Circularly Polarized Spoof Surface Plasmon Polariton Beam Splitter Based on Transmissive Spin‐Decoupled Metasurface

Circularly polarized (CP) spoof surface plasmon polariton (SSPP) functional metadevices, especially those with spin decoupling and hybrid modes, play an important role in modern photonics applications. However, currently available SSPP functional metadevices have the defect of restricted functionalities and single‐working modes for a given polarization, as it is a great challenge to simultaneously support SSPPs with hybrid modes and different wavefronts. Herein, a general strategy is proposed for designing CP SSPP functional metadevices with spin decoupling and hybrid modes based on transmissive spin‐decoupled metasurfaces and angle‐insensitive anisotropic SSPP eigenmode plates (EMPs). The metasurface can simultaneously and independently control the resonant and geometrical phases of the CP waves, and the SSPP EMP satisfies the hybrid‐mode (both transverse magnetic [TM] and transverse electric [TE] modes) momentum matching with high angular/momentum stability of the propagating SSPPs. For verification, a CP SSPP beam splitter is designed, fabricated, and experimentally demonstrated, which can convert incident right‐handed (R) and left‐handed (L) CP plane waves to CP hybrid‐mode SSPP deflected beams and decoupled beams, respectively. The work paves the way for the realization of CP SSPP multifunctional‐integration metadevices with hybrid modes and other functionalities, which can find extensive applications in different frequency domains.

Therefore, it is of great interest to achieve SSPP functional metadevices with arbitrary wavefronts and modes, which are schematically shown in Figure 1a,b. As a special case, wavefront reshaping of transverse magnetic (TM)-mode SSPPs has been investigated through plasmon metal plates and additional reflective gradient metawalls. [43] Moreover, reflective spin-coupled Pancharatnam-Berry (PB) metasurfaces have been introduced in another study [44] to realize functional metadevices with TM-mode SSPP wavefront control. But both of them can only work for TM operating mode and cannot implement SSPP functional integration on a single-planar device, which is disadvantageous for highly integrated modern devices. Recently, bifunctional SSPP metadevices were realized by a kind of reflective spin-decoupled PB metasurface, which can efficiently generate TM-mode SSPPs with arbitrarily controlled and integrated wavefronts. [45][46][47] Then, based on the anisotropic transmissive metasurface, a bifunctional SSPP metacoupler has also been proposed to generate TM-mode SSPP Bessel beams and transverse electric (TE)-mode SSPP focusing beams under excitation of x-polarized and y-polarized waves, respectively. [48] Nevertheless, to the best of our knowledge, SSPP functional metadevices are still single-mode devices with arbitrary wavefronts under a given incident polarization, since simultaneously supporting SSPPs with hybrid modes and different wavefronts under a given polarization exists great challenges (i.e., the momentum mismatch). [48] In this article, we use the transmissive spin-decoupled metasurfaces and the angle-insensitive anisotropic SSPP EMPs to design CP SSPP functional metadevices with spin decoupling and hybrid modes. As an example, a CP SSPP beam splitter in the microwave regime is experimentally demonstrated, as schematically illustrated in Figure 1c. This splitter can efficiently convert incident RCP and LCP plane waves into CP hybrid-mode SSPP deflected beams and SSPP-decoupled beams, respectively. The metasurface has been assembled to satisfy the required spindecoupled SSPP phase distributions by simultaneously and independently controlling the transmissive resonant and geometrical phases of the CP waves. Moreover, the angle-insensitive anisotropic SSPP EMP is used to match the hybrid-mode momentum of the spin-decoupled SSPP via its high angular/momentum stability to SSPPs from different propagation directions. The proposed strategy could be used to achieve a series of CP hybrid-mode SSPP metadevices with many other wavefronts and would also find extensive applications in other spectrum. As we all know, for any desired SSPP metadevice implemented by a metasurface, it is necessary