Metasurface-Based Solid Poincaré Sphere Polarizer

The combination of conventional polarization optical elements, such as linear polarizers and waveplates, is widely adopted to tailor light’s state of polarization (SOP). Meanwhile, less attention has been given to the manipulation of light’s degree of polarization (DOP). Here, we propose metasurface-based polarizers that can filter unpolarized incident light to light with any prescribed SOP and DOP, corresponding to arbitrary points located both at the surface and within the solid Poincaré sphere. The Jones matrix elements of the metasurface are inverse-designed via the adjoint method. As prototypes, we experimentally demonstrated metasurface-based polarizers in near-infrared frequencies that can convert unpolarized light into linear, elliptical, or circular polarizations with varying DOPs of 1, 0.7, and 0.4, respectively. Our Letter unlocks a new degree of freedom for metasurface polarization optics and may break new ground for a variety of DOP-related applications, such as polarization calibration and quantum state tomography.

Figure 1

Comparison of the linear polarizer, surface Poincaré sphere polarizer, and solid Poincaré sphere polarizer. (a) Schematic of a linear polarizer that converts an unpolarized incident beam into linear polarization located at the equator of the Poincaré sphere. (b) Schematic of a surface Poincaré sphere polarizer that converts an unpolarized incident beam into arbitrary polarizations located at the surface of the Poincaré sphere. (c) Schematic of a solid Poincaré sphere polarizer that converts an unpolarized incident beam into arbitrary polarizations located at the surface and within the Poincaré sphere. (d) Schematic of a Poincaré sphere and the locations of output polarization states generated from a linear polarizer, a surface Poincaré sphere polarizer, and a solid Poincaré sphere polarizer, respectively.

Figure 2

Physical mechanism for the simultaneous and independent modulation of DOP and SOP. (a) An unpolarized beam can be treated as a superposition of two orthogonal polarization states with random phase differences. The output polarization ${\overrightarrow{\beta }}^{-}$ combines a portion of its orthogonal polarization ${\overrightarrow{\beta }}^{+}$ to construct an unpolarized beam with an intensity of $|c{|}^2$. The remaining portion of ${\overrightarrow{\beta }}^{+}$ is a polarized beam with an intensity of $(1-|c{|}^2)/2$. The output is the superposition of the unpolarized and polarized beams, with the ratio controlled by $c$. (b) Schematic illustration of the locations of the polarization states ${\overrightarrow{\alpha }}^{+}$, ${\overrightarrow{\alpha }}^{-}$, ${\overrightarrow{\beta }}^{+}$, and ${\overrightarrow{\beta }}^{-}$ at the surface of the Poincaré sphere.

Figure 3

Inverse design of the metasurface-based solid Poincaré sphere polarizer. (a)–(c) FOM as a function of the iteration for linear (a), elliptical (b), and circular (c) polarizer with DOP of 1, 0.7, and 0.4, respectively. The insets are the antenna shape at the end of the iterative optimization. (d)–(f) Stokes parameter and DOP of output beams transmitted through the metasurface-based linear (d), elliptical (e), and circular (f) polarizers, respectively, with an output DOP of 0.7 under the illumination by the unpolarized incident beam at the designed wavelength of 1150 nm.

Figure 4

Experimental demonstration of metasurface-based solid Poincaré sphere polarizers. (a) Experimental setup for the measurement of the Stokes parameter of light transmitted through the metasurface. (b)–(d) Comparison between the measured and designed Stokes parameters for the metasurface-based linear (b), elliptical (c), and circular (d) polarizer, respectively, each with a designed DOP of 1, 0.7, and 0.4, respectively. The inset shows the SEM images of fabricated metasurfaces. The scale bar is $1\mathrm{\mu }\mathrm{m}$.