Dual-Band High Efficiency Terahertz Meta-Devices Based on Reflective Geometric Metasurfaces

The wavelength-dependent behavior of the metasurface is one of the severe disadvantages in the metasurface-based applications, which greatly limits its applications. In this work, a novel reflective building block (unit cell) has been proposed to work at two arbitrary terahertz frequency bands with independent phase control at each band. The geometric phase building block can reflect the incident circularly polarized wave and convert it to the wave with opposite helicity and high conversion efficiencies at both bands. As proof of concept demonstrations, a dual-band cylindrical meta-lens and two vortex beam generators operating at 0.45 and 0.7 THz are investigated to verify the performance of the proposed building block. The simulated results of the metalens agree very well with the theoretical calculations, which are consistent with the design goals. Moreover, the designed vortex metasurfaces reveal a convenient and low-cost way to realize the vortex beam carrying different/same orbital angular momentum modes at two bands.

SECTION I. Introduction

Metasurface is composed of an array of sub-wavelength scatterers or antennas in a planar surface to locally manipulate the amplitude, phase, and polarization of the incident wave [1]–​[6], which is usually deemed as the two-dimensional counterpart of bulky and lossy three-dimensional (3D) metamaterials. Since its emergence, metasurface has attracted significant attention due to its excellent abilities to shape the wavefronts and unique features, such as low profile and easy fabrication. In the past several years, a large number of novel metasurface-based applications have been demonstrated including anomalous reflection/refraction [7], cloaking [8], metalenses [9], [10], wave plates [11], [12], holograms [13], [14], and vortex beams [15]–​[17].

However, the single-layer transmission-type metallic metasurfaces usually suffer from low efficiency and have a conversion efficiency limit of 0.5 [18], [19], therefore, a lot of efforts have been devoted on improving the efficiency, including dielectric resonators [20]–​[23] and multi-layer designs [24]–​[26]. By using dielectrics or cascading more metasurface layers, one can obtain higher conversion efficiency, but at a cost of increased device thickness or fabrication challenges. In addition, another common means to realize high efficiency is to employ the reflection-type structure. Many applications have been proposed based on this principle [27]–​[30]. However, due to the dispersive nature, most of the reflection-type devices only work at one single band (e.g., [27]–​[29]). One dual-band reflective metasurface [30] has been reported recently under different polarized incidences at two frequency bands with a periodicity of about $0.44~\lambda$ at the higher frequency. As the development of the modern technologies, the devices that can operate at multiple frequencies are highly desirable. Therefore, this work focuses on the realization of high efficiency metasurface-based devices (meta-devices) that can function at two arbitrary terahertz (THz) frequencies under the same polarized incidence.

Specifically, a novel geometric phase building block is proposed to work at two arbitrary terahertz frequencies with independent phase control at each frequency within a deep-subwavelength unit cell. The building block is composed of a patterned metallic layer and a ground plane separated by a silicon spacer. The top metal layer is perforated with a double-C-shaped slot (DCSS) resonator and a circular hole, in the center of which a nano-bar resonator is seated. Due to the reflective design, the cross-polarization conversion efficiencies of the building block are around 0.8 and 0.92 at 0.45 THz and 0.7 THz, respectively. The full $2\pi$ phase coverages at two frequencies can be obtained simply by rotating the two resonators. Dual-band meta-devices can be readily realized by applying the proposed building blocks. As proof of concept demonstrations, a dual-band cylindrical metalens with the same focal length of 5 mm at 0.45 THz and 0.7 THz is theoretically calculated and numerically studied. The full-wave simulation results agree very well with the calculation results and the design goals. In addition, the vortex beams carrying different/same orbital angular momentum (OAM) modes at two frequencies can be generated by deploying the proposed building blocks, which are validated through full-wave simulations. The proposed method could open new avenues for achieving dual-band high efficiency meta-devices.

SECTION II. Building Block Design

Fig. 1 illustrates the schematic model for a dual-band vortex beam generator, which consists of an array of the proposed dual-band building blocks shown in Fig. 1(b). As can be seen from Fig. 1(b) that the building block is composed of a patterned aluminum layer and a ground plane separated by a silicon layer ($n_{si} = 3.45$ ) with a thickness of $280~\mu \text{m}$ . The top layer is constructed by a DCSS and a nano-bar resonator centered in a circular hole. The outer radius of the DCSS resonator, the width of the slot and the gap width between the two C-shaped slots are denoted as $r_{out}$ , $w$ , and $w_{cut}$ , respectively. The length and width of the nano-bar resonator are depicted as of $b_{l}$ and $b_{w}$ , respectively. The orientations of the nano-bar resonator and DCSS resonator are denoted as $\theta _{2}$ and $\theta _{1}$ with respect to the $x -$ axis, respectively. The radius of the circular hole is $r_{c}$ .

