High‐Efficiency Pancharatnam–Berry Metasurface‐Based Surface Plasma Coupler

To excite surface plasmon polaritons (SPPs) in an ultrathin way, metasurface‐based SPP couplers are widely used for converting propagating waves into driven waves bounded on their surfaces. Among them, the Pancharatnam–Berry (PB) metasurface coupler has a strong ability to control spin‐polarized waves, but is still limited by its coupling efficiency. Herein, a PB metasurface‐based SPP coupler that can support efficient circular‐polarization conversion with both the transverse magnetic and transverse electric modes of the SPP is proposed. The coupler is composed of an upper transmissive PB gradient metasurface and a lower eigenmode board to transform a circularly polarized plane wave into left‐handed circularly polarized and right‐handed circularly polarized surface waves that propagate in opposite directions. In the experimental results, it is indicated that the directionality factor of the tested SPP coupler is 28.6. The proposed PB metasurface coupler may pave the way for future integrated optical devices with high efficiency and excellent polarization‐split properties.

However, transmission-mode PB devices simultaneously exhibiting high efficiency and multiple functionalities have rarely been observed.Alù et al. experimentally verified a planar ultrathin meta-lens using anomalous cross-polarization transmission. [34]The transmission efficiency reached approximately 25% for both the LCP and RCP beams, and the remaining 50% of the energy was reflected.In recent years, various SPP couplers [31,[35][36][37][38][39][40][41] have been developed based on metasurfaces.However, most SPP eigenmodes are transverse magnetic (TM) modes, resulting in significant energy losses.Sun et al. proposed a theory that a highly efficient directional SPP excitation can be realized using a reflective PB metasurface and a guiding-out mushroom structure. [36]The working efficiency is beam-position and beam-width dependent, and moreover, the efficiency of the converted TE mode SPP is much lower than the TM one.
In this study, we propose a novel SPP coupler composed of an upper-transmissive PB gradient metasurface and a lower eigenmode board that can overcome the aforementioned low transmission-efficiency limitations.The transmissive PB metasurface was designed to efficiently convert circularly polarized waves, whereas the eigenmode board supports the simultaneous transmission of both TE and TM modes of the SPP.Through meticulous optimization of the resonant unit cell structures with a certain dielectric constant and magnetic permeability, we achieved ideal transmissive half-wave plate characteristics, enabling the efficient singular conversion of PB unit cells under circularly polarized wave excitation.After assembling both components, we obtained an SPP coupler and experimentally verified its efficiency.

