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Abstract
One of the considerable disadvantages of a metasurface (MS) is frequency-dependent behavior, which largely restricts its practical applications. To overcome this challenge, a MS is designed to generate vortex beams at three distinct terahertz (THz) frequencies. Specifically, a unit-cell structure comprising three resonators is proposed to operate at three distinct THz frequencies. The cross-polarized reflection coefficients of the unit-cell structure are greater than 70% under circularly polarized (CP) incidence. Based on the geometric phase principle, the full $2\pi$ phase shift can be obtained at each frequency by rotating the corresponding orientation angles of the three resonators. By carefully arranging the unit-cell structure, orbital angular momenta (OAMs) with topological charges of $l = {{\pm 1}}$, ${-}{{2}}$, and, ${-}{{3}}$ at 0.706 THz, 1.143 THz, and 1.82 THz, respectively, can be generated for a normally incident right CP wave, and OAMs with topological charges of $l = - {{3}}$, ${-}{{2}}$, and ${-}{{1}}$ can be generated for a normally incident left CP wave. The generated reflective vortex beams through the designed MS have good mode purity up to 85% at 0.706 THz, 84% at 1.143 THz, and 74.7% at 1.82 THz, respectively. Moreover, the designed reflective MS reveals a convenient and low-cost way to generate vortex beams with different/same OAM modes at three different resonance frequencies and is beneficial for potential applications in THz communication.
© 2022 Optica Publishing Group
1. INTRODUCTION
With the quick evolution of modern wireless communication and the multiple demands of capacity and spectral efficiency, the vortex electromagnetic (EM) wave beam carrying orbital angular momentum (OAM) has attracted tremendous attention. Due to OAM with particular orthogonal channels in different modes, communication capacity can be enlarged without increasing the bandwidth and carry more information [1,2]. Thereby, there are various approaches to generating vortex beams, such as spiral phase plates [3], spiral parabolic antennas [4], and circular patch antennas [5]. Compared with the traditional methods, the metasurface (MS) is a novel two-dimensional (2D) planar form of metamaterials (MMs), which has an ultrathin profile, and is lightweight and easy to fabricate for application in vortex beam generation. The MS consists of periodic arrays of sub-wavelength structure, and it can tailor the amplitude, phase, and polarization of an incident EM wavefront by introducing abrupt phase changes at a thin interface [2,6–11]. Yu et al. first utilized V-shaped nano-antennas to generate optical vortex beams [12]. Since then, MS-based application studies have been proposed, including planar focusing lenses, cloaking, holograms, and vortex beam generation [13–26].
So far, the main defect of most reported MSs is the frequency-dependent property, especially those depending on spatial phase profiles [27]. Wang et al. adopted geometric phase MS to generate vortex waves with order $l = + {{2}}$ at two different terahertz (THz) frequencies with high transmissivity (${\gt}{0.8}$) [28]. Ji et al. proposed a bilayer MS to generate vortex waves with order $l = + {{2}}$ at two different microwave frequencies under reflection mode [29]. Most MSs work only at one or two THz frequencies, which is limited to practical application. To realize more compact multichannel meta-devices and perform multispectral analysis, it is of great necessity to design a MS that operates at three or more frequencies to generate high-order vortex beams independently without inefficiency [30–37]. For example, Xie et al. proposed a transmission-type MS of three alternatively arranged slot and metallic resonators to manipulate a wavefront at three distinct frequencies independently [38,39]. Dong et al. proposed a transmission-type MS to generate a vortex wave with $l = {{\pm 3}}$ in the THz region [40]. To sum up, efficient vortex beam generators with high orders based on reflective MS at three THz frequencies are rarely reported.
Fig. 1. (a) Geometry outlines of the designed reflective MS made of a periodic array of unit-cell structure for a normally incident CP wave; (b), (c) top and perspective views of the unit-cell structure.
In this work, a geometric phase reflective MS is proposed to independently generate high-purity vortex beams for incident circularly polarized (CP) waves at three different THz frequencies. The unit-cell structure of the reflective MS is composed of a patterned metallic structure layer and metallic ground plane separated by a polyimide substrate. The patterned metallic structure layer is composed of three resonators: an outer and inner modified double-C-slot resonator (MDCSR) and a ring-slot with a center elliptical resonator (CER). Owing to the alternative arrangement of the outer and inner MDCSR and CER structures, the coupling and cross talk between any two resonators is ignorable. Each of the three different resonators can make an independent phase response at each corresponding frequency for a normally incident CP wave. Numerical simulation results indicate that complete phase coverage from 0 to ${{2}}\pi$ can be obtained at each frequency by independently rotating the corresponding three resonator structures. The cross-polarization reflection coefficient of the proposed reflective MS is up to 0.7, 0.75, and 0.83 at 0.706 THz, 1.143 THz, and 1.82 THz, respectively. As a proof-of-concept demonstration, the generated vortex beams carrying the same/different topological charges for normally incident LCP/RCP waves can attain high purity at the abovementioned frequencies. The proposed method can open a new avenue to achieve high efficiency and cross-talk-free vortex beam generation in multiple wavelengths.
