Polarization- and wave-vector selective optical metasurface with near-field coupling

TL;DR

This work tackles polarization control in metasurfaces by engineering near-field coupling between locally resonant waveguides to realize negative coupling and wave-vector dependent polarization eigenstates. Through sinusoidally modulated silicon waveguides, the authors demonstrate a Dirac-point polarization degeneracy and a line of circular and linear polarization in $k$-space, validated by full-wave Maxwell simulations and angle-resolved transmission measurements. The study shows that incident polarization and $k$-vector select specific eigenmodes, enabling angle-tunable polarization filtering and potential light source design, while highlighting fabrication sensitivity (e.g., width offsets) and the need for precise parameter control. The results open pathways for spin-selective sensing and reconfigurable photonics in both optical and microwave regimes by exploiting near-field coupling in metastructures.

Abstract

Metasurfaces are a powerful tool for manipulating light using small structures on the nanoscale. In most meta-surfaces, near-field couplings are treated as unfavorable perturbations. Here, we experimentally investigate a structure consisting of sinusoidally modulated silicon waveguides where near-field coupling of local resonances leads to negative coupling, i.e. a negative coupling constant. This gives rise to wave-vector dependent eigenstates of elliptical, linear and circular polarizations. In particular, fully circular polarization states are not only present at a single point in momentum-space (k-space), but along a line. This circular polarization line, as well as a linear polarization line, emanates from a polarization degeneracy at the Dirac point. We experimentally validate the existence of these eigenstates and demonstrate the energy-, polarization- and wave-vector-dependence of this metasurface. By tuning the incident k-vector, certain polarization-energy eigenstates are strongly reflected allowing for uses in angle-tunable polarization filters and light sources.

Figures (12)

• Figure 1: (a) Sketch of the discussed metasurface composed of single waveguide (SW - gray) and double waveguide (DW - black). A top view of the unit cell with all its geometrical parameters is shown in the inset/ yellow box. At resonance frequency, the incident light is reflected (see reflection $|R|$) leading to a dip in the transmission spectrum ($|T|$). Because of an additional phase shift, the reflected and transmitted light is cross-circularly polarized. (b) Side view of the unmodulated silicon waveguides on glass and mode profile ($E_z$ component) of the fundamental modes. Top: TE-like mode in the SW, Bottom: odd mode in DW. (c) Real difference of eigenenergies $E_1$ and $E_2$ in the momentum-space ($k$-space) around the Dirac point (DP). The color indicates the eigenpolarization $\sigma_d$ which is shown in (d) for the upper and lower surface separately. The black arrows illustrate the polarization state.
• Figure 2: Simulations of the metasurface. (a) Underlying eigenmode structure: eigenenergies $E$ and color coded eigenpolarization $\sigma_d$ in 2D $k$-space. The solid and dashed white line marks the eigenenergies for a $k_x$-sweep along the Dirac point for right circular polarization (RCP) and left circular polarization (LCP), respectively. (b) Eigenenergies for $k_x=0$ that are of linear horizontal polarization (HP, black) and vertical polarization (VP, pink). (c) Simulated transmission for a sweep in $k_x$ for incident RCP (top) and LCP (bottom) at $k_y=K_y=0.3\pi/b$. (d) Simulated transmission for a sweep in $k_y$ at $k_x=K_x=0$ for horizontally polarized incident light. The pink line marks the according resonances for vertical polarization (see Fig. S4 in the Supporting Information).
• Figure 3: Scanning electron micrograph of the silicon waveguide metasurface fabricated on top of a glass substrate and marked double waveguide (DW) and single waveguide (SW).
• Figure 4: (a) Calculated eigenmodes of the waveguide structure with width offset $\Delta W=3.5nm$. The white lines mark the relevant eigenmodes for a $k_x$-sweep for RCP (solid line) and LCP (dashed line) at $k_y=0.3\pi/b$. The black (pink) line marks the relevant eigenmodes for the $k_y$-sweep with HP (VP) at $k_x=0$. (b) Sketch of the unit cell modified by the width offset $\Delta W$. (c) Measured and (d) simulated transmission for a sweep in $k_x$ at $k_y=0.3\pi/b$ for RCP (top) and LCP (bottom) input light. (e) Measured and (f) simulated transmission for a sweep in $k_y$ at $k_x=0$ for horizontal polarization. The pink line marks the according resonances for vertical polarization (see Fig. S4 in the Supporting Information). The small red dots in (c) and (e) emphasize the measured resonance position and the simulated transmission (d), (f) apply to $\Delta W=3.5nm$.
• Figure 5: (a) Simulated eigenmodes along $k_y$ at $k_x=0$ without (left) and with (right) width offset $\Delta W$. The solid lines correspond to the linearly polarized eigenmodes and the dashed lines to the mirrored ones. The vertical gray lines mark the position in $k_y$ and energy of the $k_x$-sweeps discussed in the corresponding Figures. (b) Measured and (c) simulated transmission at $k_yb/\pi=0.46$ for RCP (top) and LCP (bottom). The red dots in (b) mark the positions of the measured resonances. For the simulations in (c) $\Delta W=3.5nm$ applies.