Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure

We report that normal incidence transmission of circularly polarized waves through the lossy anisotropic planar chiral structure is asymmetric in the opposite direction. The new effect is fundamentally distinct from conventional gyrotropy of bulk chiral media and the Faraday effect, where the eigenstates are a pair of counterrotating elliptical states, while the eigenstates of the lossy anisotropic planar chiral structure are two corotating elliptical polarizations.

Figure 1

Propagation of circularly polarized waves through 3D-chiral, Faraday, and anisotropic planar chiral media, and polarization eigenstates corresponding to propagation in forward and backward direction in each media. Circular arrows denote polarization states: blue for RCP, red for LCP. Vector $\mathbf{H}$ denotes the external magnetic field, while $\mathbf{W}$ indicates the 2D-chiral twist.

Figure 2

Fragments of two enantiomeric forms $A$ and $B$ of the chiral fish-scale pattern made of copper strips on a dielectric substrate. The dashed line box indicates the elementary translational cell of the structure. Part C shows a fragment of the nonchiral fish-scale structure.

Figure 3

Mean value of ${\Xi }_{ii}$ (black circles) calculated as an average over eight different sets of data, which were obtained for both enantiomeric forms of the structure ($A$ and $B$) for RCP and LCP incident waves in both forward and backward directions of propagation. The solid red and blue lines show the limits of the observed transmission variation. The solid black line shows the theoretical value of ${\Xi }_{ii}$.

Figure 4

Polarization conversion of circularly polarized waves by two enantiomeric forms of chiral fish-scale structure in forward and backward directions of propagation. Part (a) shows phase difference $\Delta \varphi$ between converted polarization components corresponding to incident waves of opposite handedness. Part (b) shows normalized differential intensity of conversion, $\Delta \Xi$. Blue and red solid circles correspond, respectively, to $A$ and $B$ enantiomers in the forward direction, while blue and red open circles correspond to $B$ and $A$ forms in the backward direction. Solid curves are obtained theoretically.