FIGURE 1.

(a) Schematic model for a dual-band meta-device; (b) the tilted view of the proposed building block.

Compared to the propagation phase involved in the design of metasurfaces, geometric phase or Pancharatnam-Berry (PB) phase features easy design, originating from the polarization change for the circularly polarized incidences. When passing a resonator or retarder, the incident circular polarization can be converted to its opposite helicity, and a relative geometric phase emerges to possess the form of $\varphi _{\mathrm {PB}} = 2 \sigma \theta$ [31], where $\theta$ is the orientation of the resonator with respect to $x$ -axis and $\sigma = + /-1$ corresponds to the helicity of right/left circularly polarized (RCP/LCP) incidence. More specifically, the resonator converts RCP (LCP) light to LCP (RCP) light along a state-space path determined by the resonator’s orientation $\theta$ , yielding a geometric phase that increases linearly from 0 to $2\pi$ as the resonator is rotated at angles from 0 to $\pi$ . Thus, the geometric phase is a simple but efficient method to achieve $2\pi$ phase coverage by changing the resonator’s orientation.

In designing a dual-band building block, it is usually hard to achieve independent phase control at two frequencies by just putting two similar resonators in a deep sub-wavelength unit cell due to the strong interference between them [32]. For the proposed dual-band building block, the abrupt geometric phases at two pre-assigned frequencies can be obtained by varying the orientations of the DCSS resonator and the nano-bar resonator (i.e., $\theta _{1}$ and $\theta _{2}$ ). By adjusting the dimensions of the DCSS resonator and nano-bar resonator, the proposed building block can operate at two desired THz frequencies. Moreover, the interference between the DCSS resonator and the nano-bar resonator can be significantly reduced by tuning the size of the circular hole, resulting in independent phase modulations at two frequencies.

To analyze the proposed building block, numerical simulations were carried out by using the commercial software package (CST Microwave Studio), with the unit cell boundary conditions applied in $x$ - and $y$ -directions and Floquet-port excitation applied in the $z$ -direction. In these simulations, the two operation frequencies are chosen as $f_{1}=0.45$ THz ($\lambda _{1}=667\,\,\mu \text{m}$ ) and $f_{2}=0.7$ THz ($\lambda _{2}=429\,\,\mu \text{m}$ ), and the incidence is a RCP wave from–$z$ -direction. The structural parameters are optimized as $r_{out}=60\,\,\mu \text{m}$ , $r_{c}=48\,\,\mu \text{m}$ , $b_{w}=20\,\,\mu \text{m}$ , $b_{l}=55\,\,\mu \text{m}$ , $w_{cut}=5\,\,\mu \text{m}$ , $w=5\,\,\mu \text{m}$ , and $p=125\,\,\mu \text{m}$ . Fig. 2(a) (Fig. 2(b)) plots the geometric phase shift at 0.45 THz (0.7 THz) of the reflected LCP wave by rotating $\theta _{1}$ ($\theta _{2}$ ) with a fixed $\theta _{2}$ ($\theta _{1}$ ) under a RCP incidence. It can be seen from Fig. 2(a) (Fig. 2(b)) that the $2\pi$ phase coverage can be realized at 0.45 THz (0.7 THz) by varying $\theta _{1}$ ($\theta _{2}$ ) with a $\pi$ phase interval. In addition, Fig. 2(c) (Fig. 2(d)) demonstrates that the high cross-polarized reflection can be obtained, which is around 0.8 (0.92) at 0.45 THz (0.7 THz). Fig. 2 indicates that the proposed building block could achieve independent phase control at the two operating frequencies with high efficiencies.

FIGURE 2.

The geometric phase shift at (a) 0.45 THz by rotating $\theta _{1}$ with a fixed $\theta _{2}$ and (b) 0.7 THz by rotating $\theta _{2}$ with a fixed $\theta _{1}$ ; (c)-(d) the corresponding cross-polarized reflection for (a)-(b).

SECTION III. Proof of Concept Demonstrations: Meta-Lens and OAM Generators

The performance of the proposed dual-band building block will be validated through the proof of concept demonstrations including a dual-band cylindrical meta-lens and two OAM generators with different/same OAM modes at two operating frequencies, which will be discussed in the following sections.

