Fundamentals and applications of spin-decoupled Pancharatnam–Berry metasurfaces

Abstract

Manipulating circularly polarized (CP) electromagnetic (EM) waves at will is significantly important for a wide range of applications ranging from chiral-molecule manipulations to optical communication. However, conventional EM devices based on natural materials suffer from limited functionalities, bulky configurations, and low efficiencies. Recently, Pancharatnam–Berry (PB) phase metasurfaces have shown excellent capabilities in controlling CP waves in different frequency domains, thereby allowing for multi-functional PB meta-devices that integrate distinct functionalities into single and flat devices. Nevertheless, the PB phase has intrinsically opposite signs for two spins, resulting in locked and mirrored functionalities for right CP and left CP beams. Here we review the fundamentals and applications of spin-decoupled metasurfaces that release the spin-locked limitation of PB metasurfaces by combining the orientation-dependent PB phase and the dimension-dependent propagation phase. This provides a general and practical guideline toward realizing spin-decoupled functionalities with a single metasurface for orthogonal circular polarizations. Finally, we conclude this review with a short conclusion and personal outlook on the future directions of this rapidly growing research area, hoping to stimulate new research outputs that can be useful in future applications.

Key words： spin-decoupled; Pancharatnam–Berry (PB) metasurfaces

1 Introduction

Metasurfaces, the two-dimensional artificial interface composed of subwavelength meta-atoms in a periodic or aperiodic manner, have received significant attention in recent decades because of their powerful ability to directly and locally manipulate wavefronts of electromagnetic (EM) waves [1–15]. Specifically, by engineering the meta-atoms with different resonant or non-resonant responses, the amplitude, phase, polarization at different frequency of EM waves can be tailored at will within sub-wavelength thickness. As such, the vigorously developed metasurfaces provide a versatile and flexible platform for high-density EM integration [16–18] to meet the increasing demands on the speed and memory of EM devices in modern science and technology. More importantly, metasurfaces are ideal candidates to integrate multiple diversified functionalities into single devices with deep-subwavelength thickness and high efficiencies. Among all the multi-functional metasurfaces, polarization has been widely used since polarization is uncorrelated with the other intrinsic properties of EM waves (e.g., amplitude, phase, and frequency) and thus can extend the information channels. For example, based on anisotropic meta-atoms with polarization-sensitive EM responses, various linear-polarization-multiplexed metadevices were realized at different frequencies, exhibiting multiple functionalities triggered by incident EM waves with different linear polarizations [19–23]. In addition to linear polarization states, circular polarization states or spins of EM waves have been commonly exploited as another degree of freedom to design multi-functional metadevices based on the Pancharatnam–Berry (PB) phase mechanism achieved with spatially-varied meta-atoms [24–30]. Despite remarkable achievements with PB metasurfaces, the functionalities for right circularly polarized (RCP) and left circularly polarized (LCP) beams are often locked or mirrored since the PB phase has intrinsically opposite signs for two spins. For example, PB metasurfaces can only realize free-space beam steering into symmetric directions [31,32], surface plasmon polariton (SPP) excitation to opposite directions [33–35], and vortex beam generation with opposite topological charges [36–38].

To extend the functionalities, a commonly applied scheme is to merge several different PB metasurfaces in a compact configuration, each exhibiting a certain functionality as the incident circularly polarized (CP) light takes a particular spin [27,30]. However, this merging method has intrinsic constraints, such as low efficiency and cross-talks, limiting practical applications. Very recently, the spin-locked limitation of PB metasurfaces has been released by combining the orientation-dependent geometric phase and the dimension-dependent propagation phase, thereby providing a general and practical guideline toward the realization of spin-decoupled functionalities with a single metasurface for orthogonal circular polarization states [25,39]. Based on this approach, various spin-decoupled multi-functional metasurfaces have been realized, such as spin-multiplexing holograms [25,40], arbitrary spin-to-orbital momentum converters [14,41], spin-decoupled multifocal metalenses [42–44], and spin-decoupled wavefront shaping and polarization conversion [45,46].

In this paper, we present a concise review of the spin-decoupled metasurfaces. We start by introducing the fundamentals of PB phase metasurfaces. We then briefly summarize a class of multi-functional PB meta-devices based on the “merging” concept for CP waves. After that, we present the spin-decoupled meta-devices by combining the geometric phase and the propagation phase. Finally, we conclude this review with a short conclusion and personal outlook on the future directions of this rapidly growing research area.

2 Pancharatnam–Berry (PB) phase metasurfaces

2.1 Fundamental of PB phase

We first briefly introduce the physics of the PB phase. As early as 1956, Prof. Pancharatnam noted that the spin-reversed scattering-wave can gain an additional phase factor when the planar resonator is rotated by an angle of θ concerning the z-axis [47]. Such an additional phase, later interpreted as a geometric phase by Prof. Berry in Ref. [48], exactly equals to half of the solid angle of the area surrounded by two different traces connecting south and north poles on the Poincaré sphere (Fig. 1) [49], representing the two spin-reversed scattering processes on two resonators. Thus, the PB phase, dictated solely by the spin state of input light and the orientation angle of the scatter, exhibits the attractive dispersionless feature, which is different from that of the resonance-induced counterpart.

