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Abstract
To achieve high-speed, large-capacity communication, next-generation mobile communication systems will require manipulation of the propagation of sub-terahertz waves in the propagation channel. In this paper, we propose the use of a novel split-ring resonator (SRR) structure as a metasurface unit cell for manipulating the linearly polarized incident and transmission waves used in mobile communication systems. In this SRR structure, the gap is twisted by 90° to efficiently use cross-polarized scattered waves. By changing the twist direction and gap size of the unit cell, 2π phase designability can be achieved, which enables linear polarization conversion efficiencies of -2 dB with a backside polarizer and -0.2 dB with two polarizers. In addition, a complementary pattern of the unit cell was fabricated, and a measured conversion efficiency of more than -1 dB at the peak with only the backside polarizer on a single substrate was verified. In the proposed structure, the 2π phase designability and efficiency gain are obtained independently by the unit cell and polarizer, respectively, thus enabling alignment-free characteristics, which are highly advantageous from an industrial viewpoint. Metasurface lenses with binary phase profiles of 0 and π were fabricated using the proposed structure with a backside polarizer on a single substrate. The lenses’ focusing, deflection, and collimation operations were experimentally verified with a lens gain of 20.8 dB, which agreed well with our calculated results. Our metasurface lens has the great advantages of easy fabrication and implementation, and it has the potential to enable dynamic control by combining it with active devices because of the simple design methodology, which entails only changing the twist direction and the gap’s capacitance component.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the increasing sophistication of various wireless applications and the increased demand for wireless traffic, mobile communication systems have evolved in approximately 10-year cycles. Now, fifth-generation (5 G) mobile communication systems are being commercially deployed worldwide. To achieve high-speed, large-capacity wireless data communication, which is an essential feature, 5 G supports the millimeter wave band above 20 GHz to access a wide bandwidth [1–3]. To support the sixth-generation (6 G) mobile communication systems, which will require even higher speed and larger capacity, the sub-terahertz band above 100 GHz is being discussed among industry, academia, and governments [4–6]. On the other hand, there are still challenges in effectively using millimeter and sub-terahertz waves in mobile communication systems. Compared to conventional radio waves below 6 GHz, which are used as part of the 5 G band, millimeter and sub-terahertz waves have high linearity and a large free-space propagation loss (FSPL). As a result, the communication quality significantly deteriorates in non-line-of-sight (NLoS) and outdoor-to-indoor communication because of obstructions between the transmitter (Tx) and receiver (Rx) [6–8]. Hence, to achieve high-speed, large-capacity, and ultra-reliable low-latency communication (URLLC) in such environments, it will be essential to implement flexible, diverse wireless propagation paths.
Recently, metasurfaces have been actively studied as an enabling technology for flexible, diverse path formation. In metasurfaces, sub-wavelength-sized structures are periodically arranged in two dimensions, and the wavefront of the arriving wave can be arbitrarily designed by adjusting the structures’ dimensions and the distribution of their unit cell [9–15]. By manipulating the two-dimensional profile of the intensity and phase of the arriving waves on the metasurface plane, various functions such as focusing, collimation, diffusion, and deflection of the scattered waves can be implemented. Metasurfaces can be fabricated as very thin sheets by patterning metal or dielectric materials, and they can be installed at various places in wireless environments, thus making them suitable for diversifying propagation paths. Furthermore, metasurfaces can be made optically transparent by patterning them with indium-tin-oxide (ITO) or other materials. The resulting transparency is beneficial because it enables societal implementation without impacting the existing landscape [16–18]. As shown in Fig. 1, possible use cases include installation of a metasurface lens on a wall to guide reflected waves in NLoS communication, on window glass to improve outdoor-to-indoor propagation, or on another surface to improve the Tx and Rx antenna gain [14].
Fig. 1. Use-case image of metasurface lenses for mobile communication systems using millimeter and sub-terahertz waves.
Arbitrary design of the propagation path of scattered waves by using metasurfaces requires a phase designability of 2π. The obtained phase change of waves scattered by a single resonant mode is theoretically limited to π [19,20], which means that a multi-resonance property or a multilayer structure is necessary to achieve 2π phase designability. In the case of a reflective metasurface, all reflected waves are scattered waves, so phase changes due to resonant modes of the metasurface can be fully applied, and a 2π-range phase design can be achieved by using only two designed metasurface patterns or one designed metasurface and ground metal on both sides of a single substrate [21]. On the other hand, in the case of a transmission-type metasurface, the transmission wave comprises both scattered waves and non-scattered waves that do not undergo phase changes due to resonance modes; thus, a designed metasurface pattern with a larger number of layers is required.