A. A Dual-Band Cylindrical Meta-Lens

A one dimensional (1D) cylindrical meta-lens with the same focal length at 0.45 THz and 0.7 THz has been designed by employing the proposed building block. As the incident wave reflects from the metasurface to the focal plane, it accumulates a different amount of phase difference on the propagation path at each wavelength, thus, a hyperbolical phase profile is required to compensate the phase difference, which can be expressed as

$$\begin{equation*} \varphi (x,y,\lambda _{i})=-\frac {2\pi }{\lambda _{i}}(\sqrt {x^{2}+y^{2}+F^{2}} -F),\quad i=1,2\tag{1}\end{equation*}$$ where $\varphi$ (x,y, $\lambda _{i}$ ) represents the required phase compensation at the position of ($x$ , $y$ ) for the operation wavelength of $\lambda _{i}$ , and $F$ is the focal length. In this case, a RCP plane wave is normally impinging on the metasurface from -$z$ -direction, and the reflected LCP wave is recorded.

Here, we investigate a dual-band cylindrical metalens with a focal length of 5 mm at 0.45 THz and 0.7 THz by both theoretical calculations with MATLAB and full-wave simulation with CST Microwave Studio. In the calculations and simulations, six-level phase modulation is adopted. The calculated and digitized phase profiles for the cylindrical meta-lens at 0.45 THz and 0.7 THz are plotted in the left half and right half of Fig. 3(a), respectively.

FIGURE 3.

(a) The calculated and digitized phase profiles at 0.45 THz and 0.7 THz for a metalens with a focal length of 5 mm; the theoretically calculated real part of the $E_{LCP}$ field distribution with MATLAB at (b) 0.45 THz and (c) 0.7 THz; the simulated real part of the $E_{LCP}$ field distribution with CST at (d) 0.45 THz and (e) 0.7 THz.

In the theoretical calculations, each building block of the meta-lens can be modeled as a dipole-like secondary source with the corresponding phase compensation at each position, and the total number of the building block is 101 along the $x$ -axis. The calculated real parts of the LCP field distribution are depicted in Fig. 3(b) and Fig. 3(c) for 0.45 THz and 0.7 THz, respectively. The normalized intensities along the focal plane and the optical axis are plotted on the top and the right (left) side of Fig. 3(b) (Fig. 3(c)) for 0.45 THz (0.7 THz). It can be seen from the normalized intensities along the optical axis that the reflected wave is well focused on the pre-set focal spot at both working frequencies. The calculated full width half maximums (FWHMs) at 0.45 THz and 0.7 THz are 0.38 mm and 0.22 mm, respectively, which shows a sub-wavelength focusing at both frequencies. The corresponding simulated results are provided in Fig. 3(d) and Fig. 3(e) for 0.45 THz and 0.7 THz, respectively, which agree very well with the theoretically calculated ones. It can also be seen from the normalized E _LCP intensities along the optical axis in Fig. 3(d) and Fig. 3(e) that the reflected wave is well focused on the pre-set focal spot (i.e., 5 mm) at both frequencies with very little discrepancy compared with the design goal. Besides, it is noticed that the simulated FWHMs are 0.41 mm and 0.24 mm at 0.45 THz and 0.7 THz, respectively, which also shows a sub-wavelength focusing. Furthermore, the focusing efficiency is defined as the fraction of the incident power that passes through a rectangular aperture in the focusing plane with a radius equal to three times of the FWHM spot size. Based on this, the simulation indicates that the focusing efficiency of the metasurface at 0.45 THz and 0.7 THz are 61% and 79%, respectively.

B. Two Dual-Band Vortex Beam Generators

Because the eigenstates of the orbital angular momentum (OAM) are infinite and orthogonal to each other, the electromagnetic wave carrying OAM or the vortex beam can greatly improve the communication capacity [33]. By deploying the proposed building block, dual-band OAM generators with different/same topological charges at 0.45 THz and 0.7 THz are demonstrated. A vortex beam carrying OAM has a phase distribution of $e^{il\phi }$ at the transverse plane [34], where $l$ and $\phi$ are the topological charge and azimuthal angle, respectively. To get the desired OAM beam with a topological charge of $l$ , the required phase distribution at each position ($x$ , $y$ ) should satisfy the relationship with the azimuthal angle around the center as

$$\begin{equation*} \lambda _{i}\varphi (x,y)=l_{i} \cdot \arctan (y/x).\tag{2}\end{equation*}$$ where $l_{i}$ represents the topological charge at the operation wavelength of $\lambda _{i}$ .