Fig.1 Illustration of the Poincaré sphere. Reprinted with permission [49]. Copyright 2002, Optics Letter

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The easiest way to reveal the relationship between PB phase and rotation angle is to use the Jones calculus [50,51]. In general, the Jones matrix of an anisotropic scatterer can be written as [52]

(1)\left[\begin{array}{l}{E}_x^{°}\\ E_y^{°}\end{array}\right]=\mathit{R}(-\theta )\left(\begin{array}{ll}{\mathrm{e}}^{\mathrm{i}{\varphi }_x}& \mathrm{0}\\ \mathrm{0}& {\mathrm{e}}^{\mathrm{i}{\varphi }_y}\end{array}\right)\mathit{R}(\theta )\left[\begin{array}{l}{E}_x^{\mathrm{i}}\\ E_y^{\mathrm{i}}\end{array}\right].

Here E_x^{\mathrm{i}} and E_y^{\mathrm{i}} represent the x- and y-components of the input electric fields, respectively. E_x^{°} and E_y^{°} are the x- and y-components of the output electric fields, respectively. \theta is the rotation angle of the meta-atom relative to the reference coordinate system. R is a \mathrm{2}\times \mathrm{2} rotation matrix that can be used for electric field transformation in the different reference systems. {\varphi }_x and {\varphi }_y represent the phase delays of the meta-atom for polarized light along the x- and y-axes, respectively. Notably, the transmission matrix can be expressed as follows:

(2)\mathit{M}(x,y)=\mathit{R}(-\theta )\left(\begin{array}{ll}{\mathrm{e}}^{\mathrm{i}{\varphi }_x}& \mathrm{0}\\ \mathrm{0}& {\mathrm{e}}^{\mathrm{i}{\varphi }_y}\end{array}\right)\mathit{R}(\theta ).

Additionally, to independently manipulate the phase of the arbitrary orthogonal polarization states, the transmission matrix of the metasurface should satisfy [14,25]:

(3)\{\begin{array}{l}M(x,y)|{\kappa }^{+}\rangle ={\mathrm{e}}^{\mathrm{i}{\varphi }^{+}(x,y)}{|{\kappa }^{+}\rangle }^{*},\\ M(x,y)|{\kappa }^{-}\rangle ={\mathrm{e}}^{\mathrm{i}{\varphi }^{-}(x,y)}{|{\kappa }^{-}\rangle }^{*},\end{array}

where |{\kappa }^{+}\rangle =\left[\begin{array}{l}{\kappa }_{\mathrm{1}}^{+}\\ {\kappa }_{\mathrm{2}}^{+}\end{array}\right] and |{\kappa }^{-}\rangle =\left[\begin{array}{l}{\kappa }_{\mathrm{1}}^{-}\\ {\kappa }_{\mathrm{2}}^{-}\end{array}\right] represent two arbitrary orthogonal polarization states, and {\varphi }^{+}(x,y) and {\varphi }^{-}(x,y) are the corresponding modulated phase, where * denotes the complex conjugate. Hence, the transmission matrix \mathit{M}(x,y) can be reformulated as follows:

(4)\mathit{M}(x,y)=\left[\begin{array}{ll}{\mathrm{e}}^{\mathrm{i}{\varphi }^{+}(x,y)}{({\kappa }_{\mathrm{1}}^{+})}^{*}& {\mathrm{e}}^{\mathrm{i}{\varphi }^{-}(x,y)}{({\kappa }_{\mathrm{1}}^{-})}^{*}\\ {\mathrm{e}}^{\mathrm{i}{\varphi }^{+}(x,y)}{({\kappa }_{\mathrm{2}}^{+})}^{*}& {\mathrm{e}}^{\mathrm{i}{\varphi }^{-}(x,y)}{({\kappa }_{\mathrm{2}}^{-})}^{*}\end{array}\right]{\left[\begin{array}{ll}{\kappa }_{\mathrm{1}}^{+}& {\kappa }_{\mathrm{1}}^{-}\\ {\kappa }_{\mathrm{2}}^{+}& {\kappa }_{\mathrm{2}}^{-}\end{array}\right]}^{-\mathrm{1}}.

