We analyze and experimentally realize coplanar imaging of transverse-electric (TE) modes surface waves using weakly anisotropic metasurface consisting of non-periodic subwavelength U-shaped metallic structures. Such metallic structures with the exciting coplanar dipole are integrated on the top surface of a thin dielectric board. A circuit model is utilized to analyze the characteristics of the surface waves supported by the metasurface. By varying the geometrical parameters of the U-shaped metallic structures, the phases of surface waves are modulated, from which a planar lens is presented for the TE-mode coplanar imaging. The analyses and measurements show that anisotropies of the U-shaped metallic structures have little influence on the imaging properties of the planar lens. The measurement results have good agreements to numerical simulations.
©2013 Optical Society of America
Metamaterials provides concepts and methods of manipulating electromagnetic (EM) waves according to the predetermined designs. This has been mostly proceeding in three-dimensional situations for the past a few years. Recently, a single layer of metamaterials (or very thin metamaterials) also referred to as metasurface or metafilm has attracted increasingly interests due to the advantages of low cost, easy fabrication, low loss, and compact size over the bulk metamaterials. For two-dimensional (2D) metamaterials, various analysis methods are established and plenty of applications are realized. For example, a general sheet transition condition (GSTC) has been utilized to analyze the ungrounded metasurfaces , and a very thin cloak was presented using the method . For grounded metasurfaces, impedance boundary condition has been adopted to design low profile antennas [3, 4]. A high efficiency bridge linking propagation waves and surface waves was realized by modulating the reflected phase of the metasurface ; the snell’s low was generalized to study the propagation phase discontinuity ; and the light polarization is manipulated with ultrathin metasurfaces .
In this letter, we focus on manipulating the surface waves on ungrounded metasurfaces. Specified structures supporting surface waves can be found in early works, such as corrugated metal surface [8, 9] or cylinder [10, 11]. These surface waves are analogy in their dispersion properties to surface plasmon polaritons (SPPs) existing on interfaces between a metal and a dielectric at the optical frequency. Actually, by structuring metal surfaces with subwavelength slits or holes, a concept of spoof SPPs has been introduced at the vicinity of metal surfaces in the terahertz and microwave frequencies [12, 13]. Broadband ultrasubwavelength waveguiding at terahertz and infraed freuquencies are also described based on strongly coupled interlaced charge density waves . This concept offers the possibility to realize compact integrated plasmonic devices with well-designed metasurfaces. Ultrathin metafilms consisting of split-ring resonators (SRRs)  and complementary split-ring resonators (CSRRs)  were proposed for guiding the spoof SPPs. Grooved metal surface with nearly-zero lateral thickness was also demonstrated to be a good candidate for guiding the tightly bounded spoof SPPs . By discretizing the periodical units of such grooved metallic surface and displacing them on a planar or curved object, an ultrathin metasurface consisting of U-shaped metallic structures can be produced for guiding spoof SPPs. Based on this, a planar lens is then presented for coplanar imaging by modulating the propagation phase of spoof SPPs. The phase modulation is accomplished by changing the geometric parameters of units. More complicated functional SPP devices can also be created by designing the units, and the presented metasurface can be another good candidate to realize integrated planar systems . In the process of preparing this paper, the authors have noticed that in-plane focusing of terahertz surface waves has been reported .
Physically, the propagation of surface waves on these guiding structures relies on the coupling of units. By introducing a groove into each metal patch, the capacitive coupling of such units is stronger than the traditional split-ring resonators (SRRs), and the inductive coupling of such units is stronger than the traditional metal patches. Hence the working frequency of surface waves or the plasma frequency of the spoof SPPs is significantly lowered. It is worth noting that the excessive magnetic coupling between units may bring in magnetoinductive waves , because in this case the spatial dispersion of a single resonant unit is involved since the wavelength of the surface waves is comparable with the unit size. And it would be better to avoid the working frequency being close to the first Brillouin zone, otherwise higher-order Floquet modes may emerge.
The waveguide model in Fig. 1(a) shows the configuration of solving the eigen modes using electromagnetic simulation software (CST Microwave Studio). Periodic boundaries are used in the x and y directions, and the perfect electric conductor (PEC) boundary is used in the z direction since the open boundary is not supported by the eigen-mode solver of CST. Because the surface waves decay rapidly in the z direction, the PEC boundary has little effect on the propagation properties of the surface waves when the distance between PEC and the unit is sufficiently large.