to design the metasurfaces to excite the surface waves and design the SSPP EMPs to support the SSPP propagation. Therefore, we describe our strategy for designing such SSPP metadevices from these two aspects. On the one hand, to generate the SSPP and tailor its EM wavefront flexibly, metasurfaces are required to fulfill the 2D phase profile Φðx, yÞ ¼ ξ x x þ φðyÞ on x-y plane, where ξ x is the phase gradient along x-direction with ξ x > k 0 (k 0 is the free-space wave vector) and φðyÞ is the phase function along y-direction. By configuring ξ x and φðyÞ, the wave vector k sspp and wavefront shape (e.g., SSPP deflecting beam, Bessel beam, and focusing beam) of the formed SSPP can be adjusted arbitrarily, respectively. Moreover, to integrate CP hybrid-mode SSPPs with two different functions on a single metadevice when illuminated with different-helicity CP waves, the metasurfaces have been assembled to many different spin-decoupled meta-atoms, which exhibit different phase distributions for LCP and RCP incident waves. The comprehensive phase profiles on the metasurfaces can be denoted as

Principle and
where Φ LCP ðx, yÞ and Φ RCP ðx, yÞ are the phase profiles on the metasurfaces for CP waves with two different helicities, and φ LCP ðyÞ and φ RCP ðyÞ are the corresponding functional phases. On the other hand, to match the momentum of the hybrid-mode SSPPs with different wavefronts and support their propagation, the critical condition is that an SSPP EMP should be placed below the metasurfaces to form a two-layer metadevice in the transmission geometry, as illustrated schematically in Figure 1. Only in this way, both the TM and TE modes of SSPP can be coupled out from the metasurfaces. More importantly, the SSPP EMP must be anisotropic to support the propagation of both the TM-mode and TE-mode SSPPs, which is usually effective for typical SSPP metacoupler (details in Section A, Supporting Information). As for novel SSPP functional metadevices, the difficulty is that the dispersion of such an anisotropic SSPP EMP is usually sensitive to the travel direction/angle of the hybrid-mode SSPPs (i.e., the functional wavefront of the SSPPs), which leads to the momentum mismatch and thus cannot support the hybrid-mode SSPPs with different wavefronts very well. [45,48] To address this challenge, we design an angle-insensitive anisotropic SSPP EMP through dispersion control engineering, which satisfies the momentum matching of hybrid-mode SSPPs propagating from different directions/ angles.
To sum up, our strategy for designing CP hybrid-mode SSPP bifunctional metadevices with spin decoupling and flexible Figure 1. Schematics of the typical SSPP functional metadevices and novel CP SSPP beam splitter. a) Typical reflective SSPP functional metadevices with arbitrary wavefronts only work for TM-operating mode (Section A, Supporting Information). b) Typical transmissive SSPP functional metadevices with arbitrary wavefronts only work in TM or TE mode under a given polarization (Section A, Supporting Information). c) Novel transmissive CP SSPP functional metadevices with spin decoupling and hybrid modes. When the designed transmissive spin-decoupled metasurface on the top layer is illuminated by the RCP plane wave, a CP SSPP deflected beam is excited on the bottom-layer anisotropic SSPP EMP and flows to the left. As for the LCP incident plane wave, a CP SSPP-decoupled beam is generated and travels to the right side.
www.advancedsciencenews.com www.adpr-journal.com wavefronts is very clear: first, it is necessary to design a series of transmissive spin-decoupled meta-atoms that carry two different arbitrary phase responses under the excitations of differenthelicity CP waves, which can be achieved by simultaneously and independently controlling the transmissive resonant and geometrical phases of the two CP waves. Second, the comprehensive phase distributions of the CP hybrid-mode SSPP bifunctional metadevices should be calculated based on Equation (1) so that the transmissive spin-decoupled metasurfaces are determined. Finally, we need to design the angle-insensitive anisotropic SSPP EMP to match the momentum of the hybrid-mode SSPPs with functional wavefronts and place it at the proper distance below the metasurfaces with maximum SSPP coupling efficiency.