If the incident light is circularly polarized, |{\kappa }^{+}\rangle and |{\kappa }^{-}\rangle are denoted as \left[\begin{array}{l}\mathrm{1}\\ \mathrm{i}\end{array}\right] and \left[\begin{array}{l}\mathrm{1}\\ -\mathrm{i}\end{array}\right], respectively. Combining Eqs. (2) and (4), the relationship between the modulated phase and the characteristics of the local field can be obtained as follows:

(5)\{\begin{array}{l}\left|{\varphi }_x-{\varphi }_y\right|=\mathrm{\pi ,}\\ {\varphi }^{+}(x,y)={\varphi }_x+\mathrm{2}\theta ,\\ {\varphi }^{-}(x,y)={\varphi }_x-\mathrm{2}\theta .\end{array}

According to this equation, the desired phase delays {\varphi }_x, {\varphi }_y and the rotation angle \theta at any position of the metasurface can be quickly solved. The modulation phase is determined by {\varphi }_x and \mathrm{2}\theta. The propagation phase {\varphi }_x is mainly related to the material refractive index and the geometry of the meta-atom of the metasurface, and the PB phase \mathrm{2}\theta is only determined by the rotation angle of the meta-atom. Note that the modulation phases {\varphi }^{+}(x,y) and {\varphi }^{-}(x,y) are the linear combinations of {\varphi }_x and \mathrm{2}\theta. When passing through the meta-atom, the LCP and RCP light beams are transformed into their orthogonal polarization states, and they obtain the same propagation phase and an opposite PB phase. Through the linear combination of the propagation and PB phases, the independent phase control of the LCP and RCP light is achieved.

2.2 Applications of PB phase metasurfaces

PB metasurfaces have received widespread attention because of their powerful control capabilities for CP waves in different frequency domains while maintaining advantages of compactness, surface-confined configurations, multiple functionalities, and high efficiency, distinct from traditional devices based on natural metamaterials, which usually have the disadvantages of being bulky and inefficient. Capitalizing on the principle of the PB phase, numerous planar optical devices have been proposed and demonstrated, such as EM wave deflectors [53,54], planar imaging lenses [55,56], orbital angular momentum (OAM) generators [57–64], and SPP couplers [65,66].

One of the most fascinating EM wave manipulation effects based on PB metasurface is the photonic spin Hall effect (PSHE). PSHE has recently received widespread attention, but most of the mechanisms require huge systems and are very inefficient. In 2011, Hasman’s team demonstrated a plasmonic device that can compactly realize PSHE. The device is constructed by milling a 200-nm-thick gold film with a collection of nanopores distributed in a curve, whose orientations are spatially varied with \theta [67]. Their results are not only based on the anisotropy caused by coupling but also directly use nanopores with anisotropic shapes to generate the PB phase they need (Fig. 2(a)). In 2012, Huang et al. experimentally realized a plasmonic metasurface that exhibits switchable anomalous refraction for CP waves [53]. As the abrupt phase change is independent of the resonance feature of the constituent plasmonic antennas, the metasurface exhibits broadband operation with dispersionless phase discontinuities (Fig. 2(b)).

To improve the efficiency of the PB metasurface, Luo et al. realized PSHE with an efficiency of about 100% with deep sub-wavelength metasurfaces composed of metal-insulator-metal (MIM) meta-atoms in the microwave range, as shown in Fig. 2(c). The strict analysis is carried out through the Jones matrix, and the basic criteria for realizing 100% efficiency PSHE metasurface are established [31]. For the visible light, Zheng et al. designed a geometric metasurface hologram working in reflection based on MIM meta-atoms that function as broadband and highly efficient half-wave plates (HWPs) [68]. At λ = 825 nm, its diffraction efficiency can reach as high as 80%. At the same time, it has a wide operation bandwidth between 630 and 1050 nm. In this case, the 16-level phase distribution has been effectively and precisely controlled by tailoring the orientation of the corresponding meta-atoms. Since the designed metasurface has an ultra-thin and uniform thickness (only 30 nm), it can be compatible with scalar diffraction theory even at sub-wavelength pixel sizes, thus simplifying the design of holograms. This technology has been flexibly applied to optical security, laser beam shaping, and other fields (Fig. 2(d)).

Besides high-efficiency reflective PB phase metasurfaces, the PB phase has been extended to realize efficient transmissive metasurfaces. As shown in Fig. 2(e), Zhou’s research group showed that 100% efficient PSHE can be achieved in the lossless transmission PB metasurface [69]. They used the Jones matrix and effective current analysis to make a preliminary understanding and design the corresponding meta-atoms in this work. After the design, they manufactured a microwave PB metasurface and consequently proved that its PSHE efficiency can be as high as 91% through experiments. The microwave metasurface they built is based on a three-layered structure, whose total thickness is much smaller than the wavelength. This research promotes the development of PB metadevices with higher efficiency and performance in the transmission mode.

However, the high intrinsic losses of the plasmonic materials in the visible range (e.g., 400 to 700 nm) have prevented the realization of highly efficient metasurfaces in this region, which can be partially overcome by using high refractive index dielectric materials with a transparency window in the visible spectrum, such as titanium dioxide (TiO₂), gallium nitride (GaN), and silicon nitride (Si₃N₄). In 2016, Capasso’s team demonstrated the high-aspect-ratio TiO₂ metasurfaces, which can be fabricated and designed as metalenses with NA= 0.8 [4]. Diffraction-limited focusing has been successfully implemented at wavelengths of 405, 532, and 660 nm with corresponding efficiencies of 86%, 73%, and 66%, respectively. The metalenses can resolve nanoscale features separated by subwavelength distances and provide a magnification as high as 170×, with image qualities comparable to a state-of-the-art commercial objective.