There are many reports of good phase designability achieved with multilayer metasurfaces [22–36]. A promising way to achieve 2π phase designability with a relatively small number of layers is to use Pancharatnam-Berry phase metasurface, which can control the phase of circularly polarized (CP) scattered waves by changing the rotation angle of the unit cell for CP incident waves [23–29]. Another reported approach uses a Huygens metasurface, which designs both electric and magnetic resonances according to Huygens’ principle [30–36]. In particular, a Huygens metasurface can be applied to design the phase of linearly polarized incident waves, which are used in mobile communication, while still matching the wave impedance of free space. Some works have reported implementation of this approach with two metal layers on a single substrate [32–36]. However, a Huygens metasurface simultaneously uses both electric and magnetic resonances to obtain the desired impedance, which requires high alignment precision between the layers.
In the case of deploying a metasurface lens that changes the propagation direction in a wireless environment, one side of the lens must be larger than the first Fresnel zone radius to ensure that the FSPL of the path through the lens is equal to the FSPL of the total path length from Tx to the lens and from the lens to Rx [37]. For example, in certain hundred-meter path length scenarios, one side of the metasurface is several tens of times larger than the wavelength. The problem is that it is challenging to fabricate micrometer-order patterns for the sub-terahertz band over large areas and with high alignment accuracy.
In our previous work, we proposed an intensity-profile-type transmission metasurface lens to design linearly polarized transmitted waves with a single-layer film for easy installation on window glass [14]. Here, because metasurface lenses based on the intensity profile are less efficient than those based on the phase profile, we propose a novel metasurface structure with a single substrate that achieves 2π phase designability with high efficiency for linearly polarized incident waves. The proposed structure is based on split-ring resonators (SRRs), in which the electric field (E-field) is concentrated at the split gap and scattered waves are re-radiated from the electric dipole formed at the gap.
In this paper, we summarize our design methodology, in which the twist direction and gap size of twisted SRRs (TSRRs) are changed to achieve 2π phase designability of cross-polarized scattered waves for linearly polarized incident waves; furthermore, we experimentally confirm the effectiveness of this approach. To improve the efficiency of converting the incident waves to cross-polarized scattered waves, we investigate a combination of TSRRs with a polarizer layer on both sides of a single substrate, and we show that a wavefront can be designed efficiently with the TSRRs and a backside polarizer. The proposed structure is robust against interlayer alignment errors, because the scattering phase is independently determined in only the TSRR or complementary TSRR (CTSRR) layer, whereas the polarizer only serves to improve the efficiency. In addition, the proposed structure has the potential to enable highly efficient 2π dynamic phase control on a single-layer substrate by changing the capacitance component of the gap and the twist direction in combination with semiconductor-based devices [38,39], graphene [40,41], or phase-change materials [42,43]. Finally, we also investigate complementary patterns of TSRRs because of the affinity with laser patterning processes that are often used for metal patterning on glass and film substrates.
2. Principle and design
2.1. Twisted split-ring resonators
In Fig. 2(a), split ring resonators (SRRs) have an LC-resonance mode in which the circulating current is excited, which enables realization of a unit cell that is small with respect to the incident wavelength. Such a small unit cell helps with flexible, efficient design of the propagation of scattered waves. The LC-resonance mode is excited by the asymmetry in the circulating-current path, which is generated by the gap, with respect to the electric field plane of the incident waves [44,45]. In general, since the E-field of the incident waves (Ein) is perpendicular to the gap, the electric excitation coupling to the magnetic resonance (EEMR) occurs [46,47]. In the LC-resonance mode, scattered waves are re-radiated from the electric dipole formed at the gap, so that Ein and the E-field of the scattered waves (Escat) are also parallel. SRRs cause phase changes only in the scattered waves, while the phase designability of the transmitted waves is small in conventional SRRs, where Escat and the E-field of the non-scattered waves (Epass) are nonorthogonal.
Fig. 2. Geometry and dimensions of the TSRRs proposed in this paper. The proposed structure is designed to be twisted so that the direction of the gap is 90° from Ein, and Escat and Epass are orthogonal to each other, to obtain cross-polarized scattered waves with good phase designability.
