Periodic Nanostructures: Spatial Dispersion Mimics Chirality

Polarization rotation in isotropic materials is commonly associated with chirality, i.e., structures with a handedness which are not identical with their mirror image. We observe this effect in the visible and near-IR regions at oblique incidence in the optical response of a subwavelength square array of holes. Mapping the complete $\overrightarrow{k}$ space via Mueller-matrix spectroscopic ellipsometry, we find that in specific directions the rotary power is orders of magnitude larger than that observed for chiral molecules. Although experimentally indistinguishable, the physics behind the two phenomena is fundamentally different: While optical activity is a consequence of magnetic interactions, nanostructures on a square lattice rotate the polarization due to spatial dispersion.

Figure 1

Scanning electron micrograph and scheme of the probing light beam. For the calculations the hole shape was approximated by rounded squares. Parameters: period $P=400\mathrm{nm}$; hole diameter $d=225\mathrm{nm}$; Au film thickness $t=20\mathrm{nm}$.

Figure 2

Mueller-matrix contour plots at $\hslash \omega =1.2\mathrm{eV}$ for a 20 nm thick unprocessed Au film. The intensity is normalized to $m_{00}$ and color coded. As expected for an isotropic sample, all off-diagonal elements except ($m_{01}=m_{10},m_{23}$) are zero.

Figure 3

Measured (a) and calculated (b) Mueller-matrix contour plots at 1.2 eV for the sample shown in Fig. 1. The agreement is almost perfect. The numbers in the lower right corners indicate the multiplication factors used for each Mueller-matrix element to enhance the contrast for better visibility. The white cross in the element $m_{03}$ corresponds to the position in $\theta \mathrm{\text{−}}\alpha$ space for which the frequency dependence is plotted in Fig. 5.

Figure 4

$\theta$-dependent polarization change with respect to incoming $p$-polarized light at 1.2 eV and an azimuthal orientation $\alpha =70°$. The hole array influences the rotation $\vartheta$ of the major axis as well as the ellipticity $ϵ$.

Figure 5

Calculated and measured CD and ORD due to reflection off the hole array for one particular point in $\overrightarrow{k}$ space (cross in Fig. 3). The plasmon resonance is at 1.4 eV.