Fig.2 (a) PSHE in the plasmon chain. Scanning electron microscope (SEM) images of the surfaces of the plasmons and spin-dependent momentum deviation of a metasurface. (b) Images and schematic illustrations of a refract dipole array, where the broadband anomalous refraction can be observed ranging from visible to near-infrared wavelengths. (c) Schematic diagram of achieving 100% efficiency PSHE on the reflective metasurface: the specular reflection mode disappears completely, and when linearly polarized light is incident, it will be split into two spin-polarized reflected beams that propagate in the directions of two illegal lines. (d) The circularly polarized incident beam is based on the illustration of the computer-generated hologram reflecting the nanorods. The linearly polarized beam passes through the quarter-wave plate and is converted into a circularly polarized incident beam. On the metasurface, the reflected beam forms a holographic image in the far-field. (e) Schematic diagram of 100% efficiency PSHE achieved by PB metasurfaces that meet the conditions in the transmission geometry. (f) Optical image of the metalens designed at the wavelength of 660 nm, the SEM micrograph of the fabricated metalens, and the image formed by the metalens in the transmission geometry. (a) Reprinted with permission [67]. Copyright 2011, Nano Letters. (b) Reprinted with permission [53]. Copyright 2012, Nano Letters. (c) Reprinted with permission [31]. Copyright 2015, Advanced Optical Materials. (d) Reprinted with permission [68]. Copyright 2015, Nature Nanotechnology. (e) Reprinted with permission [69]. Copyright 2017, Physical Review Applied. (f) Reprinted with permission [4]. Copyright 2016, Science

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3 Spin-decoupled metasurfaces based on “merging” concept

As mentioned above, PB metasurfaces can arbitrarily control the response of electromagnetic waves, thereby realizing various electromagnetic wave manipulation functions. Facing the increasing demands on data-storage capacity and information processing speed in modern science and technology, electromagnetic integration plays an increasingly important role, which has intrigued intensive attention with remarkable applications. A goal pursued by scientists and engineers along this development is to make miniaturized devices as small as possible yet equipped with powerful functionalities as many as possible. A simple scheme developed in the early years utilized the so-called “merged” meta-structures to design multi-functional metasurfaces. In such a scheme, people first designed the individual metasurfaces exhibiting their functions and then construct a multi-functional device simply by merging the two structures. Below we present several examples to illustrate how the scheme works.

Fig.3 Multi-functional devices designed with merged structures. (a) Illustration of the working principle. The state of the beam polarization can be detected without multiple measurements or an interferometric setup. (b) Schematic far-field intensity distribution of wavefronts with positive (red) and negative (blue) helicities emerging from segmented, interleaved, and harmonic response geometric phase metasurfaces composed of gap-plasmon nanoantennas (inset). Here, l denotes the topological charge of the spin-dependent OAM wavefronts. (c) Near-field open channels via disordered gradient metasurfaces. Schematic of directional SPP channels opened by a DGM. The scanning electron microscope image shows the \mathrm{10}\mathrm{\hspace{0.17em}}\mathrm{\mu m}\times \mathrm{10}\mathrm{\hspace{0.17em}}\mathrm{\mu m} metasurface, wherein r_{\min }=\mathrm{300}\mathrm{\hspace{0.17em}}\mathrm{nm} and d\mathrm{.520}\mathrm{\hspace{0.17em}}\mathrm{nm}, fabricated using a focused ion beam. The array consists of 80 nm×200 nm nanoantennas etched to a depth of 100 nm into a 200 nm thick gold film, evaporated onto a glass substrate. The diameter and width of the surrounding annular slit are 150 μm and 150 nm, respectively. (d) A metasurface that can generate multiple hologram images as shined by circularly polarized light with different helicity. (e) Design strategy, sample pictures, and experimental characterizations of a multi-functional metasurface that can generate holographic images or a vortex beam depending on the helicity of incident circularly polarized light. (f) Schematic of a metasurface with the interleaved design for helicity-dependent focusing and holograms. (a) Reprinted with permission [70]. Copyright 2015, Optica. (b) Reprinted with permission [36]. Copyright 2016, Science. (c) Reprinted with permission [37]. Copyright 2015, ACS Photonics. (d) Reprinted with permission [71]. Copyright 2015, Nature Communications. (e) Reprinted with permission [72]. Copyright 2017, ACS Photonics. (f) Reprinted with permission [30]. Copyright 2016, Advanced Optical Materials

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In 2015, Luo et al. proved that the reflective PB metasurface could be used as an efficient broadband polarization detector [31]. PB metasurfaces can efficiently reflect two spin components of input wave with unknown polarization to two different directions. Measuring the amplitudes and phases of these two anomalous reflection modes simultaneously, the original polarization state of the impinging wave can be retrieved. Similarly, on parallel lines, Pors et al. proposed the design and implementation of three birefringent blazed gratings based on the phase gradient metasurface in the reflection, which split orthogonal polarizations of different bases [70]. When at a wavelength of 800 nm, the relative diffraction contrast is equal to Stokes parameter of incident light (Fig. 3(a)).