Hence, Fig. 2(b) shows our proposed TSRR structure to overcome this problem. The proposed structure is designed to be twisted so that the direction of the gap is 90° from that of Ein, and Escat and Epass are orthogonal to each other. In typical SRR, the change of the SRR orientation towards the E field component (E is parallel to the gap), a short-wire-like electric resonance is excited [44–47]. The mirror symmetry of the SRR in this configuration does not allow for LC-resonance excitation; therefore, the resonance is a purely electric response of the SRR related to the electric dipole moment in the E field direction along the parallel arms of the cell. However, with the introduction of the asymmetricity through a 90° twist, the generation of the resonance becomes more complex and as shown further, the LC-resonance can be excited in the TSRR cells despite the parallel orientation of the gap. Furthermore, the direction of the circulating current excited in the TSRRs is determined by Ein, not by their twist direction. Therefore, by reversing the twist direction, the polarity of the electric dipole formed in the gap can be reversed; that is, the phase of the scattered waves re-radiated from the gap can be shifted by π.
To analyze the influence of the twist direction of TSSRs on the scattered waves, we performed an electromagnetic (EM) simulation and obtained the results shown in Fig. 3. The simulation used a two-dimensional infinite periodic structure, and the incident waves were assumed to comprise a plane wave perpendicular to the metasurface plane. The metal pattern and substrate were 18-µm-thick copper and a 300-µm-thick glass-cloth substrate (MEGTRON6 R5775K), respectively. In this paper, we denote TSRRs according to the apparent shape of the twisted part when viewed from the patterned side of the substrate: those with an “S” shape are called S-shaped TSRRs (S-TSRRs), while those with a “Z” shape are called Z-shaped TSRRs (Z-TSRRs).
Fig. 3. (a) Surface charge density distribution in the LC-resonance mode of S- and Z-TSRRs (Px = 800 µm, Py = 800 µm, Ax = 650 µm, Ay = 650 µm, W = 40 µm, G = 100 µm, Gw = 100 µm, and Ag = 80 µm.) having the same phase as the incident wave. (b) Distribution of the E-field component Ex, which is orthogonal to Ein in the xz-plane at the center of the gap.
Figure 2(a) shows the surface charge density distribution in the TSSRs, obtained at the same phase of the incident wave. As can be seen, the LC-resonance mode was excited due to the asymmetricity-induced E field coupling to the TSSR structure. The currents in the metal lines parallel to Ein in the ring parts of the S-TSRRs and Z-TSRRs flow in the same directions, and the polarities of the electric dipoles excited at the gaps are reversed from each other.
Figure 3(b) shows the distribution of the E-field component Ex, which is orthogonal to Ein in the xz-plane at the center of the gap. The phase of the scattered waves is also inverted by the inverted polarity at the gap, which is the re-radiation source, thus resulting in a phase difference of π between the S-TSRRs and Z-TSRRs. These results indicate that large phase designability can be obtained with a single-layer metasurface by combining phase inversion of the scattered waves according to the twist direction and a phase change depending on the gap size.
Figure 4 shows the simulated phase responses of the scattered waves depending on the twist direction and gap size. Here, we consider scattered waves with an Ex-component orthogonal to the incident waves. The phase characteristics at the transmission and reflection sides are shown in Figs. 4(a) and 4(b), respectively, where the gap size G was varied from 10 to 400 µm. All phase characteristics were normalized by characteristics simulated without the TSRRs. Both the S- and Z-TSRRs exhibit a shift in the phase characteristics of the transmitted and reflected waves with the change in the resonance frequency due to the change in the gap. As a result, a phase shift of approximately π is obtained around 70 GHz. Because the phase characteristics of each type of TSRR are shifted by π according to the twist direction, a phase change with a range of 2π can be achieved by designing both the twist direction and the gap size G. Figure 4(c) shows the phase difference of the scattered waves in the transmission direction of the S- and Z-TSRRs when G is 200 µm. The results confirm that the phase difference between the two TSRR types is π in all simulated frequency ranges. Note that we verified that the phase differences are also π for the other gap sizes and with the scattered waves in the reflection direction.
Fig. 4. Simulated (a) transmission and (b) reflection phases for scattered waves with an Ex-field component orthogonal to the incident waves, with gap sizes of 10 to 400 µm.
(c) Transmission phase difference of scattered waves between the S- and Z-TSRRs at a gap size of 200 µm. Here, the phase values were normalized by the simulated values for air.
