1. Introduction

Manipulation of the characteristics of linearly polarized (LP) light such as the polarization state and propagation direction as well as their spatial distribution is widely applied in various fields ranging from astronomy and remote sensing, polarization detection and imaging, quantum information and optical communication to molecular biological analysis [1,2]. However, applications of the conventional polarization-related optical systems, which comprise many bulky and monofunctional optical elements with precise alignment, are still limited because of the strict requirements on cost, weight, and volume. Metasurfaces are ultrathin planar structures composed by artificial unit cells with subwavelength dimensions [3–5]. Because of the superiority in arbitrary manipulating the local polarization, amplitude and phase of the scattered light at the subwavelength scale [5,6], metasurface provide a promising solution that would enable device miniaturization, system integration and photonic multitasking [3,7–9]. Moreover, various novel applications related to a synchronous rotation of the polarization direction of incident light while wavefront shaping were proposed. For example, image encoding and decoding for information encryption and authenticity verification [5,10], vectorial holographic generation for enhanced security and added data storage capabilities [11–13], and multi-foci metalens with polarization-rotated focal points for optical isolation [14].

Unfortunately, a common approach to achieve the aforementioned applications is based on the scheme of phase-nondispersive Pancharatnam-Berry (PB) geometric phase. Due to the intrinsic spin symmetry, the PB phase shifts of the LCP and RCP lights are with same value but opposite sign [2,15–17]. Thus, to fully control the wavefront of an LP incident light, two interleaved unit cell subarrays are usually employed in the metasurface [11,18,19]. This enables to achieve equal phase profiles for the LCP and RCP light components, leading, however, to unavoidable loss of pixels and low energy efficiency. Moreover, theoretical focusing efficiency of linearly polarized incident light with focusing lenses cannot exceed 50% because of the spin-flipped components of RCP and LCP light are attributed to the phase profiles of a convex and a concave lens, respectively [14]. Qingbin Fan, et al. [20]. and Zile Li, et al. [21]. also proposed single-cell and broadband design that combined the modulation of both geometric phase and propagation phase to achieve a spin-decoupled phase modulation. However, as the propagation phase shift involved in these designs are directly related to linear polarization state, a relative complex design need be carried out based on the relationship between linear and circular polarization states.

In this paper, a broadband and pixel-saving approach for simultaneously manipulating the polarization direction and wavefront of light is proposed based on metasurface composed by metal-insulator-metal (MIM) umbrella-shaped chiral unit cells. A quasi-non-dispersive and spin-decoupled phase shift covering 0-2π can be obtained by simply changing the central angle. By further merging the PB phase, the LP incident light beam can be converted with high efficiency into LCP and RCP reflected beams with similar amplitudes, desired phase profiles and controlled phase retardation on a nanoscale. Therefore, in principle, the wavevector, spatial distribution and polarization direction of light waves can be arbitrarily modulated by properly designing the central angle and orientation angle of each unit cell in the metasurface. To verify the validity of this strategy, two kinds of wavefront shaping devices, including a hologram generator and a vortex beam generator, with controlled polarization rotation function were created with application of proposed metasurfaces containing only one set of unit cells.

2. Results and discussions

2.1 Unit cell design

Figure 1(a) shows a schematic view of the proposed chiral unit cell consisting of three layers, namely an umbrella-shaped aluminum (Al) top layer (50 nm), a silicon dioxide (SiO₂) spacer (200 nm) and a bottom layer of Al mirror (200 nm). The inner radius r₁, outer radius r₂ and length l of the umbrella-shaped structure as well as the period of their location p are equal to 160, 230, 460 and 700 nm, respectively. The handle of the umbrella-shaped structure has the same width (70 nm) as its arms. Central angles α and β determine the lengths of the left and the right arm, respectively. The unit cell considered in this work was designed as a broadband and highly efficient mirror ensuring preservation of both left- and right-handed CP states in the wavelength range of 1.3-2 µm. Its optical properties were simulated, the details of the simulation method can be found in the Materials and Methods section.

 

Fig. 1. (a) Schematic illustration of the proposed reflective-type umbrella-shaped unit cell. (b) Simulated reflectance of the unit cell with α=40° and β=60°. Simulated color maps of (c) R_RR, (d) R_LL, (e) ellipticity η of the superposed light, (f) φ_LL, (g) φ_RR and (h) phase retardation δ in the light wavelength - value of α coordinates. Here, β is fixed at 60°, while α varies from 20° to 160°.

