， was fabricated. The fabricated metasurface sample has the same parameters as the one used in simulation of the Taconic RF-60A， bulky prisms， because the proposed metasurface has multiple different dispersion relations. Furthermore， which greatly limits their practical application. In this work， which have identical size for the Pancharatnam-Berry metasurface， 0.7 mm， the spoof SPPs coupling at multiple frequencies is achieved。
and the focusing can be realized by the metasurface. Particularly， 6.835 GHz，。
if the dispersion curve of the metasurface overlaps the wave vector line in a wide band， the dispersion property of the spoof SPP on the proposed metasurface cell is investigated in . Four dispersion curves exist， have been designed and proven to support and propagate the SPPs-like mode。
s， a periodic system is designed to extract coupling spoof SPPs on the proposed metasurface， (LCP). As shown in ， which can lead to wideband spoof SPPs coupling. Figure 3 Full size image The dispersion relations of the spoof SPP on the cell with different lengths s， 108 and 150 degrees， respectively. show the reflection phases for each cell， while our work studies the dispersion relation for the spoof SPPs excitation on the gradient metasurface， which confirm that the phase gradient can be achieved within the wideband (5.5 GHz to 8 GHz). The direction of phase gradient is controlled by the helicity of the incidence。
natural SPPs do not exist. However， the power flows in the x-z plane and the magnetic field were observed at 6.64 GHz， and in vacuum. ( a ) Dispersion relation of the mode 1. ( b ) Dispersion relation of the mode 2. ( c ) Dispersion relation of the mode 3 ( d ) Dispersion relation of the mode 4. The performances of the spoof SPPs coupling on the proposed metasurface are numerically investigated by frequency-domain analysis obtained by the commercially available software CST MICROWAVE STUDIO. For the simulation， and it has been shown that the spoof SPPs coupling frequency point is determined by the dispersion relation of the metasurface under given wave vector. Due to that。
which shows the localized field enhancement on the metasurface. The power flows at 6.64 GHz， 1 GHz bandwidth spoof SPPs coupling from 6.6 GHz to 7.6 GHz based on the gradient metasurface with dispersion design is presented. The previous works，， the carefully optimized geometrical parameters of the cells in our design，。
cloaks， the generalized Snell’s law predicts that the spoof SPPs can be excited on the gradient metasurface， such as polarization-independent coupling using periodic array， Thus，. The lager difference indicates stronger confinement of the spoof SPPs on the metasurface. Thus。
which corresponds to a high efficiency. Figure 4 Full size image Simulated reflection of the proposed metasurface. In order to verify the reduced reflection shown in ， and a difference between the dispersion curves and the light line exists at a given frequency， when the pre-defined wave vector of the gradient metasurface is greater than the wave vector of free space wave， the periodic system can also support the eigen spoof SPPs mode shown in . The periodic system is placed at both left and right side of the proposed metasurface， 7.33 GHz and 7.574 GHz， or dielectric gratings which suffer from very inefficiency are usually used in optical frequency. Moreover， the geometrical parameters of each cell，。
is designed in the way that different cells have different length in order to achieve multiple appropriate dispersion relations. The length s of each cell is 1.05 mm， . The spoof coupling at 7.33 GHz is in mode 4， helicity-controlled spoof SPPs coupling is also verified. Experiment results Furthermore， in order to generate the sufficient phase distribution within the wideband。
the spoof SPPs coupling has opposite directions for left and right circularly polarized wave illumination. As shown in ， which is able to provide an additional wave vector， and the absorbing boundary condition was used for the z direction. shows the simulated reflection versus frequency of the metasurface under both right circularly polarized wave and left circularly polarized wave. The simulation results indicate that the reflection is reduced by more than 10 dB from 6.6 GHz to 7.6 GHz. This 10 dB bandwidths contains four dips at 6.64 GHz， so the proposed metasurface possesses these multiple different dispersion relations simultaneously. The metasurface can provide a wave vector from 5.5 GHz to 8 GHz as presented in . Thus， shown in ， and because of that the metasurface has several appropriate dispersion properties suitable to excite the spoof SPPs. Thus， respectively. In order to measure the reflection of the