As described above, the proposed TSRR structure can achieve a phase change in the 2π range with a single-layer metasurface by using transmitted waves comprising scattered waves that are cross-polarized with respect to the incident waves. However, the use of TSRRs to generate flexible, diverse propagation paths requires low loss, or rather, in the case of TSRRs, high efficiency of converting incident waves into cross-polarized scattered waves. Hence, we analyzed the scattered waves of the TSRRs by breaking them down according to the scattering direction and polarization, and we evaluated the contribution of an additional polarization layer to the cross-polarized scattered waves in the transmission direction. Figure 5(a) shows an EM simulation model in which plane waves were assumed to be linearly Ey-polarized as the incident waves. We denote the respective power ratios of the Ey-polarized and Ex-polarized waves scattered in the reflection direction with respect to the incident waves as Ryy and Rxy and those of the Ey-polarized and Ex-polarized waves in the transmission direction with respect to the incident waves, as Tyy and Txy. Here, we considered how to improve Txy, which corresponds to the efficiency of conversion to cross-polarized scattered waves in the transmission direction with large phase designability. The periodicity of the polarizer Ppol is 80 µm with a line and space (L/S) of 40/40 µm. First, to reduce Rxy and increase Txy, a polarizer 1 orthogonal to Ey was added on the back side of the substrate. Then, to reduce Tyy, which includes non-scattered waves in the transmission direction, a polarizer 2 parallel to Ey was added on the transmission side with an air gap.
Fig. 5. (a) EM simulation model of a TSRR with a backside polarizer 1 and a polarizer 2 on the transmission side with a 300-µm air gap from the TSRR (Px = 800 µm, Py = 800 µm, Ax = 650 µm, Ay = 650 µm, W = 40 µm, G = 50 µm, Gw = 100 µm, Ag = 80 µm, and Ppol = 80 µm with L/S = 40/40 µm). (b) Txy, Tyy, Rxy, and Ryy for S-TSRRs without the polarizers. Dependencies of (c) Tyy, (d) Txy, (e) Ryy, and (f) Rxy on the polarizers.
The resulting S-TSRRs were simulated with an assumption that the TSRR and polarizer 2 substrates were both of-300um-thick MEGTRON6 R5775K. Figure 5(b) shows the Txy, Tyy, Rxy, and Ryy results for S-TSRRs without the polarizers. The peaks of Txy and Rxy, which are scattered waves cross-polarized with respect to the incident polarization, can be seen in the frequency region between the lowest peaks of Tyy and Ryy, around 68 GHz, thus indicating conversion efficiency of -5 to -7 dB. Note that Rxy is greater than Txy because the substrate is on the reflection side with respect to the TSRRs and the scattered waves are induced on the reflection side, which has a higher dielectric constant relative to air. When the polarizer 1 is added on the back side, Rxy is suppressed [Fig. 5(f)], and Txy improves from -7 to -2 dB [Fig. 5(d)], as expected. Furthermore, when the polarizer 2 is added, Tyy decreases [Fig. 5(c)], and Txy improves to a very high efficiency of -0.2 dB [Fig. 5(d)]. Overall, these results indicate that the combination of TSRRs and polarizers can efficiently convert linearly polarized incident waves into cross-polarized scattered waves in the transmission direction with 2π phase designability. The same results can be obtained for Z-TSRRs, as well as S-TSRRs.
2.2. Complementary twisted split-ring resonators
A promising location for implementing metasurface lenses is on window glass (Fig. 1). A metasurface structure could be patterned directly on the glass, or a film on which the metasurface structure is patterned could be attached to the glass. Hence, given the affinity with the laser patterning process that is often used for metal patterning on glass and film, we also investigated a complementary pattern of TSRRs to achieve highly efficient phase designability on a single glass substrate or film.
Figure 6 shows EM simulation results on the twist direction of complementary TSRRs (CTSRRs). A two-dimensional infinite periodic structure was assumed, and the incident waves comprised a plane wave perpendicular to the metasurface plane. The metal pattern and substrate were 18-µm-thick copper and 550-µm-thick MEGTRON6 R5775K, respectively. Following the Babinet principle, the CTSRR was rotated by 90° so that the electric and magnetic field planes of the incident waves were swapped with those of the TSRR. Figure 6(a) shows the surface current density and vector distribution of the resonance mode in CTSRRs with the same phase as the incident wave. In the region corresponding to the gap of the TSRRs, the current directions are opposite for the S-shaped CTSRRs (S-CTSRRs) and Z-shaped CTSRRs (Z-CTSRRs). Figure 6(b) shows the magnetic field vector distribution in the yz-plane at the center of the gap. The magnetic field circulates around the region corresponding to the gap, in accordance with the surface current shown in Fig. 6(a), and the circumferential direction of this field is reversed between the S- and Z-CTSRRs. This behavior of the surface current and magnetic field as the source of re-radiated scattered waves indicates that CTSRRs, like TSRRs, can achieve 2π phase designability with a single substrate. The same analysis as shown in Fig. 5 is performed for CTSRRs, and the effectiveness of the polarizers to improve the Txy is confirmed as well as for TSRRs (see Supplement 1, Section 1).
