Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure

Abstract

Backward wave with anti-parallel phase and group velocities is one of the basic properties associated with negative refraction and sub-diffraction image that have attracted considerable interest in the context of photonic metamaterials. It has been predicted theoretically that some plasmonic structures can also support backward wave propagation of surface plasmon polaritons (SPPs), however direct experimental demonstration has not been reported, to the best of our knowledge. In this paper, a specially designed plasmonic metamaterial of corrugated metallic strip has been proposed that can support backward spoof SPP wave propagation. The dispersion analysis, the full electromagnetic field simulation and the transmission measurement of the plasmonic metamaterial waveguide have clearly validated the backward wave propagation with dispersion relation possessing negative slope and opposite directions of group and phase velocities. As a further verification and application, a contra-directional coupler is designed and tested that can route the microwave signal to opposite terminals at different operating frequencies, indicating new application opportunities of plasmonic metamaterial in integrated functional devices and circuits for microwave and terahertz radiation.

Figure 1. Structure and dispersion relations of the CSP structures.

(a) Geometry of the traditional (top) and the proposed (bottom) symmetric CSP structures. (b) Dispersion curves for the different symmetric CSP structures. The modified one (orange dashed line) indicates the dispersion curve for the CSP pattern in which four small grooves inside each slot near the centric strip have been removed. Only the fundamental modes have been plotted. The metallic strip is considered as PEC with negligible thickness and the geometric parameters are set as g = 0.67d, h = 1.6d, a = 0.1d, w = 3.4d, respectively.

Figure 2. Simulated EM field and energy flux distribution in a unit-cell of the symmetric CSP waveguide (at βd/π = 0.5).

The distributions of (a) the y component of electric field, (b) the EM energy flux along x direction, (c) the x component of electric field, and (d) the z component of magnetic field for different slot structures. The parameters of the slot in (a) or (b) are set from left to right as g = 0.67d, and b = 0; g = 0.33d, and b = 0; g = 0.67d, and b = 0.17d; g = 0.67d, and b = 0.34d; g = 0.67d and b = 0.51d; g = 0.67d and b = 0.51d with simplified grooves; while other parameters are the same as that in Fig. 1b. EM power is fed from the left to the right.

Figure 3

Transverse electric field (E_z) distribution (a) and its evolution ((b, c)) along the proposed CSP structure. Left or right parts of (a) corresponds to point A or B as marked in Fig. 1b indicating a forward or a backward wave propagation, respectively. (b) and (c) demonstrate the field evolution of the forward and backward wave corresponding to point A and B as marked in Fig.1b. The black dashed line denotes the phase front in the field evolution, and the red arrow in (b) and (c) indicates the direction of EM power flow.

Figure 4. Structure and properties of the proposed practical symmetric CSP waveguide.

(a) The schematic of the waveguide and the photo of the fabricated prototype. (b) Calculated and measured dispersion curves and the transmission spectrum of the CSP waveguide. The 0.018 mm thick copper strip with geometric parameters of d = 5 mm, g = 4 mm, h = 3.6 mm, w = 7.5 mm, a = 0.3 mm, and b = 3 mm is printed on the dielectric substrate.

Figure 5. The coupler and the corresponding dispersion curves.

(a) The photograph of the fabricated prototype coupler with SMA connectors mounted at the four terminals. (b) Simulated dispersion relations for both the traditional and the modified CSP waveguides. The geometric parameters are set as d = 5 mm, g = 4 mm, h = 5 mm, w = 10.5 mm for the traditional CSP structure, while d = 5 mm, g = 4 mm, h = 3.5 mm, w = 7.5 mm, a = 0.3 mm, b = 3 mm for the modified CSP structure, respectively. The gap between the two waveguides is optimized at 0.6 mm.

Figure 6. Transmission spectrum and electric field distributions.

The simulated (a) and the measured (b) transmission spectrum of the coupler. The simulated transverse electric field (E_Z) distributions along the device at 2.8 GHz for the forward coupling (c), and at 6.03 GHz for the backward coupling (d).