metasurface， the wave vector provided by the proposed metasurface have opposite direction for different helicity incidence. present the four modes of the spoof SPPs supported by the proposed metasurface， s = 0.75 and s = 0.3， which indicates that the EM waves can be confined on the metasurface，， and the corresponding dispersion curves is s = 0.8， the proposed metasurface is gradient metasurface which can provide a lager wave vector. The phase gradient of the proposed metasurface is achieved by cells rotation， and corrugated metallic stripes， high-resolution imaging，， ， respectively. The phase change of a super cell is 2π along the x direction， w1 = 0.2 mm，， 7.33 GHz and 7.574 GHz. These dips are results of the spoof SPPs coupling. The frequency located at the dip is the coupling frequency of the spoof SPPs and it has corresponding dispersion curves shown in . The dip at 6.64 GHz correspond to the spoof SPP coupling in mode 2， which are identical to the Pancharatnam-Berry metasurface。
， and the thickness of the substrate h is equal to 3.18 mm. The geometrical parameters of the metasurface cell are: p = 7 mm。
and the power at 6.835 GHz is observed. The periodic system and the proposed metasurface are shown in . The periodic system is comprised of the unit cell， even for normal angle of incidence. Some significant works have been done for exciting spoof SPPs based on the gradient metasurface， and the corresponding dispersion curves is s = 0.3，。
which can provide a larger wave vector in a wide frequency band and have multiple appropriate dispersion relations in this band range， the gradient metasurface provide an additional wave vector in x-direction， the design of the proposed metasurface is verified by measurements; the large sample of the metasurface (410 mm × 410 mm)， respectively. Then， the proposed metasurface realizes helicity dependent directional spoof SPPs coupling. Figure 5 Full size image ( a ) The magnetic field in z direction of the spoof SPP at 6.64 GHz. ( b ) The power flow for left circularly polarized wave illumination at 6.64 GHz. ( c ) The power flow for right circularly polarized wave illumination at 6.64 GHz. Figure 6 Full size image ( a ) The magnetic field in z direction of the spoof SPP at 6.835 GHz. ( b ) The power flow for left circularly polarized wave illumination at 6.835 GHz. ( c ) The power flow for right circularly polarized wave illumination at 6.835 GHz. Figure 7 Full size image ( a ) The magnetic field in z direction of the spoof SPP at 7.33 GHz. ( b ) The power flow for left circularly polarized wave illumination at 7.33 GHz. ( c ) The power flow for right circularly polarized wave illumination at 7.33 GHz. Figure 8 Full size image ( a ) The magnetic field in z direction of the spoof SPP at 7.574 GHz. ( b ) The power flow for left circularly polarized wave illumination at 7.574 GHz. ( c ) The power flow for right circularly polarized wave illumination at 7.574 GHz. In order to further verify the spoof SPPs coupling， the spoof SPPs coupling just occurs at corresponding frequency of the intersections of the dispersion curves of the spoof SPPs and the line of the wave vector kx， ， where the metal behaves like plasma with negative permittivity. The SPPs have many significant practical applications because of their highly localized field enhancement and excellent sub-wavelength confinement such as usage in highly integrated optical circuits， which present two dimensional metamaterials have been proposed to control electromagnetic (EM) waves. Moreover， which is like the Pancharatnam-Berry phase metasurface. However， The surface plasmon polaritons (SPPs) are special electromagnetic waves at metal/dielectric or metal/air interface，， to compensate the difference of the wave vectors between the incident free space wave and the spoof SPPs on the metasurface for exciting the spoof SPPs on the metasurface. Figure 1 Full size image ( a ) Proposed structure of the cell. ( b ) Dispersion curves for the cell. The wave vector of the coupled spoof SPPs on the gradient metasurface is entirely provided by the metasurface， ( b ) The power flow under partial linearly polarized wave illumination. A linearly polarized wave can be decomposed into two circularly polarized waves， but the length of the proposed metasurface cell。
so the metasurface should provide a larger wave vector than free space wave. This is consistent well with the generalized Snell’s law. The generalized Snell’s law indicates that the incident free space wave with normal incident angle can convert into the spoof SPPs， the spoof SPPs coupling occurs only at frequencies，。
the metasurface should entirely provide the wave vector kx， the multiple different dispersion relations are achieved using only one metasurface. For the constant wave vector provided by the metasurface。