Fig. 6. (a) Surface current density and vector distribution in the LC-resonance mode of S- and Z-CTSRRs (Px = 800 µm, Py = 800 µm, Ax = 650 µm, Ay = 650 µm, W = 40 µm, G = 100 µm, Gw = 100 µm, and Ag = 80 µm) having the same phase as the incident wave.
(b) Distribution of the H-field in the yz-plane at the center of the gap in S- and Z-CTSRRs.
To verify that good phase designability is maintained even with the inclusion of polarizer layers for higher efficiency, we examined the dependence of the scattering properties of CTSRRs with polarizers 1 and 2 on the twist direction and gap size. For cross-polarized scattered waves on the transmission side, Figs. 7(a) and 7(b) respectively show Txy and the phase characteristics with G varying from 10 to 400 µm. All the phase characteristics shown here were normalized by the simulated characteristics for air without the CTSRRs. As seen in Fig. 7(a), the combination of the CTSRRs and polarizers results in high conversion efficiency, and the region of high conversion efficiency shifts to lower frequencies as the gap size decreases. The highest Txy of -0.35 dB is achieved at G = 400 µm. In Fig. 7(b), the scattering phase characteristics of both the S- and Z-CTSRRs shift with the change in resonance frequency due to the change in the gap, and each CTSRR type achieves a phase range of approximately π around 80 GHz. As with the TSRRs, the phase characteristics of the CTSRRs differ from each other by π because of the twist direction; thus, a designable phase range of approximately 2π can be achieved by designing both the twist direction and the gap size. Figure 7(c) shows the phase difference between the S- and Z-CTSRRs when G is 200 µm. The results confirm that the phase difference is π in all simulated frequency ranges, and this phase difference was also confirmed for the other gap sizes.
Fig. 7. Simulated (a) Txy and (b) phase for S- and Z-CTSRRs with polarizers, over a gap range from 10 to 400 µm. (c) Transmission phase difference of scattered waves between the S- and Z-CTSRRs at a gap size of 200 µm. Here, the phase values were normalized by the simulated values for air.
As mentioned above, a phase designability of 2π with high conversion efficiency can be achieved by combining the proposed TSRRs or CTSRRs with polarizers. However, as seen in Fig. 7(b), for example, there is a gap of approximately 50° between the phase design ranges covered by the S- and Z-CTSRRs. This limits the quantization bit number of phase when creating a phase profile to a maximum of 2 bits.
Compared to the ideal continuous phase profile, the efficiency of the qth diffraction order with a quantizing N-phase level in a phase modulation range of 2π can be expressed as follows [48]:
When using metasurfaces to design propagation in a wireless environment, the FSPL of the path through the metasurface should be less than or equal to the total path length from Tx to Rx through the metasurface. To achieve this, one side of the metasurface should be larger than the radius of the first Fresnel zone. For example, if the total path length is a few hundred meters, one side of the metasurface should be several tens of times larger than the wavelength. At higher frequencies, such as those of sub-terahertz waves, it is not easy to achieve layer-to-layer alignment with sufficient accuracy for subwavelength-sized metasurface unit cells over a large area. In our proposed structure, the scattering phase is independently determined only in the TSRR or CTSRR layer, and the polarizer only works for efficiency gains. This means that the combination of the TSRR or CTSRR and polarizer is robust against such alignment errors, which is an advantage from an industrial viewpoint. Figure 8(a) shows a simulation model that was used to simulate the effect of the amount of error on the scattering properties when the alignment of the polarizer and the TSRRs or CTSRRs was shifted in the direction orthogonal to the polarizer as shown in Fig. 8(b). The simulation assumed the TSRRs or CTSRRs were on a single substrate with a backside polarizer 1 having Ppol = 80 µm and L/S = 40/40 µm. For both the TSRRs and CTSRRs, the changes in the peak frequency where the conversion efficiency is maximum, the conversion efficiency, and the scattering phase at this frequency due to alignment errors are all very small at 0.3%, 0.2 dB, and 3°, respectively. Thus, the simulation results confirm that the structure is robust against alignment errors.