Spin-Decoupled Meta-Atom and Anisotropic SSPP Eigenatom Designs
Here, the Jones matrix is provided as the guideline for the meta-atom design and mechanism. As depicted in Figure 2a, the transmissive spin-decoupled meta-atom is composed of four metallic layers separated by three dielectric substrates with its main axes along x-and y-directions. For linearly polarized incidence, the EM response of such a transmissive anisotropic meta-atom is expressed as where t xx ¼ jt xx je iφ xx and t yy ¼ jt yy je iφ yy represent the transmissive coefficients when illuminated by x-and y-polarized waves, which are mainly determined by the dimensions (a and b) of the anisotropic meta-atom along its two major axes. To achieve a high-efficiency meta-atom that possesses geometrical phase, the condition of |t xx | = |t yy | = 1, φ yy Àφ xx = AE180°is required, and then the meta-atom functions as a half-wavelength plate (HWP). If the HWP (i.e., t xx ¼ À t yy ) is rotated by an angle of β with respect to the x-axis, the corresponding Jones matrix will be further transformed as follows.
Furthermore, according to the conversion relationship between LP basis and CP basis, we can obtain the CP Jones matrix T cir ðβÞ ¼ t LL t RL t LR t RR (the first/second subscript denotes the output/input CP wave, and L/R is the LCP/RCP wave), and the CP transmission coefficients can be calculated as follows.
As shown, the incident LCP and RCP waves are converted to their corresponding cross-polarized states with the cross-polarized It is worth noting that the cross-polarized CP phases are determined by both resonance and geometric mechanisms. In other words, the cross-polarized CP channels of the HWP meta-atom can be independently manipulated by the meta-atom's dimensions and orientations.
For verification, Figure 2b presents the transmission amplitude and phase spectra of a meta-atom named M2 by configuring a = 5.96 mm and b = 5 mm, which illustrates that the transmission amplitudes are near equal to each other with the relative phase difference φ yy Àφ xx = À180°at 10.5 GHz. So M2 can be regarded as a HWP meta-atom and it will carry geometrical phase under circular polarized incidences. In addition, to find a series of HWP meta-atoms with arbitrary resonant phases, Figure 2c,d shows the calculated transmission phases of the meta-atoms with varying dimensions a and b at 10.5 GHz under y-and x-polarized excitation, respectively, where HWP candidates with |φ xx Àφ yy | = 180°are marked with black dotted lines in Figure 2d. It is illustrated that the available resonant phases φ xx of HWP meta-atoms can cover the range of 2π with the high transmission amplitudes (see Figure S2a,b, Supporting Information), guaranteeing that the arbitrary wavefronts of the metadevice can be performed. Ten representative HWP metaatoms with a gradient phase of Δφ xx = 36°are choose to form a meta-atom library for metadevice design. Meanwhile, the dimensions and corresponding serial names of selected HWP meta-atoms are shown in Figure 2a.
After exploring the resonant phase, we now investigate the performance and geometrical phase of these HWP meta-atoms under circularly polarized (CP) incidences. Consider the incidence of RCP wave; the amplitude spectra of t RR and t LR are shown in Figure 2e. The incident RCP wave is converted to LCP state and the jt LR j reaches the maximum at the targeted working frequency of 10.5 GHz. The same conclusion can be drawn for the transmission of jt RL j with LCP incidence. Then, to obtain the performance and geometrical phase of these HWP meta-atoms at 10.5 GHz, Figure 2f plots the transmission phases φ RL and φ LR and their corresponding amplitudes versus the rotation angle β. Consistent with PB theory and above analysis, as β changes, φ RL and φ LR carry the geometrical phases of À2β and 2β, respectively. Moreover, cross-polarized phases φ RL and φ LR of the five HWPs exhibit an initial phase (i.e., the resonant phase φ xx ) with different values depending on the meta-atom's dimensions. So far, a series of HWPs with simultaneous and complete resonant phase and geometric phase controls is achieved.