A dual-band vortex beam generator with $l_{1}=+1$ at 0.45 THz and $l_{2}=+2$ at 0.7 THz is studied, which is composed of $21\times21$ building blocks with an overall dimension of $3.9\,\,\lambda _{1} \times 3.9\,\,\lambda _{1}$ ($6.1\,\,\lambda _{2} \times 6.1\,\,\lambda _{2}$ ) at 0.45 THz (0.7 THz). According to equation (2), the phase profile for the vortex beam generator with a topological charge of +1 at 0.45 THz (+2 at 0.7 THz) is illustrated in Fig. 4 (a) (Fig. 4 (b)), in which the phase will increase $l_{1}\times 2 \pi (l_{2}\times 2 \pi)$ along the path (black dashed line) depicted in Fig. 4(a) (Fig. 4(b)). In the full-wave simulation, a RCP Gaussian beam is used to illuminate the metasurface from–${z}$ -direction and the observation plane is 5 mm above the metasurface. The reason of utilizing the Gaussian beam is to eliminate the truncation effect caused by the edges of the metasurface. The size of the observation plane is chosen as 8 mm $\times8$ mm corresponding to $12\,\,\lambda _{1}\times 12\,\,\lambda _{1}$ ($18.7\,\,\lambda _{2}\times 18.7\,\,\lambda _{2}$ ). The near-field phase and magnitude distributions of the reflected $\text{E}_{\mathrm {LCP}}$ fields at the observation plane are depicted in Fig. 5(a) and Fig. 5(c) at 0.45 THz, respectively. The corresponding results at 0.7 THz are plotted in Fig. 5(b) and Fig. 5(d), respectively.

FIGURE 4.

The required phase distribution for the vortex beam generator with a topological charge of (a) $l_{1}=+1$ at 0.45 THz and (b) $l_{2}=+2$ at 0.7 THz.

FIGURE 5.

The phase distribution of the vortex beam (a) with $l_{1}=+1$ at 0.45 THz and (b) $l_{2}=+2$ at 0.7 THz; the $E_{LCP}$ field distribution of the vortex beam (c) with $l_{1}=+1$ at 0.45 THz and (d) $l_{2}=+2$ at 0.7 THz.

As can be seen from Fig. 5, the major features of the spiral phase and amplitude distributions of the $\text{E}_{\mathrm {LCP}}$ fields and the amplitude null caused by the phase singularity can be clearly observed at both 0.45 THz and 0.7 THz. As the rotation direction and number of the spiral arms are determined by the sign of the vortex topological charge, the phase characteristics of $l_{1}=+1$ at 0.45 THz and $l_{2}=+2$ at 0.7 THz can be identified in Fig. 5(a) and Fig. 5(b), respectively. To characterize the efficiency of the dual-band beam vortex generator with different OAM modes, we evaluate the mode purity of the generated OAM beam based on the simulated phase profiles in Fig. 5(a) and Fig. 5(b), which could be calculated by decomposing its complex field on a complete basis set of Laguerre-Gaussian modes ($E_{l,p}^{LG}$ ) [15]. The calculated mode purity of the generated OAMs is depicted in Fig. 6, which shows that the dominated mode at 0.45 THz (0.7 THz) is +1 (+2) with a mode purity of 94% (66%). Some phase noise occurs at other modes at 0.7 THz, which might be due to the larger topological charge and quantization loss.

FIGURE 6.

The calculated mode purity of the vortex beam with $l_{1}=+1$ at 0.45 THz and $l_{2}=+2$ at 0.7 THz.

To further study the properties of the vortex beam generator, the far-field radiation patterns at 0.45 THz and 0.7 THz are shown in Fig. 7. The hollow characteristic of the vortex beam results can be clearly observed at the central region from the simulated 3D radiation patterns plotted in Fig. 7(a) and Fig. 7(b). In addition, the amplitude null can be clearly seen in the far-field radiation patterns at the centers of both xoz and yoz planes shown in Fig. 7(c) and Fig. 7(d). It can also be noticed from Fig. 7(c) (Fig. 7(d)) that the side lobe of the far-field radiation pattern is suppressed into very a low level of less than −16dB (−12dB) at 0.45 THz (0.7 THz). The diffusion angle between the main lobes is 25° (26°) at 0.45 THz (0.7 THz), indicating a slow divergence speed [35].

FIGURE 7.

The 3D scattering pattern of the vortex beam (a) with $l_{1}=+1$ at 0.45 THz and (b) $l_{2}=+2$ at 0.7 THz; the normalized 2D scattering patterns in the xoz and yoz planes of the vortex beam (a) with $l_{1}=+1$ at 0.45 THz and (b) $l_{2}=+2$ at 0.7 THz.

