† Corresponding author. E-mail:
Project supported by the China Postdoctoral Science Foundation (Grant No. 2015M580849) and the National Natural Science Foundation of China (Grant Nos. 61471292, 61501365, 61471388, 61331005, 41404095, and 41390454).
A polarization-insensitive unidirectional spoof surface plasmon polariton (SPP) coupler mediated by a gradient metasurface is proposed. The field distributions and average Poynting vector of the coupled spoof SPPs are analyzed. The simulated and experimental results support the theoretical analysis and indicate that the designed gradient metasurface can couple both the parallel-polarized and normally-polarized incident waves to the spoof SPPs propagating in the same direction at about 5 GHz.
Surface plasmon polaritons (SPPs) are propagating excitations generated by the coupling of light and electron density at the surface of a metal. SPPs can be manipulated by the structure of the surface at the subwavelength scale, which means that it plays an important role in optical technology[1–4] and nano-devices.[5–7] Actually, SPP-like modes or spoof SPPs are also observed at structured surfaces in the microwave frequency and have been applied to microwave cloaks,[8–11] waveguides,[12–14] and antennas.[15,16]
Metasurfaces are planar metamaterials with one- or two-dimensional arrangements of subwavelength resonators. Metasurfaces can manipulate the amplitude,[17–19] phase,[20,21] polarization,[22–25] and propagation direction of the electromagnetic waves including surface waves.[26–30] Over the past few years, considerable interest has been focused on metasurfaces with phase discontinuities or gradient metasurfaces. Different types of gradient metasurfaces have been designed to manipulate the propagation of electromagnetic waves in the frequency range from optics to microwave.[31–42] One- and two-dimensional gradient metasurfaces have been reported to realize anomalous reflection or refraction.[31–39] Also, when the phase gradient of the gradient metasurface is sufficiently large, the gradient metasurface can couple the normal incident electromagnetic waves to the spoof SPPs propagating along the direction of the phase gradient.[40–43]
Great efforts have been made to excite SPPs or spoof SPPs in a specific direction.[44–48] Cui et al. presented a holographic metasurface composed of unit cells with different surface impedances and dispersion properties to realize surface wave coupling.[48] A gradient metasurface is another efficient choice to generate unidirectional spoof SPPs. In terms of spoof SPP couplings by gradient metasurfaces, the subwavelength resonators of the gradient metasurface should have different reflection phases to realize an appropriate phase gradient that controls the wavelength and amplitude of the coupled spoof SPPs. In addition, the resonators of the gradient metasurface should have the same dispersion properties to offer the necessary phase-matching conditions to match the dispersion properties of the coupled spoof SPPs defined by the phase gradient.[43] While, the unit cells of the holographic metasurfaces could have different dispersion properties to manipulate the wavefront of the surface waves.[48]
Types of gradient metasurfaces have been carefully designed for spoof SPP coupling.[40–43] However, these designs are polarization sensitive or are realized by complex two-dimensional arranged structures.[49] Linearly polarized gradient metasurfaces are reported as spoof SPP couplers.[40,41] They can only couple the incident wave polarized in the phase gradient direction to spoof SPPs. Circularly polarized gradient metasurfaces have also been reported.[42,43] Generally, the efficiency of the circularly polarized gradient metasurfaces is polarization insensitive; however, the directions of the coupled spoof SPPs are polarization-controlled. This means that circularly polarized gradient metasurfaces couple electromagnetic waves with different helicity to spoof SPPs in opposite directions. Also, the field distributions are only analyzed in situations where the incident wave is polarized in the phase gradient direction.[40] Thus, analysis of field distributions of the coupled spoof SPPs under different polarized incident waves and the development of polarization-insensitive unidirectional spoof SPP couplers are desirable.
