Manipulation of Longitudinally Inhomogeneous Polarization States Empowered by All‐Silicon Metasurfaces

Abstract

The evolutionary trend of the polarization state can completely reflect the vectorial information of the optical field. [7,8] The optical angular momentum (OAM) includes both spin and orbital components, which are determined by the polarization and spatial degrees of freedom of the light, respectively. [9,10] As an eigenpolarization state of the cylindrical vector optical field, the charming vector properties have led to the increasing interest in vector vortex beams (VVBs) in many fields. [11,12] Similar to scalar vortex beams (SVBs), VVBs also have a helical phase wavefront exp(ilϕ) and a doughnut-shaped intensity profile, and the number of topological charges is determined by the key parameter l. [13,14] The polarization state of a VVB is not uniformly distributed in its transmitted crosssection and exhibits a distinct change with spatial plane, including radially polarized and azimuthally polarized beams with different focusing characteristics. [12] In addition, the polarization state at the center of the cross-section cannot be uniquely determined; and is thus, also known as the polarization singularity. [15,16] VVBs have been widely used for trapping and rotating particles, [17,18] quantum information, [19,20] and superresolution imaging. [21] Metasurfaces, as quasi-periodic arrays in the subwavelength scale range, have attracted extensive research interest in opto-electronics, such as focusing, [22,23] structured light, [7,15] and polarization control. [24][25][26] Metasurfaces mainly exploit the discontinuity of phase abruptness of the structured surface to Polarization plays a key role in fundamental science, and manipulating the evolutionary trends of longitudinal polarization states can provide new implements for light-matter interaction. However, existing 3D optical devices can only manipulate the polarization conversion in a single transverse plane. Recently, methods to control polarization by cascading bulky optical systems are miniaturized using metasurfaces. Nevertheless, it is quite challenging to generate focused beams with vectorial properties for metasurfaces carrying inhomogeneous polarization profiles. Here, a single-layer all-silicon metasurface operating in the terahertz (THz) band is demonstrated to address all those aforementioned challenges in one go, and pencil-like beams with inhomogeneous polarization profiles can be imparted along the propagation direction. The introduction of a latitudinal polarization control factor representing the initial phase difference enables near-even manipulation of the evolutionary trend of the longitudinal polarization state according to the extended focal depth. By manipulating the topological charges within two orthogonal circularly polarized channels to accomplish coherent superposition, a focused vortex beam with vectorial properties can be generated in desired planes. Two functional demonstrations based on this approach are established experimentally, offering promising opportunities for structured light on meta-optics.

Polarization Detection of Terahertz Waves using All‐Silicon Metasurfaces with Tightly Focusing Behavior

“…The detailed parametric derivation model can be found in the Supporting Information Note S7. The focusing behavior with an elongated focal depth can effectively attenuate the errors introduced in the measurements, so that the phase profiles embedded within the LCP and RCP channels can be described as [ 31 ] $$$$\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} {\varphi _{\mathrm{L}}}\left( {x,y} \right) = \displaystyle\frac{{{k_0}\left( {{x^2} + {y^2}} \right)}}{{2\left[ {{f_{\mathrm{L}}} + {{\Delta}}{f_{\mathrm{L}}} \cdot {{\left( {{x^2} + {y^2}} \right)} \mathord{\left/ {\vphantom {{\left( {{x^2} + {y^2}} \right)} {{R^2}}}} \right. \kern-\nulldelimiterspace} {{R^2}}}} \right]}}\\ [12pt] {\varphi _{\mathrm{R}}}\left( {x,y} \right) = \displaystyle\frac{{{k_0}\left( {{x^2} + {y^2}} \right)}}{{2\left[ {{f_{\mathrm{R}}} + {{\Delta}}{f_{\mathrm{R}}} \cdot {{\left( {{x^2} + {y^2}} \right)} \mathord{\left/ {\vphantom {{\left( {{x^2} + {y^2}} \right)} {{R^2}}}} \right.$$…”

“…For more detailed information on the sample preparation, see the Experimental Section. As proof-of-concept experiments, the predefined electric field intensity profile in the z = 5 mm plane was characterized using a fiber-based THz near-field detecting system, [31,40] as shown in Figure 3c. The detailed measuring steps can be found in the Experimental Section too.…”

“…The detailed parametric derivation model can be found in the Supporting Information Note S7. The focusing behavior with an elongated focal depth can effectively attenuate the errors introduced in the measurements, so that the phase profiles embedded within the LCP and RCP channels can be described as [31]…”

“…By ingeniously combining Equations () and () to be able to eliminate the unknown terms in the matrix, the correspondence of the desired key parameters for different polarization bases can be obtained as follows [ 31–33 ] $$$$\begin{equation}\left\{ \def\eqcellsep{&}\begin{array}{l} {\varphi _x}\left( {x,y} \right) = \frac{1}{2}\left( {{\phi ^ + }\left( {x,y} \right) + {\phi ^ - }\left( {x,y} \right)} \right)\\ {\varphi _y}\left( {x,y} \right) = \frac{1}{2}\left( {{\phi ^ + }\left( {x,y} \right) + {\phi ^ - }\left( {x,y} \right)} \right) - \pi \\ \theta \left( {x,y} \right) = \frac{1}{4}\left( {{\phi ^ + }\left( {x,y} \right) - {\phi ^ - }\left( {x,y} \right)} \right) \end{array} \right. \end{equation}$$$$…”

“…By ingeniously combining Equations ( 5) and ( 6) to be able to eliminate the unknown terms in the matrix, the correspondence of the desired key parameters for different polarization bases can be obtained as follows [31][32][33] Compared to the meta-atoms in the diamond-shaped region for linearly polarized incidence, as mentioned in Figure S1 (Supporting Information Note S1), the selected elements that meet the decoupling condition have a phase interval of 22.5°i n the limit of Equation (7). Furthermore, the operating behavior of the selected meta-atoms is characterized as rotatable halfwave retarders (HWRs), i.e., satisfying |t x (x, y)| = |t y (x, y)| as well as 𝜑 x (x, y) + 𝜋 = 𝜑 y (x, y) under linearly polarized illumination.…”