Recently, Hasman’s group experimentally demonstrated that the alliance of spin-enabled geometric phase and shared-aperture concepts can open a new pathway to implement photonic spin-controlled multi-functional metasurfaces [29,36,37]. Helicity-controlled multiple wavefronts such as vortex beams carrying different OAMs were demonstrated in the visible regime (780 nm), as shown in Fig. 3(b) [36]. They also combined the peculiar ability of random patterns to support an extraordinary information capacity and the polarization helicity control in the geometric phase mechanism, simply implemented in a two-dimensional structured matter by imprinting optical antenna patterns [37]. By manipulating the local orientations of the nanoantennas, multiple wavefronts with different functionalities via mixed random antenna groups can be generated, where each group controls a different phase function (Fig. 3(c)).

As shown in Fig. 3(d), two different holograms corresponding to LCP incident light and RCP incident light are calculated by the Gerchberg-Saxton algorithm, and then encoded in the MIM structural metasurfaces after superimposition [71]. Identical silver nanorods with different orientation angles can provide nearly continuous 16-level phase profiles over the entire 2π range and provide uniform reflection amplitude by eliminating the unintended amplitude variations caused by the different sizes of the nanorods. The holograms exhibit an efficiency of 59.2% at 860 nm and over 40% over 475–1100 nm. Two reconstructed images, a flower, and a bee exhibit helicity-dependent behavior. In the computer-generated hologram, the phase shift method is used to stagger the reconstructed images.

Figure 3(e) presents an optical bifunctional metasurface that can realize a hologram image or a vortex beam, depending on the helicity of excitation light [72]. To achieve their end, the authors first design two individual metasurfaces (both utilizing the metal-bar structure as basic meta-atoms), realizing one of the needed functionalities when they are shined by incident light taking CP with different helicities. The PB principle creates the desired phase profiles on two metasurfaces through rotating the metallic bars at different positions by appropriate angles. Since the two metasurfaces exhibit identical periodic structures and there are enough open spaces between metallic bars, the authors then merge two metasurfaces to obtain the final design in which all metallic bars do not touch with each other. Such a device was finally fabricated out and experimentally characterized, showing excellent bifunctional performances. However, the working efficiency of the device is relatively low, which is found to be around 9%.

Although the multi-functional metasurfaces can be realized by “merged” meta-structures mentioned above, the metadevices also have locked and mirrored functionalities for the RCP and LCP beams, which limits the practical applications. Wen et al. proposed a metasurface with an interleaved design to realize two distinct functionalities under LCP and RCP illumination respectively [30]. The proposed metasurface combines two different metasurfaces with different optical functionalities, as shown in Fig. 3(f). For LCP illumination, the RCP wave emitting from the first metasurface reconstructs a holographic image of “cat” while the RCP wave from the second metasurface diverges and forms a subtle background. For RCP illumination, the LCP wave emitting from the second metasurface focuses on a spot while the LCP wave from the first metasurface diverges. Thus, this merged metasurface functions as a hologram and a convex lens for LCP and RCP illumination, respectively. Using the same design principle, Zhang et al. realized a light sword metasurface lens with a helicity-dependent focal segment [73]. Chen et al. proposed a kind of metalens comprised of three regions with different phase profiles [74]. Every region can be considered as a helicity-dependent sub-metalens, and these three sublenses have the same axis and different focal lengths. Thus, the proposed metasurface can focus LCP and RCP illumination into different spots.

In reviewing these meta-devices based on the “merging” concept, we find that the proposed design strategy is physically transparent and easy to implement. However, to make the “merging” process work, the adopted meta-atoms must be quite simple structures (say, metal bar) to avoid metallic overlapping. Unfortunately, these meta-atoms typically do not satisfy the 100%-efficiency criterion established for PB metasurfaces, and thus one type of meta-atoms can generate background noises in addition to the desired functionalities. As a result, such meta-devices typically suffer from the issues of low operating efficiencies and functionality cross-talking.

4 Spin-decoupled metasurface based on the combined phases

Although the integration of multiple functions can be realized with the “merging” concept, the spin-locked limitations of the PB metasurfaces still exist, thereby resulting in low efficiencies and intrinsic cross-talk. Recently, the spin-locked limitation of PB metasurfaces has been released by combining the orientation-dependent geometric phase and the dimension-dependent propagation phase, providing a general and practical guideline toward the realization of spin-decoupled functionalities with a single metasurface for orthogonal circular polarization [25,39]. Based on this approach, various spin-decoupled multi-functional metasurfaces have been realized, such as spin-multiplexing holograms [25,40], arbitrary spin-to-orbital momentum converters [14], spin-decoupled multifocal metalenses [42–44], and spin-decoupled wavefront shaping and polarization conversion [45,46].

