A flat and thin shape is obviously advantageous not only in terms of reducing the volume of a device, but also in handling and using it. Particularly, laminating or stacking flat devices is an intuitive and straightforward way of tailoring performance and functions. Here, we experimentally demonstrated a laminated flat lens for millimeter-wave frequencies that is based on split-ring resonators (SRRs) composed of multiple layers with different and/or identical index profiles and that exhibits characteristics that are linear combinations of those of the individual lenses. Since the characteristics of the lenses of each layer are preserved regardless of the neighbouring layers, the desired functionalities can be easily implemented simply by laminating elementary lenses designed already. When we laminated two lenses designed for bending or focusing incoming waves at 120 GHz, we clearly observed that the outgoing waves collimated and bended as desired.
© 2015 Optical Society of America
The most attractive feature of metamaterials is that properties such as permittivity and permeability can be engineered to be unnaturally large or even negative [1–4]. Accordingly, metamaterials have been investigated as a means of controlling electromagnetic waves in spectrum ranges from the microwave to visible. These artificial materials allow us to realize novel functions that are not possible with ordinary materials, such as focusing beams beyond the diffraction limit  and making objects invisible to certain electromagnetic waves [6–11]. Metamaterials have also been used to make traditional optical devices, particularly, lenses, which reshape the wavefronts of incoming waves and are used in various commercial and industrial instruments and devices [12–22]. In particular, gradient-index (GRIN) optics can be easily implemented using metamaterials without the need for precise control of the surface topography [12,13]. Recently, Luneburg lenses were demonstrated at microwave and lightwave frequencies. The reflective index changes were accomplished by varying the diameter of air holes in dielectrics  or the length of metal strips in the lens structure . However, a Luneburg lens has a spherical shape, and such a three-dimensional structure is an obvious drawback to the use of metamaterials in practical applications. On the other hand, there have been reports on lenses that have a flat shape [16–22], such as plasmonic microlenses based on nano-slits or nano-holes on optically thick metal films [16–19] and optical antenna arrays composed of V- or dipole-shaped sub-wavelength metasurface patterns on dielectric substrates [20–22]. The flat shapes enable us to reduce the size of these devices, especially the thickness, reduce fabrication costs, and increase productivity by using printed circuit board and semiconductor fabrication technologies. In addition, these advantages in shape and fabrication provide a great opportunity for monolithic integration of flat optics with other radio- or light-wave devices and circuits.
The other interesting and advantageous feature of flat lenses is that it is easy to laminate multiple lenses in order to tailor performance and functions. Unlike ordinary optic lenses, whose functions are basically come from surface curvature, lenses based on GRIN optics don’t necessarily have air gaps between them; therefore, one can imagine that a lens set consisting of multiple elementary lenses would also have a flat and thin appearance. However, considering the electrical and optical properties of metamaterials, it is likely to be hard to laminate the flat lenses mentioned above without degrading their performance and characteristics. Additional layers would be an obstacle to plasmonic waveguide modes or the lenses of each layer wouldn’t work as designed at all due to the polarization changes from one metasurface layer to the next.
In this paper, we present a laminated flat lens for millimeter-wave frequencies that is based on split-ring resonators (SRRs) (also referred to as electric-field-coupled LC resonators) [23,24] composed of multiple layers with different and/or identical index profiles and that exhibits characteristics that are linear combinations of those of the individual lenses. Since, in SRRs, the polarization of the incoming waves is preserved when the electric fields are aligned to be across the gap, and non-linear effects such as hybridization of resonant modes  in the multilayer structure can be suppressed by narrowing the gap , the overall characteristics can be made to be almost linear combinations of those of the individual lenses. This feature allows us to implement the desired lens by combining pre-designed lenses while maintaining the advantages of the flat and thin shape. In this study, we designed and fabricated a metamaterial flat lens that can bend or focus incident waves at around 120 GHz on the basis of conventional printed circuit board technology on Teflon substrates. We experimentally verified that the beam bending angle increases as the number of laminated lenses increases. In addition, we observed that the focused beam was bent when the bending lens was laminated on the focusing lens.
