Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy

The fascinating optical properties of metamaterials and metasurfaces are intrinsically wave-vector (k) dependent and spatial dispersion effects induce a complex optical response. Here, Mueller matrix spectroscopic ellipsometry, providing both amplitude and phase information in the visible, is used in a large frequency and k-space range to characterize a plasmonic meander and assign the polarization effects to the microscopic plasmonic excitations of a metasurface. This leads to a fundamental physical insight into the optical properties of the plasmonic meanders: the effect of closed-film resonant coupling is used for large polarization rotation and high transmission, and multiple optical functions are created within one compact design, which cannot be obtained by any natural crystal.

Figure 1

(a) Schematic of the sample illustrating its meander-like cross section. The coordinate system, the periodicity $p$, the azimuthal angle $\alpha$, and incident angle $\theta$ are also shown. (b) Schematic of the definition of the optical rotation $\nu$ and of the ellipticity $\varepsilon .$

Figure 2

(a) Scheme of the model with Z being a magnetic resonator, Y${}_1$ an electric resonator, and Y${}_2$ an inductance element modeling the metal film. The red arrow indicates the direction of light propagation. (b) Calculated phase retardation and transmission of the meander represented by the sum $\text{Z}+{\text{Y}}_1+{\text{Y}}_2$. (c) Transmittance of the different elements of the model. $\text{Z}+{\text{Y}}_2$ represents the SRSPP, ${\text{Y}}_1+{\text{Y}}_2$ represents the LRSPP whereas Y${}_2$ represents the bare metal film. (d) Phase retardation calculated for the different combinations.

Figure 3

(a) Experimental k-dependent transmittance spectra recorded with $p$-polarized light at azimuthal angle $\alpha =0^{\circ }.$ The value of the incident angle $\theta$ is given in two points as an indication. (b) Corresponding calculated transmittance spectra. The notation SR and LR indicate the position of the short-range and long-range SPP, respectively. The insets in panels (a) and (b) are the line cuts at $E=1.59$ eV.

Figure 4

(a) Polar representation of the measured transmittance in $p$ polarization through the meander as a function of the azimuthal angle $\alpha$ and, in the radial direction, in the wavelength range of 460 to 900 nm for different incident angles $\theta$ from 0 to 50 degrees. (b) Cross section of the transmittance plot at $\alpha =0^{\circ }$ for different incidence angles.

Figure 5

Mueller matrix contour plots of the elements $M_{02}$ and $M_{12}$ at three different energies. The top two rows display the experimental results (Expt.), the bottom two rows display the simulations (Sim) at the same energies. The dashed lines in the simulated $M_{02}$ polar plot at 1.63 eV represent the hyperbolic SR and LR arc lines.

Figure 6

(a) Experimental evolution of the polarization ellipse of a linearly polarized light transmitted through the sample as a function of the azimuthal angle (from 0${}^{\circ }$ to 170${}^{\circ }$); the blue curves correspond to normal incidence and the red curves to oblique incidence at $\theta ={20}^{\circ }$. Both are obtained for an energy of 1.675 eV. (b) Azimuthal-angle dependent optical rotation $\nu$ and ellipticity $\varepsilon$ at normal incidence and at $\theta ={20}^{\circ }$; both plots correspond to an energy of 1.675 eV and are derived from the measured data. (c) Measured contour plots of the optical rotation and ellipticity as a function of the azimuthal angle and the incident angle for three different energies. The white dashed lines in the color plot at 1.63 eV are a guide to the eye to identify the relative positions of the SRSPP and LRSPP modes.