By combining the geometric phase and the propagation phase of the reflected fields, spin-decoupled multi-functional metasurfaces have been demonstrated in reflection. In 2020, Xu et al. reported a strategy for achieving large-capacity multi-functional metasurface spin decoupling by reusing frequency and wave vector degrees of freedom, as shown in Fig. 4(a) [75]. To achieve the inherent limitation of the completely decoupled spin flipping PB phase between the two states, the researchers integrated the propagation phase and the geometric phase in an open-loop resonator and a crossbar in a checkerboard configuration. Decoupled or unlocking two spins by combining geometric phase and propagation phase is proposed as a new method [45,76,77]. Xu et al. proposed a concept of triple information multiplexer multitasking to prevent the limited system capacity. The triple information is rotation, wave vector, and frequency. Composite meta-atoms with crossbar and double gap SRRs were designed. It is characterized by a thin profile of {\lambda }_{\mathrm{0}}/\mathrm{8} even at high frequencies, and the crosstalk of modes and spins can be ignored. A kaleidoscope overclocker was designed to verify the feasibility of three-degree-of-freedom multiplexing, which was performed at two microwave frequencies. This research is carried out in the case of reflection, and this discovery can be extended to transmission geometries at multiple frequencies and other efficient achromatic devices. In 2019, Xu et al. demonstrated another kind of spin-decoupled metasurfaces, which shows the advanced property of independent wavefront control [45]. By applying the geometric phase and propagation phase of the heterogeneous and anisotropic metasurfaces, modulation can be performed separately. To combine CP versatility and extreme wavefront control in a single planar device with high work efficiency, the researchers used meta-atoms characterized by low linear polarization crosstalk. As shown in Fig. 4(b), the bifunctional device has been realized, which combines the functionalities of beam bending and focusing when the metasurface is illuminated by normally incident LCP and RCP waves. In 2019, Feng’s group proposed a reflective dual-helicity decoupled coding metasurface to realize completely independent control of OAM vortices for two orthogonal helicities, as shown in Fig. 4(c) [15]. The element combines both the propagation phase and geometric phase, thus overcoming the inherent limitation encountered by conventional geometric phase elements whose phase responses are constrained to be opposite values for different CP waves.

In 2020, Guo et al. proposed a new method for efficiently realizing independent spin control in an ultra-wideband using a spin-decoupled encoding metasurface (Fig. 4(d)) [76]. Combined with the Jones matrix, two HWPs with an intrinsic phase difference of 90° can form a 1-bit encoded metasurface, which can be used for manipulating orthogonal spins. They found a simple hybrid method, which is to rasterize when the propagation phase and geometry are the same. In this way, there can be several different meta-atoms functioning as efficient HWPs with different initial phases [77–80]. There, the operating bandwidth is broadened, and the complexity of the design is reduced because of the additional degrees of freedom. They used digital and coded metasurfaces with discrete phase elements to achieve multiple wave functions [81–83]. The researchers realized two ultra-wideband spin-decoupling meta-devices through the proposed coding elements: the first one can show different deflection angles for two spins. In contrast, the second one can create vortex beams with different topological charges when different spins are excited. The metasurface proposed here has the widest operating bandwidth for spin-decoupled wavefront control so far. It can be used in many areas, such as multi-functional low-scattering equipment in the microwave area and multi-channel metasurface antennas.

Very recently, Zhou’s group established a generic strategy to design high-efficiency metadevices that create complex vectorial optical fields with desired wavefronts and polarization distributions (Fig. 4(e)) [84]. By exploring the full capabilities of meta-atoms in controlling light polarizations and combining two different mechanisms (propagation phases and PB phases) to generate phase shifts for incident light, they designed and fabricated two metadevices working at telecom wavelengths and experimentally demonstrate their bifunctional generations of two vectorial vortex beams possessing different topological charges and distinct polarization distributions.

Fig.4 (a) Schematic diagram of a four-port multiplexer using the proposed spin-decoupled meta-atom. (b) Illustration of two completely different wavefronts: oblique planar wavefront and a focusing wavefront. (c) Schematic of a bifunctional reflective metasurface dependent on the helicity. For the LCP incidence, the reflective beams are generated to have OAM modes l=2 and l=0. For RCP incidence, two vortex beams carrying OAM modes l=1 and l=-1. (d) Schematic diagram of a meta-device designed to generate independent electromagnetic functions. (e) Left panel: schematics of light scatterings at a meta-device exhibiting vortex wavefront carrying different topological charges under illuminations of LCP and RCP incidences. Right panel: SEM images of the fabricated sample. (a) Reprinted with permission [75]. Copyright 2020, Advanced Materials Technologies. (b) Reprinted with permission [45]. Copyright 2019, ACS Photonics. (c) Reprinted with permission [15]. Copyright 2019, Physical Review Applied. (d) Reprinted with permission [76]. Copyright 2020, Annalen der Physik. (e) Reprinted with permission [84]. Copyright 2020, Nanophotonics

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The spin-decoupled metasurfaces mentioned above are mainly focused on molding propagating waves. Nevertheless, high-efficiency spin-decoupled manipulation of both propagating waves and surface waves remains so far largely unexplored. In 2020, Zhou’s Group proposed a new strategy to realize meta-devices that can efficiently and simultaneously manipulate the wavefronts of propagating waves and surface waves in a predesigned manner, with functionalities dictated by the helicity of excitation CP wave [85]. They experimentally demonstrated two kinds of meta-devices in the microwave ranges, as shown in Fig. 5(a). One can convert an input CP propagating wave to a surface wave with a wavefront depending on the helicity of the excitation CP wave. The other microwave meta-device can realize either an anomalously deflected propagating wave or a focused surface wave, upon excitations of CP propagating waves with different helicities. In the same year, Zhou's group extended this concept and experimentally achieved a similar bifunctional metasurface in the terahertz band, shown in Fig. 5(b) [86].

