Ultrathin metasurface with topological transition for manipulating spoof surface plasmon polaritons

Metasurfaces, with intrinsically planar nature and subwavelength thickness, provide us unconventional methodologies to not only mold the flow of propagating waves but also manipulate near-field waves. Plasmonic metasurfaces with topological transition for controlling surface plasmon polaritons (SPPs) recently have been experimentally demonstrated, which, however, are limited to optical frequencies. In this work, we proposed and experimentally characterized an ultrathin metasurface with the topological transition for manipulating spoof SPPs at low frequency. We demonstrated rich interesting phenomena based on this metasurface, including frequency-dependent spatial localization, non-diffraction propagation, negative refraction, and dispersion-dependent spin-momentum locking of spoof SPPs. Comparing with traditional three-dimensional metamaterials, our metasurface exhibits low propagation loss and compatibility with the photonic integrated circuit, which may find plenty of applications in spatial multiplexers, focusing and imaging devices, planar hyperlens, and dispersion-dependent directional couplers, in microwave and terahertz frequencies.


Introduction
Metasurfaces are with planar profile and subwavelength thickness composed of arrays of optical scatterers 1 . The metasurfaces introduce abrupt changes of optical properties, which is due to the strong interaction between light and the subwavelength scatterers or antennas, and can control the amplitude 2 , phase 3 , and polarization 4 of propagating light at will. The fascinating properties of planar metasurfaces provide us unparalleled methodologies to manipulate the manner of propagating light and promise a bright future for useful devices with compact volume 5,6 . The metasurfaces can not only mold flow of the propagating light but also manipulate near-field waves, such as surface plasmon polaritons (SPPs) 7 . The SPPs propagate at the interface between metasurface and the dielectric materials, and by tailoring the dispersion of the metasurface we can manipulate the propagation and spin manners of the SPPs. Based on this concept, a metasurface composed of silver/air grating was theoretically proposed, whose dispersion gradually changes from elliptical to flat and finally to hyperbolic, showing an unprecedented capability to control the SPPs 7 . This metasurface with feasible geometries has been experimentally realized recently by applying lithographic and etching techniques 8 .
Comparing with the traditional bulky metamaterials, the planar metasurfaces have lower propagation loss and compatibility with the integrated metamaterials circuit. It shows plenty of interesting phenomena, including negative refraction of SPPs propagation, non-diffraction SPPs propagation, and dispersion-dependent plasmonic spin Hall effect. It may find broad applications in planar focusing and imaging devices, hyperlens, integrated photonic circuits, and quantum optics.
The metasurfaces with the topological transition (MTT) will be extremely useful not only at optical spectrums, but also at the low frequencies, i.e., far-infrared, terahertz, and microwave frequencies. Though successfully demonstrated, this optical metasurface can't be directly applied at low frequencies, as the noble metals, e.g., silver and gold, behave akin to perfect electric conductor (PEC) at low frequencies, and the surface wave modes known as Sommerfeld or Zenneck waves 9 with weak confinement are difficultly controlled by using the metal/air grating structure. In the far-infrared frequency, the graphene can support SPPs due to the strong light-matter interaction. Gomez-Diaz et al. have proposed an ultrathin metasurface based on graphene strips 10 . These uniform graphene sheets can be treated as a homogenous anisotropic conductive surface and exhibit topological transition of equifrequency contours (EFCs) associated with a dramatic tailoring of the local density of electromagnetic states. However, realizing such a graphene-based metasurface will need to face some technical challenges, and it has not been realized yet.
In 2004, the spoof SPPs was proposed by Pendry et al., which are composed of structured PECs to mimic the optical properties of SPPs, e.g., dispersion behavior and light confinement 11 .
Though physically different, i.e., the SPPs arise from the interaction between light and the free electrons in noble metals, while the spoof SPPs result from the interaction between electromagnetic wave and the spatial capacitances and inductances induced by the structured metal surface. The intrinsically close connections between SPPs and spoof SPPs have brought a plenty of phenomena, such as localized SPPs [12][13][14] , and applications in SPPs, e.g., sensor 15 , laser beams 16 , imaging, and directive emission 17 , to spoof SPPs. This also gives us a clue to design an MTT operational at low frequency, namely, an MTT for manipulating spoof SPPs. Therefore, in this paper, we proposed and experimentally demonstrated an MTT for manipulating the spoof SPPs. Based on an equivalent model theory, we design a complementary H-shape resonator metasurface (CHRM), whose EFCs in the wave vector space is experienced a topological transition from a closed elliptical curve to a straight line, and finally to an open hyperbolic curve. As a result, normal and non-divergent diffraction, negative refraction are achieved when the spoof SPPs propagate along the metasurface. This metasurface also shows a dispersion-dependent spin-momentum locking of spoof SPPs, where anomalous spin Hall effect will be shown when the EFCs are hyperbolic. Our metasurface will find potential applications in the spatial multiplexer, focusing and imaging devices, hyperlens, dispersion-dependent directional coupler, and photonic integrated circuits.

Theories
The unit cell of the ultrathin MTT for manipulating spoof SPPs is shown in Fig.1 (a), which is a sandwich structure: copper ground layer, substrate with permittivity of 2.55, and a complementary H-shape layer 18 . The electromagnetic properties of this unit cell are controlled by the geometries, for example, p=6 mm, l=5 mm, w=0.5 mm, g=0.25 mm, t=1 mm, and the thickness of the metal is 0.035 mm in our case. When imposing EM waves to the metasurface, surface currents will be induced and oscillate on the metal surface due to the special geometries.
It is obvious that due to the lack of C4 symmetry, this unit cell design will show different responses when EM wave propagates along x and y directions, respectively. For better understanding the unit cell design, we give equivalent circuit models when spoof SPPs propagating along x and y directions in Fig. 1 (b) and (c), respectively. Thus, we can get the spoof surface plasma frequency, vector is along an x direction; when wave vector is along the ydirection, which mimics the surface plasmon frequency of the noble metals in optical frequency.
When 0   Moreover, the additional ground layer gives more freedoms to control and excite the spoof SPPs, such as the directional coupler we designed at the last of this paper.