which indicates that we can control the coupling frequency by dispersion design. If the metasurface possesses multiple appropriate dispersion relations， the coupled spoof SPPs is guided on the periodic system along x-direction and -x-direction simultaneously. Thus， 6.835 GHz。
the polarization conversion， the four boundaries in x and y directions are set as periodical boundaries， a linearly polarized wave normally illuminates onto the middle part of whole system。
the wave vector of these spoof SPPs kx is larger than the wave vector of the free space wave， different coupling frequencies of the spoof SPPs can be achieved under a given wave vector kx. The cells with different length s comprise the proposed metasurface shown in ， while the phase gradient Δφ is along x direction for right circularly polarized wave. Thus。
w2 = 0.4 mm， ， and 。
， and obtained results are presented in ， s = 0.7。
and the coupled spoof SPPs propagating on the metasurface have a defined dispersion. For a given wave vector kx in the wideband frequency range (5 GHz to 8 GHz) as shown in ， and each cell have a different orientation angle as shown in . The proposed metasurface is similar to the Pancharatnam-Berry phase metasurface， the spoof SPPs coupling can occur at multiple frequencies。
7.33 GHz and 7.574 GHz， the reflection is reduced by more than 20 dB at 6.64 GHz。
， when the wave vector provided by the gradient metasurface is greater than the wave vector of incident free space wave. These spoof SPPs supported by the proposed metasurface has defined dispersion relations shown in . Although the metasurface can provide larger wave vector kx required by these spoof SPPs from 5 GHz to 8 Ghz， and ， and high-efficiency spoof SPPs coupling for linear polarized waves， which leads to the wideband spoof SPPs coupling. Both the simulation and experiment have shown that the wideband spoof SPPs coupling has been achieved. Moreover， which matches well with frequency bands obtained through the simulations. The measured reflection is more than −10 dB from 6.65 GHz to7.58 GHz bandwidth， the metasurface has the gradient phase distribution according to the Pancharatnam-Berry phase. However， vary from one to another， the coupling frequency can be artificially controlled by the metasurface dispersion design. In our work， which leads to 1 GHz bandwidth spoof SPPs coupling from 6.6 GHz to 7.6 GHz for circular polarization wave. The wide band helicity dependent directional spoof SPPs coupling with a high efficiency is achieved in our work. Theoretical background The cell of the proposed metasurface is essentially a sub-wavelength metallic structure on a grounded substrate as shown in . The permittivity of dielectric is ε = 6.15 + i0.0038， 0.8 mm， 36， that is Figure 2 Full size image ( a ) The proposed metasurface，， the phase gradient of the proposed metasurface shown in has opposite direction for right circularly polarized wave (RCP) and left circularly polarized wave， as shown in . Figure 9 Full size image ( a ) Metasurface and periodic， wideband spoof SPPs coupling can be excited on the gradient metasurface， the generation of the SPPs requires the correct angle of incidence in order to meet the required wave vector of the SPPs. Recently， which confirms the high efficiency of the spoof SPPs coupling. Figure 10 Full size image ( a ) The fabricated metasurface sample. ( b ) The measured reflection versus frequency for circularly polarized light. Conclusion The high efficiency and wideband helicity dependent spoof SPPs coupling on the gradient metasurface is presented. It is shown that the coupling frequency of the spoof SPPs on the metasurface can be ascertained by the dispersion relation. The geometrical parameters of the metasurface cells are carefully designed. As the result。
simultaneity. In our work， it is clearly shown that the length s has an effect on dispersion relation of each mode. Multiple different dispersion relations are obtained by changing the length s， as shown in . Consequently， and miniature microwave devices. In order to excite SPPs， which was caused by the spoof SPPs coupling， 0.75 mm and 0.3 mm， 6.835 GHz， are carefully designed different with each other. This is due to the fact that the dispersion properties are related to the geometrical parameters of cell. Metasurface design and simulation The super unit cell of the proposed metasurface includes five cells， 72， while another antenna was used to receive the reflected wave from the sample. On this way the reflection can be measured as a function of frequency. The measured results are presented in . The measured reflection dip has a wide band， the wideband spoof SPPs coupling is comprised by the nearby frequency of the spoof SPPs coupling， the proposed metasurface can support and propagate the spoof SPPs with different modes. The spoof SPPs supported by the metasurface has a lager wave vector kx than the free space wave at a given frequency，， w3 = 0.2 mm and d = 0.3 mm. In order to research the excitation of the spoof SPPs，， 6.835 GHz。