2. Design and results
Figure 1(a) shows the geometry and dimensions of the SRRs used as the unit cell of the flat lens. Because of the symmetric configuration of the SRRs, magnetic responses cancel out and the polarization of the incoming waves is preserved. For a flat GRIN lens, a reflective index gradient was created by varying the gap of the SRRs. Varying the gap induces resonant-frequency shifts that in turn cause frequency shifts in the transmission characteristics (loss and phase delay). Full 3D electromagnetic (EM) simulations were performed using commercial software based on the finite element method (Ansys HFSS) for gaps ranging from 75 to 260 µm. The sweep range of the gap was limited by the fabrication technology. Figure 1(b) shows the phase responses normalized to that for a 75-µm gap in the frequency range of 100 ~140 GHz. The + sign in the phase shift means the lead (fast wave) of the wavefront and a lower reflective index. As the gap widens, the resonance frequencies of the SRRs vary in the range of 65 ~85 GHz. Although a large phase shift, which is preferable for a GRIN lens, is possible around the resonance frequencies, the insertion loss is too large for a flat lens. At 120 GHz, which is slightly away from the resonance frequencies, the phase shift varies up to approximately π/3, while the insertion loss remains less than 2 dB [Fig. 1(c)].
For the bending and focusing lenses, the spatial distribution of the phase shift, φ should obey the following equations:Eq. (1), the reflective index gradient is only on the x-axis, and therefore, the incoming waves only bend in the xz plane.
Figure 2(a) shows the layout of the designed bending lens with an aperture of 7.5 mm or approximately 3λ. Narrow-gap SRRs that have higher reflective indexes were located on the left side of the lens. Therefore, the phase of the local waves on the left side should lag accordingly, and the outgoing waves should bend counterclockwise on the xz plane or the H-plane of the incoming waves. The phase responses to the designed lens are shown in Fig. 2(b), wherein the phase varied from 0 on one side to π/3 on the other side.
The bending angle with the single layer lens was expected to be approximately 3.3 degrees from the full 3D simulation [Fig. 2(c)], which is also in agreement with Eq. (1). Since the gap of the SRRs in this bending lens is optically narrow (λ/30 ∼λ/10), even if we laminate multiple lenses, there is little interference, such as hybridization, between layers. This implies that the phase profiles of the individual layers are preserved and a multi-layer lens provides a larger bending angle. In the case of the lens shown in Fig. 2(a), the bending angle is expected to be arcsin(N⋅π/18), where N is the number of layers. The simulation results for one, two, four, and ten layers in Figs. 2(d)-2(g) clearly shows that the beam bends approximately 3.3, 6.7, 13.5, and 36 degrees in agreement with the estimation. Moreover, we get almost the same result when the index gradient is on the y-axis or E-plane of the incoming waves [Fig. 2(f)].
On the basis of the design illustrated in Fig. 2(a), we fabricated laminated bending lenses consisting of up to ten layers and conducted far-field and near-field measurements on them. The metamaterials lenses were fabricated with commercial printed circuit board technology that consists of optical lithography, wet-etching for metal patterning, mechanical punching, and electrochemical plating for coating gold on the metal surface. The SRRs were patterned on polytetrafluoroethylene (PTFE) based commercial substrates (RT5880 with ½ oz copper) with a permittivity of 2.2 and loss tangent of 0.0009 at 10 GHz. The thickness of the PTFE substrate was 254 µm. The wet-etching processes limited the minimum gap between the metal patterns to 75 µm. 38-um-thick bonding film (CuClad 6700) was used to attach the lenses to each other. The relative permittivity and loss tangent of the film were 2.35 and 0.0025 at 10 GHz, respectively. Figure 3 shows a photograph of the fabricated lens. Since the unit cell in this study is the SRR surrounded by the PTFE substrate, the lens pattern shown in Fig. 2(a) cannot be seen in Fig. 3.