Next, we design an angle-insensitive anisotropic SSPP EMP to support the hybrid-mode functional SSPPs coupled out from the transmissive spin-decoupled metasurfaces by matching the momentum of the hybrid-mode SSPPs. The anisotropic SSPP eigenatom contains a sandwich structure with very small anisotropy, since its dimensions and dispersion relation have been elaborately optimized through dispersion engineering. The dimension difference between a x and b y of the eigenatom is as small as possible. Figure 2g shows the dispersion curve of the anisotropic SSPP eigenatom with both the TM-and TE-mode wavevector k sspp ¼ 1.12k 0 at 10.5 GHz to match the phase gradient of the spin-decoupled CP metasurfaces. Moreover, with the www.advancedsciencenews.com www.adpr-journal.com wavevector k sspp keeping 1.12k 0 , Figure 2h depicts both the TM-and TE-mode eigenfrequencies of the anisotropic eigenatom with different rotation angles (i.e., different travel directions of SSPP). The results illustrate that the eigenfrequencies almost do not change with the rotation angle, so the momentum of this anisotropic eigenatom always matches the hybrid-mode functional SSPPs that exhibit different propagation angles. Such characteristics pave the basic step to support the propagation and the further manipulation of the orthogonal output hybrid-mode CP SSPPs with different functionalities (details in Section C, Supporting Information).

Metadevice Design and Simulation
Specifically, based on the proposed transmissive spin-decoupled metasurface and angle-insensitive anisotropic SSPP EMP, we now design a CP SSPP beam splitter that exhibits hybrid-mode SSPP deflected beams with spin decoupling for LCP and RCP incident waves. According to the principle analyzed earlier, to realize this spin-decoupled SSPP beam splitter at the center frequency of 10.5 GHz, the composite phase patterns of the anisotropic metasurface are described as where ξ x ¼ k sspp ¼ 1.12k 0 , ξ y ¼ 0.34k 0 . Employing Equation (7), the calculated phase profiles of Φ RCP ðx, yÞ and Φ LCP ðx, yÞ at each location on the metasurface occupied by a HWP meta-atom are depicted in Figure 3a,b. Then, by solving Equation (5) and (6), the relative resonant phase distributions (φ R ) and the relative geometric phase distributions (φ G ) of the HWP meta-atoms can be calculated, as depicted in Figure 3c,d. The relative resonant phase can be fulfilled with the HWP meta-atom library contributed by the dimensions a and b, and the relative geometric phase can be satisfied by the HWP meta-atom's rotation angles β. As a result, based on Equation (5)-(7) and the EM response of the meta-atoms shown in Figure 2, we calculate the structural parameters aðx, yÞ, bðx, yÞ, and βðx, yÞ of the metasurface (see details in Figure S2, Supporting Information). After designing the metadevice, we then employ the finite-difference-time-domain (FDTD) method to demonstrate the theory predictions of our CP SSPP beam splitter. When illuminating an RCP wave on the top-layer metasurface, Figure 4a,e shows the simulated ReðE z Þ and ReðH z Þ field distributions on a reference plane (xÀy plane) 6 mm above the SSPP EMP, respectively. The field distributions demonstrate a good deflection beam effect and the beam flows to the left side with an oblique direction about 17.5°. Meanwhile, Figure 4c,g respectively shows the simulated ReðE z Þ and ReðH z Þ field patterns on the left-side xoz plane, which clearly illustrate that the illuminated RCP plane wave is coupled to a very well-defined SSPP. The coupled SSPP shows an obvious local field enhanced effect, and its wave vector agrees well with the theoretical one. For LCP incident waves, similar hybrid-mode SSPP deflected beam effects can be observed with the field patterns illustrated in Figure 4b,d,f,h. It is worth noting Figure 3. Design of the circular-polarized SSPP beam splitter. a,b) Theoretically calculated composite phase profiles of (a) φ RCP and (b) φ LCP encoded in the designed metasurface for circular-polarized SSPP beam splitter manipulation. c,d) Distributions of (c) resonant phase φ R and (d) geometrical phase φ G on the proposed metasurface calculated by Equation (5) and (6). www.advancedsciencenews.com www.adpr-journal.com that the excited hybrid-mode-decoupled SSPPs are deflected to the right and have the same oblique direction as the left SSPP beams due to the spin-decoupled metasurface, which is in good agreement with theoretical predictions and principles.

Experimental Verification
Finally, as depicted in Figure 5a, the near-field wave-manipulation performances of this CP SSPP beam splitter have been also experimentally demonstrated in a microwave anechoic chamber. Metadevices composed of a transmissive spin-decoupled metasurface and an angle-insensitive anisotropic SSPP EMP were fabricated with printed circuit board (PCB) technology (details in Section D, Supporting Information). The metasurface contains 12 Â 30 HWPs with a total size of 102 Â 255 mm, and the SSPP EMP occupied a total area of 442 Â 255 mm is placed below the metasurface, separated by four media screws. In particular, each column of the fabricated metasurface contains a HWP supercell, which has different rotation angles β along the x-axis to generate the phase gradient AEξ x contributed by the geometric phase. At the same time, each row contains a HWP meta-atom array with different dimensions a and b to yield the phase function φðyÞ of the resonant phase contribution.