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According to the definition of circularly polarized light, the electric field vector of LCP and RCP rotates clockwise and counterclockwise respectively when observes against the propagation direction of the light. Therefore, the circularly polarized incident light will flip the absolute rotation direction of the electric field (or spin state) upon reflection, thus preserving its circular polarization state as the wavevector is also reversed [22]. Since PB geometric phase shifts originate in the process of circular polarization conversion (i.e., spin-flipping), high reflectance of spin-flipping component is essential. Figure 1(b) shows the dependence of the simulated reflectance of the components of light reflected from the unit cell under study, on the light wavelength at fixed values of α=40° and β=60°. As can be seen from this figure, the results of simulations demonstrate that the reflected light contains both spin-preserving (R_RL (LCP→RCP) and R_LR (RCP→LCP)) and spin-flipped components (R_LL (LCP→LCP) and R_RR (RCP→RCP)). As further shown in Fig. 1(c) and (d), at the values of the central angle α in the range of 20°-160° and the constant value of β=60°, the reflectance of the spin-flipped components exceeds 0.7 almost in the entire wavelength range except for the wavelengths corresponding to the weak resonances (such as α=80° at 1.55 µm). Nevertheless, the values of reflectance near the weak resonances are remained above 0.5. Here, one needs to notice that the materials and structure parameters are chosen considering the preparation difficulty and cost. The reflectance can be greatly improved by changing the metallic material from aluminum to gold, and utilizing optimized the structure parameters (see Fig. S1 in Supplement 1). In addition, the values of R_LL and R_RR of the unit cell with equal α are roughly equal in the entire wavelength range. Considering the superposition of the spin-flipped components of reflected light, its ellipticity η can be calculated by the intensity ratio τ of LCP and RCP components as follows [23]:

The values of η equal to 1, 0 and -1 correspond to the RCP, LP, and LCP state, respectively. As shown in Fig. 1(e), the absolute value of η for the unit cells under study does not exceed 0.05, indicating the polarization state of the superposed light can be approximated as a linear polarization state.

Then, the polarization direction of the superposed light is considered. Any linearly polarized light beam with the polarization direction φ with reference to the x-axis as shown in Fig. 1(a) can be decomposed into the superposition of two orthogonal CP light components with equal amplitude, and this superposition can be expressed via the Jones vector as follows:

This formula can be rewritten as

We may conclude from the expression (3) that LP light beam with the polarization direction φ with reference to the x-axis is a superposed light of two orthogonal CP light components with phase retardation δ=2φ [24].

As shown in Fig. 1(f) and (g), owing to the spin-dependent response of the chiral structure [25,26], the phase of R_LL and R_RR can be independently modulated by the central angle α (corresponding to the length of left arm) and β (corresponding the length of right arm). At the increase of the central angle α and the constant value of β, φ_LL (the phase of R_LL) varies from 0 to 360°, and the curves of phase-angle of different wavelengths are parallel, while φ_RR (the phase of R_RR) remains nearly constant at the same wavelength. Moreover, as the unit cells were designed non-resonant or weakly and low-Q resonant as shown in Fig. 1(d), the phase shift φ_LL is quasi-non-dispersive in the considering wavelength range [27]. The phase retardation δ is nearly independent from the wavelength and can vary from -180° to 180° with the change of the central angle α (see Fig. 1(h). Therefore, nearly non-dispersive arbitrary rotation of polarization direction can be realized by choosing proper value of α.

Based on the possibility to flexibly manipulate φ_LL and δ as described above, a strategy to realize broadband wavefront shaping with controlled rotation of polarization direction by using metasurface composed by only one set of unit cells is proposed as shown in Fig. 2. A chiral structure with desired phase retardation δ is chosen as an initiator. After interacting with such initiator, the polarization direction of the incident LP light is rotated by an angle δ/2. By rotating the initiator by an angle θ, non-dispersive PB phase shift ±2θ is obtained for R_LL and R_RR, respectively. On the other hand, change of the value of α induces a phase shift φ_LL to R_LL. Here, the phase shift φ_RR is negligible as the phase of R_RR is mainly dominated by the value of angle β (fixed at 60°). When these phase shifts satisfy Eq. (4), the two spin-flipped components will be imposed the same phase shift value.

Thus, accurate design of the unit cell ensuring proper values of the phase retardation δ of initiator, the central angle α, as well as correct choice of the rotation angle θ of the unit cells in the metasurface enable to obtain the metasurface with desired phase profile and polarization rotation of LP light. It should be noticed that only the spin-flipped components are considered. Therefore, phase gradients, leading to a generation of off-axis deflections should be addressed in the metasurface design to minimize the influence of R_LR and R_RL.