Principles and Method
Conventional PB couplers, usually consisting of a PB metasurface and an eigenmode board, always have a low coupling efficiency.Because the eigenmode board can only support the propagation of the TM-mode SPP, more than half of the incident wave energy is scattered on the eigenmode board, as shown in Figure 1a, and some of the energy generates zero-order reflections owing to the inefficiency of the PB metasurface.Figure 1b shows a schematic of the proposed SPP coupler based on a transmissive PB metasurface.The coupler consists of an upper-layer-transmissive PB phase-gradient board and a lowerlayer eigenmode board.The transmissive PB gradient board enables efficient circular-polarization conversion, whereas the eigenmode board supports the transmission of the circularly polarized mode of the SPP.The operating principle of the proposed SPP coupler is illustrated in Figure 1c.For incident waves with different rotational directions, chirality-modulated SPP waves were excited.Since the phase gradients for LCP and RCP waves on the gradient board are opposite, the excited SPP propagation will efficiently transmit to the opposite directions.Consequently, the developed SPP coupler achieved highly efficient manipulation of the SPP transmission direction.
To verify this hypothesis, we constructed an effective medium model.Here, the working frequency was set to f 0 = 10.6 GHz, and the phase gradient was ξ = AE1.12k0 , where the AE sign is determined by the circular-polarization rotation direction.
According to the efficient transmissive method, the unit cell exhibited high transmissivity and a phase difference of 180°u nder excitations of both x and y polarization.The transmissive PB metasurface unit cell was placed on the x-y plane.Therefore, the material parameters were set as ε eff = μ eff , ensuring impedance matching between the metasurface unit cell and free space everywhere.Additionally, under the two polarization states, ε xx = μ yy = 1 and ε yy = μ xx = 1 þ 0.5 ξ/k 0 were set to maintain a 180°phase difference.Subsequently, an effective medium model of the PB metasurface gradient surface was considered, assuming that the metasurface unit cell was not rotated, and its dielectric constant was As the unit cell is rotated by an angle θ along the crystal axis, the rotation matrix can be represented as . Each unit cell along Â direction will have a different rotation angle to satisfy the required phase gradient; thus, the effective medium model was developed for the PB metasurfaces at different positions.Furthermore, an effective medium model of an eigenmode board that could support both TM-and TE-mode SPP transmissions was established.The established effective medium model was simulated using the finite-element method.Figure 2 illustrates the field distribution in the x-z plane when different circularly polarized waves were excited.It is evident that the incident circular wave was efficiently converted into an SPP wave by the metasurface.Furthermore, the SPP propagation direction varies with different circular-polarization directions.It should be noted that the eigenmode board at the same height has different effects on the TE and TM modes of an SPP, as depicted in Figure 2e,f.When 1 W of power was excited in the left-side ports to generate TM-and TE-mode SPPs separately, there were noticeable differences in the signal intensity at the right-side ports.Therefore, an optimization process was required to determine the optimal height to achieve the maximum SPP conversion efficiency.In this study, the optimized conversion efficiencies under RCP and LCP excitations were found to be 92% and 91%, respectively, as shown in Figure 2a-d, respectively.
The following is the experimental verification: Equation (1) shows the high-efficiency implementation condition for transmissive PB metasurfaces.
This implies that the unit cell of a highly efficient transmissive PB behaves as an ideal transmissive half-wave plate.The optimized unit cell of the transmissive PB metasurface is illustrated in Figure 3.The unit cell consisted of a dielectric layer and metal resonant structures that were uniformly replicated above and below.The dielectric layer was composed of a Printed Circuit Board substrate FR-4 with a thickness of h = 2 mm, ε r = 4.3, and tanδ = 0.004.The resonant structures include complementary circular elements to adjust the magnetic permeability parameters of the unit cell and orthogonal cross elements to control the anisotropic behavior of the unit cell for different polarization states.The dimensions of the structure were carefully optimized to achieve perfect half-wave plate characteristics at a design frequency of f 0 = 10.6 GHz.The designed unit cell was fabricated, and the assembled sample consisted of 50 Â 50 unit cells, as shown in Figure 3b, with a total size of 400 Â 400 mm.By illuminating the metasurface sample with antennas of different polarizations and using a same-polarization antenna as the receiver, the transmitted amplitude and phase spectra of the metasurface were measured, as shown in Figure 3c,e, respectively.The corresponding finite-difference time-domain (FDTD) simulation spectra are shown in Figure 3c,e.The simulation and measurement results exhibit good agreement, with slight frequency discrepancies attributed to fabrication flaws.In the frequency range 10.3-10.85GHz, the transmissive PB metasurface unit cell achieves high transmissivity for mutually orthogonal linearly polarized waves and exhibits an approximate 180°phase difference, thus confirming the effectivity of Equation ( 1).