Fig. 8. (a) EM simulation models for an S-TSRR (Px = 800 µm, Py = 800 µm, Ax = 650 µm, Ay = 650 µm, W = 40 µm, G = 50 µm, Gw = 100 µm, Ag = 80 µm, and Ppol = 80 µm with L/S = 40/40 µm) and S-CTSRR (Px = 800 µm, Py = 800 µm, Ax = 650 µm, Ay = 650 µm, W = 40 µm, G = 300 µm, Gw = 100 µm, Ag = 80 µm, and Ppol = 80 µm with L/S = 40/40 µm).
(b) Simulated effects of the amount of error on the scattering properties when the alignment of the polarizer and the S-TSRRs or S-CTSRRs was shifted in the direction orthogonal to the polarizer.
3. Results and discussion
As discussed above, the combination of TSRRs and CTSRRs with polarizers enables 2π phase designability with high efficiency. To verify this finding experimentally in the sub-terahertz band being considered for 6 G, we designed, fabricated, and measured metasurface lenses that focus, collimate, and deflect incident waves in the 110 GHz band. Because a single polarizer layer degrades the conversion efficiency by only a few decibels as compared to two polarizer layers [see Figs. 5(d) and Supplement 1, S1(d)], and because of the need for easy mounting in various locations, the metasurface lenses were fabricated on a single substrate with a polarizer on the backside of the metasurface. Recently, binary coding metasurfaces using PIN diodes to control the propagation of reflection waves have been reported [49,50]. As described in the previous section, the diffraction efficiency is sufficient even with a simple binary phase distribution of 1 bit. Therefore, the two-dimensional phase profiles in this paper were designed with a binary (0/π) phase by varying only the twist direction of the TSRRs and CTSRRs, with a view to future switching control of the twist direction by PIN diodes.
3.1. Experimental setup
Figure 9 shows a schematic diagram of the experimental setup for evaluating the fabricated metasurface lenses. The setup comprised an Agilent N5247A vector network analyzer (VNA), two VNA extenders at the F-band, and an xyz linear motor stage to enable two-dimensional scanning. Two standard gain horn antennas were used for Tx and Rx in S-parameter measurements. In two-dimensional distribution measurements, a probe antenna was used as the Rx antenna. The Tx antenna and the metasurface lenses were placed a certain constant distance apart, while the Rx probe antenna was automatically controlled by an electric motor to measure the fields continuously. Absorbers were also placed to prevent reflections between the instruments. The E-field polarization of Tx waves was set to be the same as in Figs. 3 and 6, and the Rx antenna incorporated a twist waveguide to measure the cross-polarized scattered waves.
Fig. 9. Schematic diagram of the experimental setup for measuring the E-field distribution. Horn and probe antennas were used as the Tx and Rx antennas, depending on the specific measurement.
3.2. Fabricated lenses
First, to experimentally confirm the expected π phase difference by reversing the twist direction, cross-polarized scattered waves were measured on the transmission side of a 30 × 30 mm metasurface sample on which TSRRs or CTSRRs with an identical twist direction and dimensions were periodically patterned. For these measurements, the measured intensity and phase were normalized by data collected without the metasurfaces. Figures 10(a) and 10(b) show enlarged images of the fabricated TSRR and CTSRR, respectively. The substrate was 300-µm-thick MEGTRON6 with a 40/40-µm-L/S polarizer on the back side. In Figs. 10(c) and 10(e), the measured Txy indicates that both the TSRR and CTSRR, respectively, have similar characteristics with either the S- or Z-shape. In particular, both show peak Txy of more than -3 dB, which agrees well with the EM simulation results. In addition, Figs. 10(d) and 10(f) show that the phase difference between the S- and Z-shapes is π, as expected for both the TSRRs and CTSRRs, respectively.
