Active polarization control with a parity-time-symmetric plasmonic resonator

Control of the polarization state of light is essential for many technologies, but is often limited by weak light-matter interactions that necessitate long device path lengths or significantly reduce the signal intensity. Here, we investigate a nanoscale plasmonic aperture capable of modifying the polarization state of far-field transmitted light without loss in the probe signal. The aperture is a coaxial resonator consisting of a dielectric ring embedded within a metallic film; parity-time ($\mathcal{P}\mathcal{T}$) -symmetric inclusions of loss and gain within the dielectric ring enable polarization control. Since the coaxial aperture enables near-thresholdless $\mathcal{P}\mathcal{T}$ symmetry breaking, polarization control is achieved with realistic levels of loss and gain. Exploiting this sensitivity, we show that the aperture can function as a tunable waveplate, with the transmitted ellipticity of circularly polarized incident light changing continuously with the dissipation coefficient from $\pi$/2 to 0 (i.e., linear polarization). Rotation of linearly polarized light with unity efficiency is also possible, with a continuously tunable degree of rotation. This compact, low-threshold, and reconfigurable polarizer may enable next-generation, high-efficiency displays, routers, modulators, and metasurfaces.

Figure 1

(a) Schematic of the $\mathcal{PT}$-symmetric coaxial waveguide with alternating sections of the gain (yellow) and loss (red). (b) Transmission spectra of the 300-nm-long coaxial aperture when $\kappa =0$ and $\kappa =0.018$. Significant linewidth narrowing and increased transmission intensity are present when $\kappa =0.018$. The inset is a cross section of the normalized electric field for $\kappa =0$ on resonance with a 120-nm scale bar. (c) Dispersion of the imaginary wave vectors of an infinite $\mathcal{PT}$-symmetric coaxial waveguide with varying $\kappa$ at 1117 nm. (d) Modal profiles of an infinite coaxial waveguide for $\kappa =0$ and 0.02. Electric field intensity for modes labeled in part (c). The loss and gain modes for $\kappa =0.02$ are linearly polarized along the direction of high intensity.

Figure 2

(a) Illustration of the illumination and transmission characteristics of the $\mathcal{PT}$-symmetric coaxial aperture showing CPL to LPL conversion. (b) Electric field intensity at the end of the aperture as a function of $\kappa$ when the aperture is illuminated with CPL. The intensity is azimuthally symmetric at $\kappa =0$ and becomes increasingly oriented toward the gain sections (${45}^{\circ }$ and ${225}^{\circ }$) as $\kappa$ increases to $\kappa =0.018$. (c) Poincaré sphere of the transmitted polarization state shows the far-field polarization transitions from CPL to LPL. (d) Far-field phase difference between $E_x$ and $E_y$ shows good agreement between model and simulation for the transition from CPL to LPL.

Figure 3

(a) Electric field intensity at the end of the aperture when the aperture is illuminated with LPL aligned to $-{35}^{\circ }$. The field intensity rotates around the coaxial structure. Each field is self-normalized, with the intensity for $\kappa =0.0187$ being approximately an order of magnitude lower than that in Fig. 2. The output intensity is still greater than the passive ($\kappa =0$) case. (b) Poincaré spheres are oriented so that the perimeter of the projection represents linear polarization. The polarization state moves along the perimeter. Input polarizations of $-5^{\circ }$ and $-{35}^{\circ }$ rotate with increasing $\kappa$ to the gain angle of ${45}^{\circ }$. (c) Output polarization angle as a function of the input polarization and $\kappa$, shows polarization is pulled toward the gain axis (${45}^{\circ }$) as $\kappa$ is increased to 0.0187. (e) Simulation and model of the output polarization as a function of $\kappa$ showing $-5^{\circ }$, $-{15}^{\circ }$, $-{25}^{\circ }$, and $-{35}^{\circ }$ input polarizations rotated to ${45}^{\circ }$.

Figure 4

Phase and amplitude as a function of $\kappa$ for the polarization aligned to the gain axis. The model transmission intensity is plotted as a dotted line.