The high-efficiency conversion of the metasurface was validated under circularly polarized wave excitation.In this case, the metasurface was vertically incident using an LCP antenna, and the response signals were received using both the LCP and RCP antennas.The simulated and measured transmission spectra are shown in Figure 3d,f Figure 4 shows the electromagnetic characteristics of the unit cell when rotated along the coordinate axis.When the unit cell is rotated by an angle θ along the y axis as shown in Figure 4a  phase experienced a phase shift Δφ = 2θ due to the presence of the PB operator, which is in complete agreement with predictions.
After validating the feasibility of the direction-controllable SPP coupler, we designed the actual structure of a transmissive PB metasurface.To satisfy ξ ¼ AE1.12k 0 , the rotation angle of the unit cell can be calculated as θ ¼ 1 2 pξ.Here, the calculated value of θ is AE57°, indicating that the metasurface does not exhibit periodicity.Fifteen unit cells with a period of 8 mm were selected for the fabricated sample, shown in Figure 4a.The samples exhibited periodicity along the y axis and had a total size of 120 Â 120 mm.
The generated SPP can be decomposed into a superposition of the TM and TE signals.The unit cell structure of the eigenmode board consisted of an upper metallic resonant patch, an intermediate dielectric layer, and a lower metallic ground plane.The dielectric layer was an FR4 substrate with thickness h = 2 mm, as shown in the inset of Figure 4c.By adjusting the values of parameters a and b, the ideal μ yy and μ xx parameters can be obtained, ensuring that the eigenmode board exhibits the same dispersion for both TM and TE modes at the operating frequency f 0 = 10.6 GHz.The optimized unit cell parameters were determined as a = 2.2 mm, b = 5.8 mm, and p = 8 mm; the periodically arranged structure is shown in Figure 4c.It can be observed that the simulated and measured results are in good agreement as shown in Figure 4d.The TM and TE modes intersect at the frequency f 0 = 10.6 GHz, and the wave vector k x at the intersection point was determined to be 250 m À1 , which is very close to the design value of k x = 249 m À1 , verifying the rationality of the eigenmode board design.
The fabricated transmission PB gradient plate and eigenmode board were assembled by placing the PB gradient plate directly above the eigenmode board at a distance of l = 12 mm to ensure optimal coupling efficiency of the SPP coupler.The assembly was secured around the perimeter using dielectric screws, as shown in Figure 5a.
Figure 5b-e shows the field distributions in the x-z plane at the operating frequency for different incident circular polarizations obtained by FDFD simulation.Owing to the larger horizontal wavevector contributed by the PB gradient plate compared to the free-space propagation wavevector, the incident circularly polarized transmission wave was converted into localized SPP waves, as confirmed by Figure 5b-e.For the RCP incident waves, the generated SPP signal propagated toward the right.Both the TM component (H y component in Figure 5b) and the TE component (E y component in Figure 5c) were converted into SPP signals.The total incident wave energy, P tot , was obtained by integrating the incident energy impinging on a transmission PB gradient plate.The converted SPP energy, P SPP , was obtained by integrating the energy of the transmitted TE and TM components.The SPP coupling efficiency is calculated as follows: η ¼ P SPP P tot Â 100%.The calculated coupling efficiency was 83%.The energy loss can be attributed to three factors: reflection (%12%), transmission toward the left side of the eigenmode board (%3%), and absorption by the materials (%2%).For the LCP incident waves, both the TM and TE components of the SPP signal propagated toward the left side, achieving a conversion efficiency of 82%.Therefore, the designed SPP coupler effectively controlled the direction of the SPP signal transmission based on the polarization of the incident wave and exhibited high efficiency.
In the experimental verification of the SPP coupler, an RCP antenna was used to emit vertically incident waves onto a transmissive PB gradient plate.A monopole antenna was fixed to a stepper motor, with a step size of 0. Finally, the efficiency of the SPP coupler was tested.The total input energy consists of the converted SPP energy, reflection energy R, and absorption energy A. A far-field testing method was used to evaluate the total reflection of the SPP coupler, as shown in Figure 6c.When RCP waves are incident, the reflected waves are a combination of RCP and LCP fields.Therefore, the total reflection must consider the superposition of these two field components.The simulated and measured far-field distributions at the center frequency are shown in Figure 6d.Compared with a metallic plate of the same size, the SPP coupler exhibited significantly suppressed reflection.The total reflection R was obtained by integrating the reflected energy over all angles.The reflection spectra at different frequencies are shown by the orange curve in Figure 6e, where the reflection dip appears near the center frequency with a reflection rate of approximately 0.15.The intensity spectra of the TM-and TE-mode SPPs measured in the near field are also plotted in Figure 6e.The SPP energy for both modes reached its maximum near the operating frequency and propagated predominantly to the right.The energy transmitted toward the left side is only about 0.03 and 0.04 for the TM and TE modes, respectively.The directionality factor of the SPP coupler is characterized by the ratio of the energy transmitted on both sides of the eigenmode board, that is, D ¼ P TM SPP R þP TE SPP R P TM SPP L þP TE SPP L .Thus, the directionality factor of the tested SPP coupler was 28.6, indicating excellent directionality.This confirms that the SPP coupler design exhibited strong directionality and high efficiency.