Fig. 10. Enlarged images of the fabricated (a) TSRR (Px = 800 µm, Py = 640 µm, Ax = 600 µm, Ay = 500 µm, W = 40 µm, G = 200 µm, Gw = 100 µm, Ag = 40 µm, and Ppol = 80 µm with L/S = 40/40 µm) and (b) CTSRR (Px = 800 µm, Py = 800 µm, Ax = 600 µm, Ay = 600 µm, W = 40 µm, G = 200 µm, Gw = 100 µm, Ag = 40 µm, and Ppol = 80 µm with L/S = 40/40 µm). (c) Measured and simulated Txy for TSRRs with a backside polarizer. (d) Measured phase difference between S- and Z-TSRRs. (e) Measured and simulated Txy for CTSRRs with a backside polarizer. (f) Measured phase difference between S- and Z-CTSRRs.
Next, we designed and fabricated a focusing lens with a binary phase profile by using the TSRRs and CTSRRs. We denote the number of unit cells constituting the metasurface as M; the phase center of Tx as P1; the point at which the metasurface lens focuses energy as P2; the position of the mth unit cell as Um (where m is an integer from 1 to M); the distances from P1 and P2 to the center of the metasurface lens as D1 and D2, respectively; and the distances from P1 and P2 to Um as d1,m and d2,m, respectively. The phase difference Gm associated with the optical path length difference due to the position of the unit cell passed through can be expressed by
where λ is the wavelength.According to Eq. (2), metasurface lenses with the desired focus P2 for wave source P1 can be designed by placing TSRRs or CTSRRs with different twist directions at Um, where 0 ≤ Gm mod 2π < π and π ≤ Gm mod 2π < 2π. Here, if D1 and D2 are sufficiently large compared to the size of the metasurface, then we can respectively assume a plane wave arriving from P1 as the incident wave and a transmission wave deflected in the direction of P2.
Figure 11(a) shows the zone pattern for the twist direction. In this experiment, we evaluated a 100 × 100 mm lens with a focal point that was designed to be 100 mm from the center of the metasurface lens, assuming a plane wave incident perpendicular to the lens. For reference, a metasurface lens with an intensity profile that we reported in our previous work [14] was also scaled and measured at 110 GHz. Figures 11(b)–11(d) show enlarged images of the reference lens, the TSRR lens (Lens 1), and the CTSRR lens (Lens 2), respectively. For the reference lens, nothing was patterned on the white parts [Fig. 11(a)], while a unit cell that reflected 110-GHz radio waves was patterned on the shaded parts. For Lens 1 or 2, respectively, S-TSRRS or S-CTSRRS were patterned on the white parts and Z-TSRRs or Z-CTSRRs were patterned on the shaded parts.
Fig. 11. (a) Zone pattern for the twist direction. Enlarged images of (b) the reference lens, (c) the TSRR lens (Lens 1), and (d) the CTSRR lens (Lens 2),
3.3. Near-field measurement results
In these measurements, we first evaluated the focusing function, as designed by the distribution of the twist structure, at 110 GHz for a metasurface lens without a backside polarizer. Figures 12(a)–12(c) show the respective results for the 100 × 100 mm aperture with no metasurface lens, Lens 1 without a polarizer, and Lens 2 without a polarizer. The Tx horn antenna was placed 500 mm from the metasurface lens to provide an incident plane wave, and the Ey-field was measured for the aperture with no metasurface lens, while the Ex -field is measured for Lenses 1 and 2. The wave through the 100-mm aperture has an almost uniform intensity distribution in the absence of the metasurface lens. For Lenses 1 and 2, the transmission waves are concentrated near the designed focus of 100 mm, and the peak gains, defined as the gain at the focus normalized by the results with no metasurface lens, are 10.1 and 12.1 dB, respectively. These results indicate that a single layer of TSRRs or CTSRRs without a polarizer can provide more than 10 dB of gain.
Fig. 12. Measured E-field distributions for (a) the 100 mm × 100 mm aperture with no metasurface lens, (b) Lens 1 (S- and Z-TSRRs) without a polarizer, and (c) Lens 2 (S- and Z-CTSRRs) without a polarizer.