In the experiment, the near-field scanning technique was adopted to measure both the ReðE z Þ and ReðH z Þ field distributions on different planes. We first measured the field distributions on xoy plane. A CP horn antenna connected port 1 of the vector network analyzer (Agilent E8362C VNA) to emit EM waves to spin-decoupled metasurfaces and the scanning monopole (coil magnetic) probe connected port 2 of VNA to test the locally enhanced ReðE z Þ (ReðH z Þ) field distributions of the TM-mode (TE-mode) SSPP, which were placed 6 mm above the SSPP EMP. As for the detection regions, when RCP (LCP) waves were irradiated on the metasurfaces to generate hybridmode SSPP deflected (decoupled) beams, the field distributions were measured at the left (right) side of the metadevice with a range of 170 mm Â 255 mm (the range of z distance is from 0 to 30 mm). Figure 5b,d respectively shows the experimentally measured ReðE z Þ and ReðH z Þ field patterns on the xoy plane at 10.5 GHz. Next, using an identical experimental setup with that of the xoy plane, the field distributions ReðE z Þ and ReðH z Þ on xoz plane of the metadevice were also investigated, as shown in Figure 5c,e, respectively. In addition, measured cross-channel fields of the SSPP deflected (decoupled) beams on the right (left) side of both xoy and xoz planes have been investigated under RCP (LCP) incidence. Compared to the results of the main channel, the cross-channel fields are very weak, which substantiates that the SSPP deflected (decoupled) beams only appear on the expected side with high efficiency (see details in Figure S5, Supporting Information). To sum up, the measured field distributions in Figure 5 and S5, Supporting Information, clearly demonstrate the expected helicity-dependent hybridmode SSPP deflection beam manipulations of our splitter. At the targeted working frequency of 10.5 GHz, most incident RCP waves generate the CP SSPP deflected beams with hybrid modes on the left side of the metadevice; meanwhile, most LCP waves generate the CP hybrid-mode SSPP-decoupled deflected beams on the right side with a same oblique angle, which are consistent with both theoretical calculations and FDTD simulations. The deflection angle of the hybrid-mode SSPP deflected and decoupled beams is %17°, which is consistent with the theoretical design θ d = sin À1 (ξ y /k sspp ) = 17.7°(details in Section E, Supporting Information).
Moreover, the coupling efficiency of our proposed SSPP beam splitter can be quantitatively calculated by the absorption rate and scattering rate. [5,39] After corresponding analysis and far-field experiments, the measured maximum coupling efficiency is %73.9% at 10.5 GHz (details in Section F, Supporting Information), which indicates the high-efficiency performance of this SSPP metadevice. It is worth noting that the distance d between the spin-decoupled metasurface and the anisotropic SSPP EMP has a significant impact on the SSPP coupling efficiency, and the maximum coupling efficiency is achieved when d = 10 mm (details in Section G, Supporting Information). www.advancedsciencenews.com www.adpr-journal.com

Conclusion
In this article, a strategy to design CP hybrid-mode SSPP multifunctional metadevices is proposed, which is achieved by transmissive spin-decoupled metasurfaces and angle-insensitive anisotropic SSPP EMPs. To verify, we experimentally demonstrate a CP hybrid-mode SSPP beam splitter that can couple irradiated RCP and LCP waves into CP hybrid-mode SSPP deflected beams and decoupled deflected beams, respectively. Furthermore, many other wavefront shapes, such as SSPP focusing beams and Bessel beams, could be integrated on the CP hybrid-mode SSPP metadevices. The exploration of simultaneously supporting SSPPs with hybrid modes and different wavefronts could give rise to a series of SSPP functional metadevices and stimulate their potential applications, including on-chip photonics, near-field sensing, and super-resolution imaging.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.