The circuit models shown in Fig. 1(b) are utilized to analyze the propagation characteristics of the metasurface. The thin anisotropic unit is represented by a tensor surface admittance matrixEq. (2) can be written as
3. Simulations and design
With the configuration shown in Fig. 2(a), we obtain the dispersion relation of the U-shaped unit by sweeping the phase variations in the x and y directions using the eigen-mode solver of CST. From the dispersion surface shown in Fig. 2(b), we notice that the surface waves on the presented ultrathin metasurface is able to mimic spoof SPPs in two dimensions. To manipulate the behaviors of the surface wave, we need to know how the geometrical parameters of the element affect the phase changes at a specified frequency.
Figure 3 illustrates the iso-frequency curves of the unit elements with different groove heights at 11 GHz which is far away from the edge of Brillouin zone. From Fig. 3, we clearly observe that the isofrequency curve approaches a circle when the groove length becomes smaller and smaller, implying that the degree of anisotropy decreases.
In the design of a coplanar lens presented in Fig. 4, the elements with deep grooves are placed in the middle of the lens. Then the surface wave passes through these elements in a line nearly parallel to the x axis. According to previous analysis, the TE surface waves feel these elements as isotropic ones with admittance and the wave number of the surface wave is . The elements with shallow grooves can be safely treated as isotropic since their dispersion curves are close to circles no matter whether the propagation direction of the surface wave is along the principle axis or not. When calculating the phase changes of the surface wave when passing through the coplanar lens, the propagation direction is assumed to be along the x axis. Thereby the phase of surface wave can be modulated by relating the groove lengths and phase changes in the x direction. The imaging system is illustrated in Fig. 4, in which a coax-fed dipole which is parallel to the lens is used to excite the TE surface waves. As the phases of surface waves are purposely modulated, an image of the source is formed by focusing the transmitted waves.
Figure 5(a) displays the relationship of the phase change in the x direction to the groove length at specific frequencies. The operating frequency is designed as 11 GHz, and both positions of the source and image are designed to be 50 mm away from the lens.
As the dipole is not a perfect point source, the phase distribution at the left edge of the lens, which is closer to the source, is extracted from CST as is depicted by the blue line in Fig. 5(b). Because the source distance equals to the image distance, the optical length from the source to the lens is symmetrical to that from the image to the lens. Then the equality of optical length leads to the following equationFig. 5(a), we obtain the distribution of groove lengths h along the y direction, as demonstrated by the green line in Fig. 5(b). Note that the grooves with heights less than 1mm have been represented by grooves with heights of 1mm as the phase changes of these units are almost identical.
4. Experimental results
After obtaining all the necessary information for designing the metasurface lens, we have fabricated the imaging system using the standard printed circuit board. In the process of designing the lens, we assume the propagation paths of the waves are parallel to x axis so as to utilize the theory of geometrical optics. Because the propagation path of the surface wave on the planar lens is not strictly along x axis as in the theoretical design, a deviation of 4.5mm of the focus point between the theory and the structural simulations is observed. The structural simulations show that the working frequency of the lens is 10.5GHz and image distance is 45.5mm. In measurements, the sample is fixed on a motor station, another dipole having the same size as the source is fixed 1mm above the metasurface by a trestle. Both dipoles are connected to an Agilent N5230C network analyzer with coaxial lines. By moving the motor station, the y components of the electric fields on the measuring plane shown in Fig. 6(c) is recorded. In the measurement, there is no metal cover placed above the sample. That is, the measurement is processed in an open environment. Because the record results by the test probe are actually the amplitudes and phase of S21, extra propagation losses between the two dipoles are introduced, and the mismatch of the probe with the connecting coaxial line will also reduce the amplitudes of S21. As a result, Differences in quantities between the simulation and measurements are emerged as shown in Fig. 6(c). Nevertheless, the relative phases at each position are not affected by the losses and have been recorded by the probe. As can be seen from Fig. 6(c), the measured distributions of the y-component electric fields on the measurement plane are in good agreements with the simulated results.
In summary, U-shaped metallic structures are introduced to compose an ultrathin metasurface to support TE-mode surface waves, which is analogy in their dispersion properties to spoof SPPs. By varying the groove heights of the U-shaped units, phases of the surface waves are modulated and a metasurface lens is presented for coplanar imaging. More complicated functional metasurfaces or plasmonic devices are also able to design with these ultrathin U-shaped metallic structures.
This work was supported by the National Science Foundation of China under Grants 60990320, 60990324, 61138001, and 60921063, the National High Tech (863) Project under Grants 2011AA010202 and 2012AA030402, and the 111 Project under Grant 111-2-05.
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