Furthermore, we also investigate another dual-band vortex beam generator with $l_{1}=l_{2}= -2$ at both 0.45 THz and 0.7 THz, of which the near-field phase and field distributions are depicted in Fig. 8. With the way to identify the topological charge mentioned above, the characteristics of $l_{1}=l_{2}= -2$ at both frequencies can be recognized in Fig. 8. Fig. 9 illustrates the calculated mode purity of the generated OAMs, which displays that the dominated mode at 0.45 THz (0.7 THz) is −2 (−2) with a mode purity of 87% (70%). Moreover, Fig. 10 plots the normalized 2D scattering patterns of the second vortex beam generator in both xoz and yoz planes. It can be seen from Fig. 10(a) (Fig. 10(b)) that the amplitude null can be observed at the center and the side lobe is less than −13dB (−12dB) at 0.45 THz (0.7 THz). The diffusion angle between the main lobes is $42^{\mathrm {o}}$ ($27^{\mathrm {o}}$ ) at 0.45 THz (0.7 THz) in Fig. 10(a) (Fig. 10(b)). Comparing Fig. 7(c)–​Fig. 7(d) and Fig. 10, it can be concluded that the diffusion angle decreases when the frequency increases or the topological charge decreases, where a smaller diffusion angle means a slower divergence speed.

FIGURE 8.

The phase distribution of the vortex beam (a) with $l_{1}=-2$ at 0.45 THz and (b) $l_{2}=-2$ at 0.7 THz; the $E_{LCP}$ field distribution of the vortex beam (c) with $l_{1}=-2$ at 0.45 THz and (d) $l_{2}=-2$ at 0.7 THz.

FIGURE 9.

The calculated mode purity of the vortex beam with $l_{1}=-2$ at 0.45 THz and $l_{2}=-2$ at 0.7 THz.

FIGURE 10.

The normalized 2D scattering patterns in the xoz and yoz planes of the vortex beam (a) with $l_{1}=-2$ at 0.45 THz and (b) $l_{2}=-2$ at 0.7 THz.

From the above proof of concept demonstrations, the proposed building block has been verified to operate at two arbitrary THz frequency bands with the independent phase control at each band. As mentioned before, many reflective metasurfaces have been realized. Comparisons for different reported reflective metasurfaces in terms of several pivotal parameters (e.g., working polarization, reflection coefficient, and periodicity) are tabulated in Table 1. It can be seen that most of the reflective metasurfaces work at a single frequency band, and the only dual-band one [29] is for different polarizations.

TABLE 1 Comparisons for Reflective Metasurfaces Realized in Literature

SECTION IV. Conclusion

In conclusion, we have proposed a novel reflective dual-band building block with high efficiency and independent phase control at two arbitrary THz frequencies, which could be used for realizing the dual-band meta-devices based on geometric metasurface. The building block is composed of a top patterned layer and ground plane separated by a silicon spacer. The top layer consists a DCSS resonator and a nano-bar resonator seated in a circular hole. The $2\pi$ phase modulations at two preset frequencies can be achieved by rotating the DCSS and nano-bar resonators according to the PB phase principle. Based on the proposed building block, a dual-band cylindrical metalens and two vortex beam generators are designed to work at 0.45 THz and 0.7 THz. The cylindrical metalens is studied by both theoretical calculation and full-wave simulation. The simulation results of the meta-lens agree very well with the theoretical calculations, which show that the reflected wave are focused at the pre-assigned focal plane and a sub-wavelength focusing can be obtained at both frequencies. Besides, two vortex beam generators carrying different/same OAM modes at each band are investigated, which could be used to further improve the communication capacities. The full-wave simulation results show that both vortex metasurfaces could generate the OAM modes with the pre-assigned topological charges and high performance at the operating frequencies. Due to its single-layer structure, the proposed method would be beneficial to design high efficiency and low-profile meta-devices in a convenient and low-cost way. The design scheme could provide a new means to manipulate the terahertz waves and open up an avenue towards developing more sophisticated dual-band or dual-functional meta-devices with different fascinating functionalities for practical applications, such as THz communications and THz radar. Although the ohmic loss of metal will increase at high frequencies especially in optical band and the proposed method would encounter fabrication challenges, the proposed method could be readily scaled down to microwave and millimeter wave regions.

ACKNOWLEDGMENT

(Tailei Wang and Rensheng Xie contributed equally to this work.)