 

Fig. 2. (a) Illustration of a metasurface beam splitter to show the spin-decoupled ability of metasurface based on spin-dependent phase manipulation. (b) Schematic representation of the phase manipulation of LP light by metasurface with polarization rotation function. The initiator provides a phase retardation δ between LCP and RCP components to control the polarization rotation angle of the composite LP light. PB phase and spin-decoupled phase are involved to impart the same phase shifts to the spin-flipping components.

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2.2 Polarization-independent hologram with polarization rotation function

Vectorial holography is a special kind of holography in which holographic images with multiple arbitrary polarization states can be diffracted [11–13]. Our proposed strategy provides an alternative and simple approach to implement vectorial holography utilizing only one set of meta-atoms and modulating only two structural parameters. As an experimental proof of the possibility to obtain holographic imaging utilizing polarization rotation function, we present a hologram metasurface with polarization rotation angle of 45° designed and fabricated with the use of umbrella-shaped unit cells. Considering both the image fidelity and fabrication cost, the pixel number was chosen as 300×300 and leaded to an image angle of about 51° [22]. A scanning electron microscope (SEM) image of the sample metasurface and the experimental setup are shown in Fig. 3(a) and (b), respectively. Detailed information on the experimental procedure can be found in the Materials and Methods section.

 

Fig. 3. (a) SEM image of the fabricated metasurface hologram generator (scale bar: 1 µm). (b) Schematic illustration of the experimental setup for reconstruction of holographic images. L: lens; P: polarizer; QWP: quarter-wave plate. (c) Theoretical reconstructed image. Reconstructed images are obtained under the incidence of (d) CP light and (e) arbitrary LP light with the wavelength of 1550 nm (without P₂). (f) Reconstructed images obtained with polarization analyzer P₂ under the incidence of the light polarized in x-direction. Polarization direction of the incident (reflected) light is indicated by a blue (yellow) double-headed arrow. (h) Phase retardation between R_LL and R_RR of the initiator versus wavelength of incident light.

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Figure 3(c) shows the theoretical reconstructed image. The phase profile Φ(x,y) of the target image was calculated using the Gerchberg-Saxton (GS) algorithm for the phase-only hologram. Phase gradients along the x-axis were introduced to provide a 20° deflection of the holographic image to avoid the influence of the spin-preserving components [28].The initiator with the central angles α=80° and β=60° was used to provide a phase retardation δ=45°. The value of φ_RR (the phase of R_RR) at each pixel was modulated by the rotation angle θ of each unit cell in the metasurface. The value of θ(x,y) was equal to Φ(x,y)/2. The value of φ_LL (the phase of R_LL) at each pixel was modulated by changing the central angle α of each unit cell, and φ_LL=2Φ(x,y). The structural parameters of each unit cell were designed according to the respective relationship between the central angle α and φ_LL′ (φ_LL of unit cell with each α minus the φ_LL of initiator) at 1550 nm as the phase shift is quasi-non-dispersive.

We studied first the dependence of the image reconstruction on the polarization state of incident light. Unlike the broadband polarization-sensitive hologram generator based on the propagation phase metasurface, the hologram generator proposed here is polarization-insensitive owing to that any LP state can be decomposed into two orthogonal CP states. In addition, only two parameters need be adjusted simultaneously, which greatly simplifies the design [29,30]. As the image size increase rapidly due to the large image angle, only part of the reconstructed image can be observed due to the bulky size of the lens or splitter. As shown in Fig. 3(d) and (e), similar reconstructed images of a part of the word ‘NWPU’ are observed at 1550 nm wavelength of incident light, no matter whether it is linearly or circularly polarized. Moreover, the broad operation band of the fabricated metasurface was confirmed. Namely, similar reconstructed images were observed at the 1245, 1300 and 1450 nm wavelengths of the incident light (see Fig. S2 in Supplement 1). In addition, the holographic efficiency of the device cannot be directly obtained through the test since only part of the holographic image can be received. Nevertheless, the efficiency of the hologram and the ellipticity of the superposition light were roughly estimated by taking the weighted average of the simulated reflectance of each unit cell contained in the sample (see Fig. S3 in Supplement 1). Results show that the values of average reflectance of R_LL, R_RR and the ellipticity at the central wavelength (1550 nm) are 0.68, 0.71 and 0.009, respectively. As mentioned in Section 2.1, these values can be improved by using metallic materials with lower loss in this wavelength range.