The fabricated lenses were evaluated with near and far-field measurements. The near-field measurement setup was composed of an Agilent N5247A vector network analyzer (VNA), two VNA extenders at the F-band for the transmitter (Tx) and receiver (Rx), and an xyz linear motor stage to perform the 2D scans. As a source antenna, we utilized standard gain horn antennas for the plane waves and a WR-8 open-ended waveguide for the spherical waves. The fabricated flat lenses were placed in front of the Tx antenna such that their surface plane was parallel to the aperture plane of the antenna. The other open-ended waveguide was used as the Rx antenna in the near-field measurements to obtain the 2D field distributions. In the far-field measurement setup, a spherical rotating arm was used to measure the beam pattern of the wave passing through the lens. The lens was placed at the spherical center of the setup. In the far-field measurements, the standard gain horn antenna was used as an Rx antenna. All the measured far-field beam patterns were normalized by the data without a lens. In these setups, the Tx antennas and lenses were fixed, and the Rx antenna were automatically controlled by an electronic motor to measure the fields continuously. RF absorbers were also used to prevent reflections between the instrumentation. The gap of the SRRs was set to be parallel to the electric-field polarization of the wave.
Figure 4(a) illustrates far-field radiation patterns on the H-plane measured 1 meter away from the lens under test. Here, it is clear that the measured bending angles with respect to the number of layers fit the arcsin (N⋅π/18) relationship [Fig. 4(b)]. Although the insertion loss slightly increases as the number of layers increases, the average insertion loss per layer is approximately 0.3 dB. This small loss must be due to that the SRRs located at the center of these bending lenses exhibit very small losses, as shown in Fig. 1(c). From the near-field measurement, we mapped the phase shift of the four-layer lens 3 mm above the lens surface. Figure 4(c) clearly shows that the measured phase shift is approximately four times what is shown in Fig. 2(b), and this implies that the phase shifts of the layers add up almost linearly. In addition, we clearly observed wavefront bending at the surface of the lens, and there was neither abnormal leakage nor radiation in the near field images [Figs. 4(d) and 4(e)] on the xz plane in the measurements with and without the four-layer lens.
3. Laminating bending and focusing lens
To examine the performance of a laminated lens with bending and focusing functions, we designed a focusing lens with the focal length of 20 mm using Eq. (2) [Fig. 5(a)]. Figure 4(b) illustrates the phase distributions in the resulting lens for the required focal length. The aperture of the lens was increased to 15 mm or approximately 6λ at 120 GHz for the performance and the SRRs used as unit cells provide a maximum phase shift of approximately π/3 per layer, and thus, we should laminate five identical elementary layers whose phase profiles are scaled down to 1/5th that of the design. It should be noted that, according to the theoretical relationship, shown in Eq. (2), between the phase profile and the focal length, we cannot control the focal length by laminating multiple focusing lenses unlike the bending lens.
The results of the full 3D EM simulation in Figs. 5(c)-5(e) clearly show that the incident plane waves come to a focus around 20 mm above the lens in both the E- and H-plane, particularly from the abrupt change in the wavefront shown in the near field phase distribution of the electric fields [Fig. 5(e)]. The characterization of the fabricated focusing lens was conducted with spherical incoming waves, instead of plane waves because of the experiment setup. As a spherical wave source, an open-ended waveguide that had an antenna gain of approximately 8 dB was located 20 mm away from the lens. From the near field measurement, we verified that the wavefront of the incoming waves [Figs. 6(a) and 6(b)] from the open-ended waveguide antenna was nearly spherical. After passing through the focusing lens, the spherical incoming waves became flat and showed a uniform phase distribution [Figs. 6(c) and 6(d)]. In addition, the outgoing waves did not diverge, but were collimated, and the beam width was similar to the lens’ aperture. We got the same results from the far field radiation pattern with and without the focusing lens. The approximately 60- to 70-degree-wide beam became narrower (around 7 degrees) in both the E- and H-planes. In addition, the measured field intensity at the right front of the lens increased by around 11 dB in comparison with the case without the lens [Fig. 6(e)]. These experimental results are in a reciprocal relationship with those from the simulation, and therefore, it is reasonable to conclude that the phase shift profiles of the elementary layers that have 1/5th the desired value linearly accumulate and that the fabricated focusing lens provides the desired function.