Conclusion
We experimentally designed a PB metasurface-based SPP coupler to convert incident circularly polarized waves into TE and TM SPPs with high coupling efficiency and excellent directionality.Our coupler can excite chirality-modulated SPP waves and transmit them to the left and right sides.As a practical implementation of the proposed concept, we designed and fabricated a PB meta-coupler and experimentally demonstrated a conversion efficiency of 83%.We expect our novel strategy to find application in integrated optical devices such as photonic nanoroutings.

Figure 1 .
Figure 1.Working principle of the Pancharatnam-Berry (PB) metasurface coupler.a) Conventional reflective PB coupler, b) proposed novel transmissive PB coupler, and c) efficient direction control of surface plasmon polariton (SPP) signals for different incident circular polarizations using the proposed SPP coupler.
, respectively.Around the center frequency, the simulated and measured transmission amplitudes reached a maximum value of |t RL | = 0.95, whereas the remaining scattering modes |t LL |, |r LL |, and |t RL | were significantly suppressed with amplitudes close to zero.In the frequency range 10.3-10.85GHz, the transmission amplitudes of the unit cell exceeded 0.8.
,b illustrates the frequency spectra of the transmission amplitude |t RL | and the transmission phase φ RL .The transmission amplitude |t RL | remained consistently high and exhibited minimal variation with rotation angle.However, the transmission

Figure 2 .
Figure 2. Finite element method simulation results based on the effective medium model.When the SPP coupler was excited by a,b) right-handed circularly polarized (RCP) and c,d) left-handed circularly polarized (LCP); a,c) the E x distribution and b,d) the E y distribution on the x-z plane.Electric field distribution for e) the transverse magnetic (TM) mode and f ) transverse electric (TE) mode excitations at a distance between the metasurface and eigenmode board of 0.2λ 0 .
1 mm and the E z field (TM mode) and H z field (TE mode) were measured in the x-y plane at an operating frequency of 10.6 GHz, right above the eigenmode board.The distance between the antenna and the eigenmode board was 6 mm.The measured field distributions are shown in Figure 6a,b.By evaluating the wavelengths of the different modes of SPP, we obtained λ TM SPP = 25.1 mm and λ TE SPP = 25.1 mm, which are very close to the designed value of λ TM SPP = 25.2 mm.This indicates that the SPP signal on the eigenmode board contained both TM and TE components.

Figure 4 .
Figure 4. a) Schematic of the unit rotation.b) FDFD simulation results for the transmission amplitude |t RL | and transmission phase φ RL spectra at the operating frequency f 0 = 10.6 GHz.c) Fabricated eigenmode board sample with an illustration depicting the unit cell structure in the insert.d) Simulation and experimental results of the dispersion curves for the TM and TE modes of the eigenmode board.

Figure 5 .
Figure 5. FDFD simulation results for the SPP coupler.a) Schematic of the SPP coupler.b,c) Incident by RCP and d,e) LCP waves.b,d) H y and c,e) E y field distributions at f 0 = 10.6 GHz in the x-z plane.The efficiency of each mode is calculated by the ratio of the energy of the converted TE/TM-mode SPP and the incident energy of the certain component, respectively.

Figure 6 .
Figure 6.Measured a) E z and b) H y fields using monopole and helical antennas.c) Far-field experiment setup.d) Simulated and experimentally measured scattering field distributions of the SPP coupler and an equally sized metallic plate.e) Total reflectance and SPP intensity spectra.