In 2019, Yin et al. demonstrated a kind of terahertz spin-decoupled bifunctional meta-coupler, which can realize anomalous reflection for LCP waves and convert the incident waves into the surface wave for RCP waves, as shown in Fig. 5(c) [87]. But such work just stays in theoretical calculation. In 2020, Meng et al. designed the efficient spin-decoupled multi-functional Gap Surface Plasmon (GSP) gradient metasurfaces and experimentally demonstrated simultaneous spin-controlled unidirectional SPP excitation and anomalous beam steering in the optical regime under orthogonal RCP and LCP light incidence, respectively (top panel of Fig. 5(d)) [88]. The spin-decoupled GSP gradient metasurface, consisting of rotated GSP-based nanoscale HWPs, combines both resonance and PB phases to produce two different spin-dependent linear phase gradients, thereby enabling SPP excitation and anomalous reflection simultaneously at normal incidence (bottom panel of Fig. 5(d)). The proof-of-concept fabricated metasurface exhibits broadband (850−950 nm) operation featuring efficient (>22%) unidirectional SPP excitation and high-efficiency (48% on average) anomalous beam steering for RCP and LCP incident light, respectively.

Fig.5 (a) Schematics of the proposed metasurfaces to achieve helicity-delinked manipulations on both propagating wave and surface waves, which can convert incident CP waves of opposite helicity to surface waves possessing different wavefronts and traveling to opposite directions, both exhibiting extremely high efficiencies. Numerically computed Re[E_z] field patterns on the surface of a plasmonic metal supporting a surface wave mode with an eigen wavevector are placed on the top surface of the plasmonic metal. Color maps show the phase distributions. (b) Picture of part of the fabricated sample consisting of a PB meta-device connected with two artificial metals. Simulated and measured near field pattern on a plane 50 µm underneath the sample. (c) Schematic view of the bifunctional meta-coupler that can realize circular polarization controlled unidirectional SSP excitation and anomalous reflection. (d) Left panel: schematic of the spin decoupled multi-functional GSP gradient metasurface for unidirectional SPP coupling and anomalous beam steering under normally incident RCP and LCP light, respectively. Right panel: SEM images of the fabricated spin decoupled GSP gradient metasurface and the calculated reflection phase profiles of the spin decoupled GSP gradient metasurface under RCP (red dots) and LCP (black squares) incidence at 850 nm. (a) Reprinted with permission [85]. Copyright 2020, Nanophotonics. (b) Reprinted with permission [86]. Copyright 2020, Advanced Science. (c) Reprinted with permission [87]. Copyright 2019, Optics Express. (d) Reprinted with permission [88]. Copyright 2020, ACS Photonics

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Compared to reflective devices, the spin-decoupled multi-functional metasurfaces in transmission geometry are more appealing to practical applications. In 2018, Cai et al. proposed a novel approach to design a new type of PB bifunctional metasurfaces with extremely high efficiencies in a single device by using multi-layered meta-atoms composed of metallic resonators and dielectric layers, which can operate in both transmission and reflection modes, relying on the incident chirality [89]. Due to the Lorentz reciprocal phenomenon in metasurfaces, the asymmetric transmission has been demonstrated theoretically and experimentally [90,91]. Asymmetric transmission effects can be realized by converting the incident polarization states, which provides a possibility to realize two different functions depending on the propagations of the incident waves on the metadevices. As a proof of concept, two kinds of meta-atoms under the framework of Jones matrices are designed. The former carries PB phases in both reflection and transmission schemes, while the transmission mode exhibits a reverse chirality compared with incident one. The latter keeps the handedness of incidence for RCP and LCP waves while carrying the PB phase only in the reflection scheme. Both metadevices exhibit high efficiencies within the range of 88%−94% (Fig. 6(a)). In 2020, Ding et al. proposed a transmissive metasurface based on multi-layered cascaded structures, which functionalities can be independently and arbitrarily designed for two orthogonal spin states. Geometric phase and propagation phase responses are combined to realize spin-decoupled phase tuning [92].

Even though the multi-layered meta-atoms could achieve high transmission for the spin-decoupled devices in the microwave range, it is almost impossible to be extended to the high-frequency range, such as the optical range, because of the complex transmission structure design and fabrication as well as the high absorption of metals. Therefore, all-dielectric spin-decoupled meta-devices have been proposed. In 2017, Mueller et al. proposed a new approach that combines PB and propagating phases to encode arbitrary phase profiles on any two orthogonal polarization states (linear, circular, or elliptical), and experimentally demonstrated chiral holograms based on transmissive TiO₂ metasurfaces, which can efficiently generate different far-field images for RCP and LCP excitations at λ = 532 nm (Fig. 6(b)) [25].