Finally, we experimentally examined the linear combination of two different functions, i.e., bending and focusing, with a single laminated lens. The bending and focusing lenses were designed for a bending angle of around 13 degrees in the H-plane and a focal length of 20 mm. The lenses respectively consisted of seven and five SRR-based GRIN layers. The results reported above prove that the phase profiles made by spatially modulating the gap of the SRRs are preserved and linearly accumulate in the two different multi-layer structures. Hence, we expected that the laminated lens consisting of the bending and focusing index profiles mentioned above would bend and focus the incoming waves simultaneously. The measured far field radiation pattern apparently shows that the incoming spherical waves from the same source antenna at the focal point of the lens were collimated and bent [Fig. 7(a)]. The radiation angle and beam width of the outgoing waves were approximately 14 degrees and 7 degrees, respectively, and conform to the design. The field intensity of the outgoing waves dropped by around 2 dB compared with that of only a focusing lens, and this decrease must have been due to the number of the layers for the bending function.
In order to evaluate the bandwidth of the lenses, the far-field field intensity was measured in the frequency range of 100 ~140 GHz for the five-layer focusing lens and the twelve-layer bending-focusing lens at fixed angles of 0 and 13 degrees, respectively; the results are plotted in Fig. 7(b). Though the laminated lens is based on resonant elements, the measured bandwidth is quite large because the operating frequency of the lens was designed to be slightly away from the resonance frequencies of the SRRs. The 3-dB bandwidths for the five-layer focusing lens and the bending-focusing lens were approximately 20 GHz and 8 GHz, respectively, or approximately 15% and 6.7% at 120 GHz, respectively. It should be noted that the radiation angle of the bending lens varies with the frequency because the phase shift characteristics of the SRRs themselves are frequency dependent and the index profile for the bending lens is asymmetric. This resulted in a smaller bandwidth with the bending lens at a fixed angle.
In this study, we experimentally demonstrated a laminated flat lens that exhibits a linear combination of functions in the millimeter-wave band. The lens exploits the features of the SRRs used as the unit cell; modulating the reflective index by varying the gap, maintaining the polarization of the incident waves, and little interference between layers when the gap is small enough. Because of these features, the overall characteristics of the laminated lens are almost linear combinations of those of the elementary layers. Although the maximum phase shift provided by the SRRs is limited to around 1/3 of the theoretical maximum phase shift, π, provided by a single resonant mode, it was due to a technical issue related to the fabrication process rather than a fundamental limit. A larger phase shift can be achieved with a more advanced process that can fabricate finer patterns for modulating the gap over a wide range and through further optimization of the design of the SRRs.
The flat and thin shape is advantageous not only for reducing the volume of a device, but also for handling or using it. Laminating or stacking is the most common and efficient way of handling flat electronic devices and components for performance and/or size. For instance, the electric circuit boards in almost all electric and electronic equipment consist of multiple layers of electric circuits. Solid-state integrated circuits are also stacked for saving space and increasing density . Although various metamaterial flat lenses have been proposed and experimentally demonstrated, there has been less attention on whether there are any actual advantages from a flat and thin appearance. Here, we have clearly showed both functionalities of bending and focusing incident waves with laminated structures by observing the near- and far-field patterns. In particular, we compared the measured properties with those of designs based on gradient index optics theory and found that the two functions can be linearly merged in a single flat lens by laminating the two lenses together. The laminated metamaterial flat lens will lead to new uses of metamaterials in the millimeter and terahertz-wave bands, particularly for reshaping the incoming beam and changing the propagation of EM waves.
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