Then, the rotation of polarization direction was controlled by placing a polarization analyzer P₂ before the camera (see Fig. 3(f)). Under the incidence of LP light with the wavelength of 1550 nm, the reconstructed image changed from clear to vague, then almost disappeared, and then became clear again upon rotation of polarizer. In addition, clear image with the highest precision and without distortions was obtained at the angle between the analyzer P₂ and polarizer P₁ close to -45°. The image nearly disappeared when this angle was close to 45°, which corresponded to the phase retardation as shown in Fig. 3(g). In addition, we have done some estimation and simulation to verify the device performance. A metasurface hologram with 50×50 pixels was simulated (see Fig. S4 in Supplement 1). This phenomenon demonstrates the polarization rotation ability of the proposed metasurface. Due to the considerably small number of pixels (300×300) contained in the metasurface, the phase and amplitude deviation between the design and ideal modulation required by the hologram, the fabrication imperfections and the oxidation of aluminum structure, the intensity in the observed image is distributed not uniformly over the letters. The quality of the image may be improved by increasing the quantity of pixels and optimizing the reflectance and phase of each pixel.

2.3 Generation and superposition of optical ring vortex beams

Recently, generation and superposition of optical vortex beams carrying orbital angular momentums (OAMs) have become a hot topic of research for applications in both classical physics and quantum science. Various exciting applications, including high-capacity optical communications, OAM microlasers, optical quantum memories, optical tweezers, improved focusing elements, and ultrasensitive angular measurement applications have been proposed. In this paper, we demonstrate that the strategy proposed here can be also used to generate arbitrary optical vortex beams carrying OAMs and superposition of different OAM states.

To generate ring-shaped OAM beams and realize their superposition, two different types of phase profiles for the LCP and RCP light were designed combining a vortex beam generator, an axicon and a beam deflector. These phase profiles can be described by the following equations [31]:

Here, l₁ and l₂ are the topological charges (TCs) of the generated ring vortices under RCP and LCP incident light, respectively, γ=20° is the off-axis deflection angle, and d=10 µm is the period of axicon related to the radius of the generated ring vortex beam, respectively. Similar parameters of the unit cell design to the ones mentioned in the Section 2.2 were used, but with θ(x,y) =φ_R(x,y)/2, φ_LL=2φ_L(x,y), and the central angle α of the initiator chosen to be 60° (for δ=0°), 80° (for δ=45°) and 108° (for δ=90°), respectively.

First, ring vortices with different TCs under RCP and LCP incident light (l₁=-1 and l₂=2) were generated by the metasurface. The phase retardation between the R_LL and R_RR was taken to be 90° (i.e. the polarization rotation angle was 45°). The electric field distributions under different incident lights were simulated. Then the far-field diffraction spots were calculated based on the vector diffraction theory. The details of the simulation method can be found in the Materials and Methods section. As shown in Figs. 4(b(i)) and (b(ii)), the annular intensity patterns of the ring vortex beams under the RCP and LCP incident light with the wavelength of 1550 nm are consistent with respective theoretical patterns. Moreover, the patterns obtained at the light wavelengths of 1350, 1450, 1650, 1750 and 1950nm are similar to the ones corresponding to 1550 nm, which proves the ability of a quasi-non-dispersive phase manipulation of the proposed metasurface.

 

Fig. 4. (a) Theoretical phase profiles and intensity patterns produced under the RCP and LCP incident light with the wavelength of 1550 nm, respectively (l₁=-1, l₂=2). (b) Simulated intensity patterns for the metasurface with polarization rotation angle of 45° at different wavelengths of the (i) LCP and (ii) RCP incident light and (iii) incident light with x-polarization direction and filtered out y-component of output electric field.

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As the subsequent step, the polarization property of the superposition of the two ring vortices was simulated. According to the previous report, when the incident light has an elliptical or linear polarization state, the number of dark gaps in the annular spot of superposed light obtained after passing through the LP analyzer is determined by |l₁ − l₂| [31]. Figure 5 presents a comparison of the spots of the superposition obtained for different TC values and with different polarizers and analyzers. As shown in Figs. 5(a(v)) and (a(vi)), when incident light is polarized in the x-direction, three dark gaps are obtained in the simulated intensity patterns after filtering out the polarization components in the x- or y-direction.

