High efficient metasurface quarter-wave plate with wavefront engineering

Metasurfaces with local phase tuning by subwavelength elements promise unprecedented possibilities for ultra-thin and multifunctional optical devices, in which geometric phase design is widely used due to its resonant-free and large tolerance in fabrications. By arranging the orientations of anisotropic nano-antennas, the geometric phase-based metasurfaces can convert the incident spin light to its orthogonal state, and enable flexible wavefront engineering together with the function of a half-wave plate. Here, by incorporating the propagation phase, we realize another important optical device of quarter-wave plate together with the wavefront engineering as well, which is implemented by controlling both the cross- and co-polarized light simultaneously with a singlet metasurface. Highly efficient conversion of the spin light to a variety of linearly polarized light are obtained for meta-holograms, metalens focusing and imaging in blue light region. Our work provides a new strategy for efficient metasurfaces with both phase and polarization control, and enriches the functionalities of metasurface devices for wider application scenarios.

functionalities with great potential in applications are demonstrated, such as metalens [11][12][13][14][15], meta-holograms, [16][17][18] and polarizers, [19][20][21] to name a few. Among them, simultaneous control of the polarization and phase plays a vital role and has already aroused numerous researches to explore its full potential. [22][23][24][25][26] Attempts such as utilizing two plasmonic nanopillars per period with different distance and orientation angle only work for oblique incidence. [27] Another method is exploiting the superposition of the two output circular polarization (CP) beams through two sets of nanopillars with different dimensions and starting orientation angles under linear polarization (LP) incidence. [28] Both of them are based on super unit cells with spatial superposition of inclusions, which would result in lower efficiency, inferior image quality, and lower space-bandwidth product. Recently, it is of great interest to combine the propagation phase and geometric phase (i.e., Pancharatnam-Berry (PB) phase) to realize full control of the polarization and phase on a single subwavelength unit cell. [29][30][31] However, they are usually focused on the polarization multiplexing to enhance the information capability, e.g., differe nt functionalities are encoded with different polarization states. In fact, incorporating the same wavefront engineering with different polarization states to realize specific polarizatio n conversion is quite useful but remains rarely explored. As a basic optical component, quarter waveplate (QWP) (normally convert the CP light to LP light and vice versa) plays an important role in light manipulation. [32,33] It would be highly desirable to find ways to implement QWPs on a single metasurface.
Here, we provide a straightforward design principle for metasurfaces (e.g. meta-hologra ms and metalens) to achieve the QWP functionality by utilizing both the co-and cross-polarized spin light. By combing the propagation phase with PB phase, we first demonstrate the modulate capacity with spin-selected holographic images (the commonly unmodulated co-polarized light and cross-polarized light) with SiNx metasurfaces in the visible spectrum. We further realize the QWPs with wave manipulation abilities by controlling the superposition of two output CP light. Other elliptical polarizations with designed wavefront are also produced experimenta lly.
The polarization reconstruction and wave manipulation based on two orthogonal CP bases certainly expands the practical application possibilities and could trigger versatile functio n integrations for advanced compact systems.

The Design Principles
PB phase-based metasurfaces can achieve a full phase control by adjusting the orientation angle of the meta-atoms with identical geometry. [34] The cross-polarized light will have extra ∓i2σθ phase modulation under normal CP light incidence, where θ is the rotation angle from the x-axis, and σ indicates the handness of the CP light. However, the co-polarized scattered light is usually ignored, which unavoidably results in background noises or a dazzling spot in the hologram image. [28,31,35,36] In order to surmount this restriction, we propose to modulate the co-and cross-polarized light independently by combining the propagation phase and PB phase. The total Jones matrix describing the relation between the input electric field (Ein) and the output electric field (Eout) in a circular base can be written as: where Rc(θ) is the rotation matrix, ϕRL, ϕLR, ϕRR and ϕLL is the propagation phase. In this work, we consider the widely used rectangular nanopillars, so the phase shift ϕRR=ϕLL and ϕRL=ϕLR due to the mirror symmetry. In this case, if the incident wave is right circularly-polarized (RCP), the output electric field Eout becomes:

Phase modulation capability
As a proof of concept, we consider the Silicon nitride (SiNx) metasurfaces consisting of nanopillars with different shapes covered on the fused-silica substrate. SiNx was chosen because of its low loss in visible light and compatibility with CMOS processes. The design wavelength is 470 nm and the metasurface works in a transmitted way. As illustrated in Figure   1(a), the unit cell period is chosen as 300 nm satisfying the Nyquist theory. [37] The nanopillar height is set as 800 nm to provide phase change covering 0~2π. To verify the phase modulation ability, we first demonstrated an independent spin polarization hologram metasurface with RCP light incidence. The transmitted RCP light is modulated to produce a far-field hologram image with "NJU" based on propagation phase (ϕRR) and LCP light is manipulated to present a representative building of Nanjing University (i.e. a 600-years building named Bei-Da) in the far field based on propagation phase (ϕRR) and PB phase (ϕRL-2θ). The optimized phase profiles are based on Gerchberg-Saxton algorithm. [38][39][40] The metasurface with a footprint of 150 μm × 150 μm is fabricated using a conventio na l nanofabrication process (see Experimental Section) and its scanning electron microscopy (SEM) image is shown in Figure 2

Meta-holograms with QWP effect
After verifying the phase modulation capability, we further demonstrate the polarization state manipulation. The output RCP and LCP light are designed with the same function (e.g. the same focal length or the same hologram image) by modulating the propagation phase ϕRR(x,y) and the compensatory PB phase -2θ(x,y). To realize the QWP functionality, we choose the same nanopillars as marked in Figure 2(b) to obtain equal aR and aL. The reference phase φ (related to the extra rotation angle θ0) is modulated to get different LP light. As shown in Figure 3(a), the red dots on the Poincaré sphere mark the designed output linear polarization state under RCP incidence. The SEM image of the metasurface with a footprint of 150 μm × 150 μm for xpolarized (dot A) hologram is shown in Figure 3(b). The insert picture is the enlarged image.
The directly (without analyzer) measured holographic image is shown in Figure 3(c). Due to the utilization of both the co-and cross-polarized light, the middle zero spot is nearly negligib le, indicating a very high diffraction efficiency (98%). The zero spot is difficult to completely disappear because of k-space imaging of the light passing through the gap between nanopillars.
To verify its polarization properties, we add a polarizer to detect the relative intensity profile.
When the polarizer is set as 0° (the transmission axis is parallel to the x-axis), the hologram intensity profile (see Figure 3(d)) is nearly the same as the measured image without analyzer (Figure 3(c)). When the polarizer is rotated as 45° and 90°, the intensity of the output hologram image change from attenuation to disappearance that surely verifies the linear polarization (xpolarized) properties (see

Metalens with QWP effect
To further demonstrate the manipulation capability, we design a meta-QWP for focusing and imaging. As illustrated in Figure 4(a), the designed single-layer metasurface can act as a QWP and a lens at the same time. The phase profile follows [41]   where the focal length f=100 μm. Figure 4(b) shows the SEM image of the fabricated metalens (D=150 μm, NA=0.6) with x-polarization output under RCP incidence (the detailed analysis are provided in Supplementary Figure S2). As demonstrated above, other LP output can also be obtained as long as rotating the metasurface. The directly measured focus spot is shown in

Metalens with elliptic polarizations generation
In addition, this method can be scaled to other polarization states, such as elliptic polarizations E and F on the Poincaré sphere (see Figure 5(a)). Specifically, for the polarizatio n state E, aR/aL=1/2 and φ=0, the amplitude distribution of the selected nanopillars are shown in  Figure   5(f) and the focusing efficiency is calculated as 87%. Figure 5(g) illustrates the image of Sector Star Target which resolution at the central circle is 8.7 μm. SEM images of these samples can be found in Figure S6.

Conclusion
In conclusion, we have demonstrated a straightforward method for realizing phase

Experimental Section
Numerical simulations: The simulated material parameters of SiNx is adopted from the experimental measurement. The wavelength is fixed at 470 nm, and the refractive index is

Supporting Information
High efficient metasurface quarter-wave plate with wavefront engineering Chen Chen 1,2