation between the incident and reflected light. The basic setup here is the same as Fig. 3, except for the value of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}$. As a typical example of imperfection, here we set ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}\ne -1$. (a) Reflection and transmission coefficients as a function of the incident angle under the scenario of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}=-0.8$. (b) Proportion of TE waves among all reflected waves as a function of ${\sigma }_{\chi ,\mathrm{x}}{\sigma }_{\chi ,\mathrm{y}}$. Here the incident light is TM polarized (same as Fig. 3), and we set the incident angle to be 60 °, namely the critical incident angle at which the perfection polarization transformation happens in Fig. 3.