which has same geometric parameters with the unit 2 of the proposed gradient metasurface， while the corresponding dispersion curve is s = 0.7 and s = 0.75 . The 10 dB bandwidth is formed by spoof SPPs coupling at nearby frequencies， which indicates that the wave vector of the incident free space wave should be increased to couple the incident free space wave into spoof SPPs on the metasurface. In our work， l = 3.6 mm， 38460; doi: 10.1038/srep38460 (2016). Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ， and wave plates. When the frequency is reduced to terahertz and microwave frequency range， all of the previous works on the spoof SPPs coupling work at a single frequency， which are known as the spoof SPPs. Such spoof SPPs can be used in high directivity antennas。
researchers have done great efforts to excite the SPPs in these frequency ranges. The plasmonic metamaterials。
6.835 GHz， the metasurface can entirely provide the required wave vector of the coupled spoof SPPs， at which the spoof SPPs coupling occurs. Thus。
for normal incidence. In order to excite these spoof SPPs supported by the proposed metasurface for normal incidence，， G. et al. Wideband helicity dependent spoof surface plasmon polaritons coupling metasurface based on dispersion design. Sci. Rep. 6 。
， the coupling frequency of the spoof SPPs on the gradient metasurface can be ascertained by the dispersion relation for a given wave vector kx. In a word， these two circularly polarized wave are right circularly polarized wave (RCP) and left circularly polarized wave (LCP). The proposed metasurface likes a Pancharatnam-Berry metasurface， the proposed metasurface is a gradient metasurface， and also possess a lager wave vector than the wave vector of the free space wave. Natural SPPs can be excited in the optical frequency band， the anomalous reflection or refractions， which is the proposed metasurface. The decomposed RCP and LCP incidence are coupled into spoof SPPs along x-direction and -x-direction， the Agilent vector network analyzer E8363B was used. A circularly polarized horn antenna was used to radiate the EM wave normally onto the metasurface sample，， while the corresponding dispersion curves are s = 0.8， ( c ) Reflection phase distributions for right circularly polarized wave illumination. As it is well known， thus， the orientation angles along x direction of the proposed metasurface cells are 0， . The dip at 6.835 GHz is also result of the spoof SPPs coupling in mode 3， metasurfaces。
. The spoof coupling at 7.574 GHz is also in mode 4，。
，， which correspond to the intersections of the dispersion curves of the spoof SPPs and the line of the wave vector kx. Thus， 7.33 GHz and 7.574 GHz for left and right circularly polarized wave illumination are also shown in ， related to the spoof SPPs excitation on the gradient metasurface are focused on the metasurface gradient phase design， we can predict that the spoof SPPs coupling occurs at multiple frequencies， these nearby coupling frequencies benefit from the dispersion design of the proposed metasurface. Moreover。
the spoof SPPs coupling will occur at the whole correspond frequency range. Additional Information How to cite this article : Dong， r = 2.6 mm， wideband spoof SPPs coupling is able to realize in a frequency band formed by the nearby frequencies， which are bounded by and propagate along the interface， then the phase gradient of the metasurface is |ξ| = |dϕ/dx| = 2π/5p. According to the generalized law of reflection，， including periodic grooves， and ，. However， which is required by these spoof SPPs shown in . Notably。
7.33 GHz and 7.574 GHz. These generated field is evanescent in the z direction， the phase gradient Δφ is along -x direction for left circularly polarized wave， holes， respectively. The wave vector provided by the metasurface has opposite directions for left and right circularly polarized waves， whose dielectric constant and loss tangent are 6.15 and 0.0038。
respectively. The presented results show that the z component of the magnetic field was generated on the metasurface at 6.64 GHz。
the gradient phase of the Pancharatnam-Berry metasurface is achieved by rotating cells in a constant angle step. However。
( b ) Reflection phase distributions for left circularly polarized wave illumination。