 

Fig. 5. (a) Theoretical phase profiles and intensity patterns obtained at the wavelength of the incident light of 1550 nm (l₁=-1, l₂=2). Theoretical phase profiles of (i) LCP and (ii) RCP components. Simulated intensity patterns obtained for the metasurface with polarization rotation angle of 45° under the (iii) RCP and (iv) LCP incident light with the wavelength of 1550 nm, respectively. (v) Simulated intensity patterns obtained at the x-polarization direction and filtered out (v) x- and (vi) y-components of output electric field at the wavelength of 1550 nm. (b) Theoretical phase profiles and intensity patterns obtained at the wavelength of incident light of 1550 nm (l₁=-2, l₂=2). Theoretical phase profiles of (i) LCP and (ii) RCP components. Simulated intensity patterns obtained for the metasurface with polarization rotation angle of 45° (iii) at the x-polarization direction and filtered out x-component of output electric field and (iv) at the y-polarization direction and filtered out y-components of output electric field. Simulated intensity patterns observed for the metasurface with polarization rotation angle of (v) 0° and (vi) 90° at the x-polarization direction and filtered out x-components of output electric field.

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Furthermore, the polarization property of a superposition generated by RCP (l₁=-2) and LCP (l₂=2) vortices with different phase retardations was simulated. As shown in Figs. 5(b(iii)) and (b(iv)), at the value of the phase retardation equal to 90°, the same intensity patterns can be observed in the case of x-polarization direction of incident light /filtering component with x-polarization direction and y-polarization direction of incident light / filtering component with y-polarization direction. When the phase retardation value changes from 0° to 180°, the intensity patterns obtained in the case of x-polarization direction of incident light / filtering component with x-polarization direction rotate by nearly 45°, which is consistent with previous reports (see Figs. 5(b(v)), (b(iii)) and (b(vi))). Therefore, based on the proposed strategy, it is possible to achieve multiple vortices, including vortex beams possess OAMs and higher order superpositions.

3. Conclusion

In conclusion, a strategy to simultaneously manipulate the polarization direction and the wavefront based on application of a spin-decoupled metasurface composed by reflection-type chiral umbrella-shaped unit cells is proposed. Therein, non-resonant or low-Q and weakly resonant chiral unit cells were designed for negligible circular dichroism and quasi-non-dispersive/decoupled phase modulation. By accurate design the central angle and orientation angle of each unit cell in the metasurface, the LP incident light can be converted with high efficiency into LCP and RCP reflected beams with similar amplitudes, specific phase profiles and controlled phase retardation on a nanoscale. Therefore, high-performance polarization rotation with wavefront shaping can be realized based on metasurface composed only one set of umbrella-shaped unit cells, rather than supercells of two interleaved unit cells. To verfity the proposed strategy, a hologram generator, and a generator of multiple ring vortex beams with controlled polarization rotation function were designed based on the proposed metasurface. This work shows promising approach to achieve polarization-related waveshaping devices without compromising the number of pixels and energy efficiency as well as having broadband operation range.

4. Materials and methods

4.1 Simulation methods

Numerical simulations of meta-atoms and metasurfaces were performed using the finite element method. The periodic and open boundary conditions were applied in the x- and y-directions, and the wave-guide port boundary condition in the z-direction, respectively, in the unit cell and metasurfaces simulations. Circularly or linearly polarized light was normally incident in the positive direction of the z-axis in all the simulations. The permittivity of Al was obtained from Palik [32], and the refractive index of SiO₂ was taken to be 1.5.

4.2 Sample fabrication

The metasurface for hologram generation was fabricated by electron beam evaporation (EBE, Kurt J. Lesker LAB line PVD 75), plasma enhanced chemical vapor deposition (PECVD, Oxford PlasmaPro 100 PECVD), and electron-beam lithography (EBL, JEOL JBX-9500FS at 100 keV), followed by the lift-off process. First, an aluminum (200 nm) and a silicon dioxide (80 nm) films were sequentially deposited onto a silicon substrate using EBE and PECVD. Then, after spin-coating of a positive ZEP520A electron-beam resist (100 nm), the sample was undergone a standard EBL process with developing time of 150 s to form a pattern mask. Finally, an aluminum film (50 nm) was deposited by the EBE process. The remaining resist was removed with acetone to obtain the final metasurface.

4.3 Experimental test

The sample was tested using a laboratory made optical system. A fiber laser operating at the wavelength of 1550 nm was used as the light source in the measurements. After being collimated, the light passed through a lens (f=75 mm) and a polarizer (or a polarizer and a quarter-wave plate) to generate normally incident linearly (or circularly) polarized light to irradiate the sample. The size of the reflection holographic image was adjusted by using a 4f system with two lenses (f=75 mm), and finally detected by a short-wavelength infrared camera (Leading 640 SWIR camera LD-SW6401725-CTE2-G, operation range of 900 to 1700nm) with an active area of 16 × 12.8 mm and a pixel size of 25 µm.