In 2020, Fan et al. proposed a new class of metasurface polarization optics, which enables the imposition of two arbitrary and independent amplitude profiles on any pair of orthogonal states of polarization [93]. In this research, by constructing a meta-atoms interference system and introducing two wavefront modulation mechanisms with propagation phase and geometric phase, the interaction between incident polarized light and the meta-atoms system is analyzed. Then the meta-atoms system can satisfy Jones Matrix. In this system, phase control plays an important role. It serves as a bridge to establish the relationship between polarization and amplitude. This work also proved a new class of optical devices, including chiral grayscale metasurface and chiral shadow rendering of structured light (Fig. 6(c)), which expands the scope of metasurface polarization optics, establishes the relationship between polarization and amplitude, opens a new path for multi-functional photonic integration.

In 2021, Chen et al. proposed a new route for the phase manipulation of metasurfaces based on the anisotropic dielectric nanoantennas with subwavelength height, modulating two orthogonal CP light phases independently (Fig. 6(d)) [94]. Different holograms are presented in high performances as the spin switched.

In 2020, Xu et al. proposed a general method for generating cylindrical vector beams in the terahertz range, which utilizes all-dielectric metasurfaces (Fig. 6(e)) [95]. Two circularly polarized output beams in cross-polarization are generated under circularly polarized incidence, and the two beams are superimposed with each other to achieve multiple spatially distributed beams. They have realized two metasurface cylindrical vector beam generators, among which one is for generating vector vortex beams, and the other can produce vector Bessel beams under polarized incidence.

In 2020, Huo et al. proposed a spin-multiplexed optical imaging system incorporating an all-dielectric metasurface that can perform a two-dimensional spatial differentiation operation and achieve isotropic edge detection, which can be used for either diffraction-limited bright-field imaging or isotropic edge-enhanced phase-contrast imaging (Fig. 6(f)) [96].

Fig.6 Spin-decoupled metadevices. (a) Manipulating CP waves in desired multi-prescribed manners, especially in both transmission and reflection schemes, is of particular importance. Specially tailored PB meta-atoms with helicity-dependent transmissions and reflections are used to design high-efficiency CP bifunctional metasurfaces. Two kinds of bifunctional metadevices are designed and characterized at microwave frequencies, and both exhibit remarkably high efficiencies (88%−94%). (b) Experimental demonstration of chiral holograms realized with a single TiO₂ metasurface encoding two independent hologram phase profiles for LCP (dog) and RCP (cat) at λ = 532 nm. (c) Experimentally captured optical images of the metasurface nanoprinting illuminated with LCP and RCP light. (d) Spin-decoupled holograms with chiral meta-atoms. (e) Schematic of cylindrical vector beam generation in dielectric metasurfaces. (Left) vector vortex beam generation. (Right) vector Bessel beam generation. Each schematic contains four excitation cases marked by different colors. The color maps illustrate the corresponding phase distributions, where the number represents the value of the topological charge and the carrying OAM. (f) Spin-multiplexed optical imaging system. For a light incident on the device with LCP, the metasurface imprints a masking function on the output beam resulting in a constant phase profile and a Gaussian intensity distribution and flips the handedness of the incident polarization. For a light incident on the same device with RCP, the metasurface imprints another masking function, resulting in a spiral phase profile and a donut-shaped intensity distribution, and again flips the handedness of the polarization. (a) Reprinted with permission [89]. Copyright 2018, Annalen der Physik. (b) Reprinted with permission [25]. Copyright 2017, Physical Review Letters. (c) Reprinted with permission [93]. Copyright 2020, Physical Review Letters. (d) Reprinted with permission [94]. Copyright 2021, Nano Letters. (e) Reprinted with permission [95]. Copyright 2020, Nanophotonics. (f) Reprinted with permission [96]. Copyright 2020, Nano Letters

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5 Conclusion

In summary, we have presented a brief review of the developments of spin-decoupled PB metasurfaces. We first briefly introduced the mechanism of PB metasurface and then summarized a class of multi-functional PB meta-devices based on the “merging” concept for CP waves. After that, we present the spin-decoupled meta-devices by combining the geometric phase and the propagation phase and review such kinds of spin-decoupled metasurface from two aspects of transmission and reflection geometries. Before concluding this review, we would like to mention many promising research directions on spin decoupled PB metasurfaces, based on our perspectives. We take active and tunable spin decoupled PB metasurfaces/meta-devices as an example. So far, most of the polarization-encoded metasurfaces can only achieve passive and static functionalities. Thus, it is highly desired to make tunable spin decoupled PB meta-devices exhibiting actively tunable manipulations on CP waves with fast switching speed, which is now an extremely popular topic in metasurface research.

Acknowledgements

S. Tang acknowledges the support from the National Natural Science Foundation of China (Grant No. 11604167), and Zhejiang Province Natural Science Foundation of China (No. LY19A040004). F. Ding acknowledges the support from Villum Fonden (Nos. 00022988 and 37372).

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