Polarization effects in the diffraction of light by a planar chiral structure

We analyze polarization changes of light diffracted on a planar chiral array from the standpoint of the Lorentz reciprocity lemma and find biorthogonality in the polarization eigenstates for waves diffracting though the grating in the opposite direction. Both reciprocal and nonreciprocal components in the polarization azimuth rotation of the diffracted light are identified. The structural chirality of the array arrangement and the chirality of individual elements of the array give rise to polarization effects.

Figure 1

Coordinate systems and waves in the direct (a) and reversed (b) diffraction scenarios.

Figure 2

Structural elements of the arrays: planar straight cross tilted against the array greed on the tilt angle $\psi$ and chiral right-handed gammadion with bending angle $\phi$.

Figure 3

Schematic representation of diffraction on the Poincaré sphere. For a chiral grating polarization eigenstates in the direct scenario ($1d$ and $2d$) and reversed scenario ($1r$ and $2r$) are elliptical. Polarization eigenstates (underlined) for nonchiral gratings are mutually perpendicular linear polarization.

Figure 4

Polarization azimuth rotation $\Delta =\theta -\alpha$ on diffraction from chiral arrays as a function of incident polarization azimuth. Straight line: direct scenarios. Dashed line: reversed scenarios (all results are presented in the direct scenario coordinate frame). The influence of chirality is manifested as a split between corresponding solid and dashed lines: (a) Array of straight crosses. The insert shows the chiral difference in polarization azimuth for the two polarization eigenstates as a function of the tilt angle of the crosses. (b) Array of left (L) and right (R) gammadions. The inset shows the chiral difference in polarization azimuth for the two polarization eigenstates as a function of gammadion bending angle.