Simulations and experiments
In the following, we will demonstrate the main electromagnetic properties of the CHRM, including the topological transition of EFCs in wave vector space, frequency-dependent spatial localization, non-diffraction propagation, negative refraction, and dispersion-dependent spin-momentum locking of spoof SPPs. In Fig.3 Fig. 3(a)). When the frequency increases to 8.75 GHz, the EFC becomes extreme anisotropic. As the group velocity vector of the spoof SPPs should be perpendicular to the EFCs, the spoof SPPs are guided and split into two beams as a consequence of the special shapes of EFCs. The propagation direction of the spoof SPPs is frequency-dependent, as shown from Fig. 3

(b) and
(c). This phenomenon can be applied to design a spatial multiplexer. At the transition point around 9.75 GHz, the spoof SPPs propagates with self-collimation manner due to the flat dispersion 19 . This self-collimation phenomenon has been also found in photonic crystals and maybe find potential applications in the integrated surface wave circuit system and hyperlens 20 ( Fig. 3(d)). From 9.75 GHz to 11 GHz, the spoof SPPs propagate with convergent manners due to the hyperbolic EFCs ( Fig. 3(e) and (f)).  This topological transition phenomenon has been also experimentally demonstrated. In the implementation, we printed the complementary H-shape resonator structure on a substrate, which is a 1 mm Teflon woven glass fabric copper-clad laminates with a permittivity of 2.55 and tan( ) 0.001   at 10.0 GHz. We used a dipole between two metal layers to excite the spoof SPPs, the same source setting in the simulations. Therefore, the measured field distributions will be exactly matched with the simulated ones as shown in Fig. 4. In order to obtain the field distributions, we used a dipole antenna 1 mm over the metasurface to detect the z-oriented electric (Ez) field point to point by a three-dimensional movement platform, and the measured region is 240 mm * 230 mm. From Fig. 4, we can directly observe the transition of wavefronts from a convex, to flat, and to concave. The transition point shifts slightly from 9.75 GHz to 9.5 GHz, due to the imperfection of the fabrication. At the transition point, the spoof SPPs propagate with non-diffraction manner, which is very similar to the spatial solitons in nonlinear optics, however, it's only based on a linear optical system 21 .
If properly designing the dispersion of the background metasurface ( Fig. 5(b)), negative refraction of spoof SPPs will occur at the interference between CHRM and background medium, as shown in Fig. 5(a). The EFCs of the background metasurface and the CHRM at 10.6 GHz is shown in Fig. 5(c). One can see that all incoming wave vectors at such a frequency are included within the EFCs of the CHRM, thus, all-angle negative refraction is enabled, which can be applied to surface waves focusing and imaging 22 . In the experiment, we chose air as the background, when the spoof SPPs scatter into the air, it will be focused, as shown in Fig. 5(d).
Therefore, the CHRM can work as an ultrathin planar imaging device, which will be very useful, especially at terahertz and far-infrared frequencies.   Based on dispersion-dependent spin Hall effect, we designed a coupler to launch diverge, soliton-like or convergent spoof SPPs directionally on the CHRM, controlled by the polarization of the incident EM waves. As shown in Fig. 7(a), the coupler is composed of two columns of sub-wavelength narrow apertures in the bottom metal film of the CHRM. It is well-known that if the coupler is well predesigned, destructive interference will occur at one side of the columns and constructive interference at the other side of the columns simultaneously, leading to the unidirectional launching of the surface wave 27,28 or spoof SPPs in our case. Here, by choosing w=0.5 mm, l=3 mm, p=4 mm, and g=λ0/4=4.1 mm, where λ0 is the wavelength of the spoof SPPs at 9.75 GHz, we can excite soliton-like spoof SPPs on the CHRM uni-directionally ( Fig. 7(b)-(c)) or bi-directionally ( Fig. 7(d)) at 9.75 GHz. By further engineering the apertures, we can even tailor the wavefronts of spoof SPPs with arbitrary shape 28 . The CHRM can work as a platform to study the properties of transverse spins of spoof SPPs with different dispersions and will find broad applications the signal processing.

Conclusions
In this paper, we proposed and experimentally demonstrated an ultrathin MTT for manipulating spoof SPPs at low frequency. Comparing with three-dimensional metamaterials, this metasurface with 2D nature can achieve various dispersions, including elliptical dispersion, extreme anisotropic dispersion and hyperbolic dispersion with lower loss, the convenience of fabrication, and compatibility with the photonic integrated circuit. We demonstrated plenty of interesting phenomena based on this metasurface, including frequency-dependent spatial localization, non-diffraction propagation, negative refraction, and dispersion-dependent spin Hall effect, etc. Our metasurface will find broad applications in spatial multiplexers, focusing and imaging devices, planar hyperlens, dispersion-dependent directional coupler, and photonic integrated circuits. If involved with active components 29 , such as semiconductor devices, we can even dynamically tailor the dispersion of the metasurface and control the manner of spoof SPPs, including propagation and spins. Besides, this anisotropic metasurface can also work as a brick of two-dimensional transformation optics based devices.