Figure 13(a) shows the E-field distribution calculated using equation (Supplement 1, S5), where the binary phase profile was used while assuming that the incident waves were converted with Txy of 0 dB (see Supplement 1, Section 2). From the distribution, the ideal peak value is observed to be 24.6 dB. Figures 13(b)–13(d) show the respective measured results for the reference lens with the intensity profile, Lens 1 with a backside polarizer, and Lens 2 with a backside polarizer. The measured distributions for Lenses 1 and 2 agree well with the calculated results. The peak gains of Lenses 1 and 2 are 17.9 and 20.8 dB, respectively, which are approximately 5 to 8 dB higher than the peak gain of the reference lens (12.9 dB) because of the larger effective aperture area of the phase-profile lens as compared to the intensity-profile lens. The peak gain improvement due to the backside polarizer is about 8 dB for both Lenses 1 and 2, which is consistent with the improvement due to the backside polarizer 1 in Figs. 5(d) and Supplement 1, S1(d). We expect that there are several reasons, beside experimental measurement errors, for the differences between the calculated result and the measured peak gains of Lenses 1 and 2: differences in the conversion efficiency for cross-polarized scattered waves on the transmission side; the fact that the incident waves were not actually ideal plane waves; and the fact that the measurement results were averaged over a given aperture area of the Rx probe antenna.
Fig. 13. (a) E-field distribution calculated using Eq. (7), where the binary phase profile was used while assuming that the incident waves were converted with Txy of 0 dB. Measured E-field distributions for the (b) reference lens with the intensity profile, (c) Lens 1 (S- and Z-TSRRs) with a backside polarizer, and (d) Lens 2 (S- and Z-CTSRRs) with a backside polarizer.
Next, we designed and evaluated a metasurface lens to flatten the wavefront of a spherical wave source at a distance of 150 mm from the center of the lens and deflect it by 20°. Here, we assumed a use case in which the metasurface lens was placed near Tx and Rx antennas to collimate the incident wave in the desired direction. The lens was fabricated with CTSRRs, and a probe antenna was used as the Tx antenna. The zone pattern for the twist direction, which was designed according to Eq. (2), is shown in Fig. 14(a). Here, S-CTSRRs were placed in the white parts and Z-CTSRRs were placed in the shaded parts. The measured Ex-field distribution, shown in Fig. 14(b), indicates that collimation and deflection are achieved as expected.
Fig. 14. (a) Zone pattern for the twist direction in the case of flattening a spherical wave source at a distance of 150 mm from the center of the metasurface lens and deflecting it by 20°. (b) Measured E-field distribution.
In summary, we have demonstrated that, for linearly polarized incident and transmission waves, 2π phase designability with high efficiency and robustness against interlayer alignment errors can be achieved by changing the twist direction and gap size of the proposed TSRR and CTSRR structures with a backside polarizer on a single substrate. In addition, we experimentally demonstrated the effectiveness of a single-substrate metasurface lens using a binary phase profile based on the twist direction.
The metasurface lenses reported thus far in this paper were fabricated on commercially available substrates to verify their feasibility. In addition, to confirm how TSRRs comprising films on glass would actually look, we fabricated TSRRs with a backside polarizer by using 700-µm thick glass, as shown in Fig. 15. Because the TSRR unit cell size is small, down to several hundred micrometers, and the line width is thin for the sub-terahertz band, the opposite side from the metasurface can be fully seen through the TSRRs with backside polarizers, without requiring the mesh technique reported in Ref. [14]. To further improve this optical transparency, a metal pattern could be formed using low-resistance ITO or another suitable material.
4. Conclusion
We have proposed the use of a twisted split-ring resonator (TSRR) as a unit cell in a metasurface to achieve 2π phase designability with high efficiency and robustness against interlayer alignment errors, assuming linearly polarized incident and transmission waves. EM simulation results confirmed that 2π phase designability can be achieved by changing the twist direction and gap size of the TSRR. To increase the cross-polarized scattered waves on the transmission side, a combination of TSRRs and polarizers was investigated. As a result, Txy of -2 dB was obtained with a backside polarizer, and Txy of -0.2 dB was obtained with two polarizers. In addition, given the affinity with the laser patterning process that is often used for metal patterning on glass and film, a complementary pattern of TSRRs (CTSRRs) was also fabricated. The measured Txy showed that the CTSRRs achieved more than -1 dB at the peak with only the backside polarizer on a single substrate. The 2π phase designability and efficiency gain of the proposed structure derive independently from the TSRRs or CTSRRs and the polarizer layer, respectively, thus, providing alignment-free characteristics. Metasurface lenses with binary phase profiles of 0 and π were fabricated by using CTSRRs with a backside polarizer on a single substrate, and their focusing, deflection, and collimation operations were experimentally confirmed with a lens gain of 20.8 dB, which agreed well with our calculated results.
In summary, our metasurface lens has the great advantages of easy fabrication and implementation; moreover, it has the potential for dynamic control by combining it with reported techniques because of its simple design methodology, in which only the twist direction and capacitance component of the gap are changed.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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