In this article, we present a gradient metasurface with one-dimensional arrangements of subwavelength resonators supporting polarization-insensitive unidirectional spoof SPP coupling. Theoretical analysis of the situations with both gradient direction polarized incident wave and its cross-polarized incident wave is presented based on the generalized Snell law. The proposed gradient metasurface can couple arbitrary polarized electromagnetic waves at normal incidence to spoof SPPs propagating along the same direction at about 5 GHz. However, for different polarizations of the incident waves, the coupled spoof SPPs propagate in the same direction but with different modes. Thus, the coupled spoof SPPs preserve the polarization information of the incident wave and the proposed gradient metasurface has the potential to realize polarization analyzers.
The subwavelength resonators of the gradient metasurfaces are each individually designed to tune the reflective phase and to realize a phase gradient. As shown in Fig.
As shown in Fig.
Equations (
Equation (
When the incident wave is a normal-polarized wave as shown in Fig.
Similar to the condition with the parallel-polarized incident wave, when
According to Eqs. (
Consequently, both parallel-polarized and normal-polarized incident waves can be coupled to spoof SPPs propagating in the same direction, but in different modes. The parallel-polarized incident wave coupled spoof SPPs have a z component of the electric field, while the normal-polarized incident wave coupled spoof SPPs do not. Thus, the polarization state of the incident wave can be analyzed by detecting the z component of the electric field of the coupled spoof SPPs.
To verify the above theoretical analysis, we designed a polarization-insensitive gradient metasurface as shown in Fig.
The geometry of the structure was optimized by simulations. The geometric parameters of the resonator were chosen to be a = 0.5 mm, b = 0.3 mm, c = 0.15 mm, d = 2.2 mm, e = 1.6 mm, w = 0.4 mm, and p = 8 mm (0.133λ0). The unit cell (shown in Fig.
The simulated dispersion curves of the subwavelength resonators in Fig.
The designed gradient metasurface with unit cells shown in Fig.
The simulated reflection coefficients are shown in Fig.
The simulated electromagnetic fields under parallel-polarized incident wave illumination at 5.09 GHz are shown in Figs.
To verify the above theoretical analysis, the phase of the coupled spoof SPPs is discussed. The z component of the electric field is induced and has a 90° phase difference to the x component of the electric field. The y component of the total magnetic field of the spoof SPPs has a −90° phase difference to the x component of the electric field and a 180° phase difference to the z component of the electric field as shown in Fig.
For a normal-polarized (y-polarized) incident wave, the simulated electromagnetic fields and power flow are shown in Fig.
The z component of the magnetic field is induced and has a 90° phase difference to the x component of the magnetic field. The y component of the electric field of the spoof SPPs has a −90° phase difference to the x component of the magnetic field and a 180° phase difference to the z component of the magnetic field. The wavelength of the spoof SPPs is 6 × p = 48 mm. Thus, the simulated results are in agreement with Eqs. (
According to the above discussion, the properties of the simulated electromagnetic field agree well with the above theoretical analysis and demonstrate the spoof SPP coupling capability of the designed gradient metasurface. Since an arbitrary polarized wave can be decomposed into a parallel-polarized wave and a normal-polarized wave, the designed gradient metasurface can couple an arbitrary polarized wave to spoof SPPs propagating in one direction (the x direction, or the phase gradient direction).
To verify the simulated results, a 432 mm × 280 mm (7.2λ0 × 4.67λ0) sample was fabricated and the reflectance was measured as shown in Figs.
Figure
The z component of the electric field at parallel-polarized incidence and the z component of the magnetic field at normal-polarized incidence of the coupled spoof SPPs at 4.95 GHz were measured by probes at 5 mm (0.083λ0) above the sample and are shown in Figs.
A polarization-insensitive unidirectional spoof SPP coupler that can couple both parallel-polarized and normal-polarized incident waves to spoof SPPs is realized using a gradient metasurface. The theoretical analysis gives the field distributions and the average Poynting vector of the coupled spoof SPPs. The measurement results of the designed gradient metasurface conform to the simulated results and also verify the theoretical analysis. This work can be applied to novel microwave devices and antennas and also has a potential value for optical applications.
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