2. STRUCTURE DESIGN AND THEORETICAL ANALYSIS
Figure 1(a) illustrates the function of the proposed reflective MS for tri-frequency vortex beam generation. It can be seen that normally incident CP waves can be reflected and transformed to their orthogonal components for incident THz waves at three resonance frequencies of ${f_1},\;{f_2}$, and ${f_3}$. To acquire the predetermined phase distributions and almost fixed amplitude of the reflective orthogonal CP wave, it is important to rotate separately the three resonator structures. Figures 1(b) and 1(c) show the top and perspective views of the unit-cell structure of the designed reflection-type MS. The unit-cell is made of a patterned metallic structure and ground-plane separated by a dielectric substrate. The patterned metallic structure layer is composed of outer and inner MDCSRs and a ring-slot with a CER. Notably, the three distinct resonators are responsible for independently modifying the wavefronts at three corresponding THz frequencies. In our design, the dielectric substrate is polyimide (lossy) with a permittivity of 3.5 and loss tangent of 0.0027, and the metallic part is copper with conductivity of $\sigma = {5.8} \times {{1}}{{{0}}^7}\;{\rm{S}}/{\rm{m}}$. The optimized geometric parameters of the proposed unit-cell structure are as follows: $p = {{115}}\;\unicode{x00B5}{\rm m}$, ${r_1} = {{25}}\;\unicode{x00B5}{\rm m}$, ${r_2} = {{30}}\;\unicode{x00B5}{\rm m}$, ${r_3} = {{35}}\;\unicode{x00B5}{\rm m}$, ${r_4} = {{40}}\;\unicode{x00B5}{\rm m}$, ${r_5} = {43.5}\;\unicode{x00B5}{\rm m}$, ${r_6} = {{47}}\;\unicode{x00B5}{\rm m}$, ${r_7} = {{56}}\;\unicode{x00B5}{\rm m}$, ${r_8} = {{19}}\;\unicode{x00B5}{\rm m}$, ${r_9} = {{6}}\;\unicode{x00B5}{\rm m}$, and ${t_1} = {{2}}\;\unicode{x00B5}{\rm m}$, ${t_2} = {{28}}\;\unicode{x00B5}{\rm m}$, ${t_3} = {2.5}\;\unicode{x00B5}{\rm m}$. In addition, the orientations of the outer MDCSR, inner MDCSR, and CER are denoted as ${\theta _1},\;{\theta _2}$, and ${\theta _3}$ with respect to the $x$ axis, respectively. The reflection phase ${{0 - 2}}\pi$ shifts at ${f_{\:1}},\;{f_2}$, and ${f_3}$ (0.706 THz, 1.143 THz, and 1.82 THz) can be obtained by rotating ${\theta _1},\;{\theta _2}$, and ${\theta _3}$, respectively.
The Pancharatnam–Berry (PB) phase, also called geometric phase, has the advantage of being non-dispersive and easy to design, and can be introduced to manipulate the CP wave. In the design of reflection-type MS, the interfacial phase change $\varphi$ is determined only by rotating the orientation angles $\theta \;({\theta _1},\;{\theta _2},\;{\theta _3})$ of three resonators. The relationship between interfacial phases and self-rotated angles of three resonators can be expressed by $\varphi = {{2}}\sigma \theta$, where the “${{\pm}}$” sign of $\sigma = {{\pm 1}}$ corresponds to the helicity of normally incident right/left CP (RCP/LCP) waves. Consequently, by varying the orientation angles of the three resonators of the proposed MS, an arbitrary phase shift $\varphi$ can be easily obtained and cover the phase range of ${{0}}\sim{{2}}\pi$ [41]. When the reflective MS is illuminated by the CP wave, the complex reflection coefficients of the CP wave related to a linearly polarized (LP) wave can be defined by the general reflection matrix ${R_{\textit{CP}}}$ as [42]
Fig. 2. Amplitudes and phases of the reflected orthogonal CP wave for eight unit-cells at different frequency ranges by rotating the orientation angle: (a), (b) ${\theta _1}$; (c), (d) ${\theta _2}$; and (e), (f) ${\theta _3}$.
To obtain the required amplitudes and phase shifts of the reflected orthogonal CP wave of eight unit-cell structures at three frequencies, numerical simulations are carried out by CST Microwave Studio, where the “unit-cell” boundary conditions are applied in both $x$ and $y$ directions and “Floquet-port” excitations with CP waves are applied in $z$ direction. As shown in Fig. 2, the three different resonance frequencies are evident clearly around ${f_{1}} = {0.706}\;{\rm{THz}}$, ${f_{2}} = {1.143}\;{\rm{THz}}$, and ${f_{3}} = {1.82}\;{\rm{THz}}$, respectively. As shown in Figs. 2(a), 2(c), and 2(e), the amplitude of the reflected orthogonal CP wave can be nearly fixed to a near constant of about 0.7 at the three different frequencies when rotating the orientation angles (${\theta _1},\;{\theta _2},\;{\theta _3}$) of the three resonators. The phase of the reflected orthogonal CP wave will be changed linearly and achieve full ${{2}}\pi$ coverage at three different resonance frequencies when rotating independently the orientation angles (${\theta _1},\;{\theta _2},\;{\theta _3}$) of the three resonators, as shown in Figs. 2(b), 2(d), and 2(f). It means that the proposed unit-cell structure can achieve phase control at the selected three resonance frequencies individually with high-reflection coefficients.
The previous unit-cell structure had difficulty completing phase modulation independently at three different resonance frequencies by simply arraying three independent resonators because of intense interference among them. By contrast, the coupling and interference among the three different resonators (outer MDCSR, inner MDCSR, and CER) can be decreased by optimizing the geometrical parameters of the proposed unit-cell structure. To illustrate the resonance response mechanism, distributions of the localized electric field ($|{E_z}|$) and instantaneously induced surface current (cut at the $xoy$ planes) on the surface of the unit-cell structures at three different resonance frequencies are depicted in Fig. 3. It can be observed that the $z$-components of the electric field ($|{E_z}|$) and surface current are focused on the different resonator structures at different resonance frequencies. These results indicate the magnetic dipole effects produced by the different resonator structures at different frequencies without interfering with each other [44,45]. At the first resonance frequency 0.706 THz, as shown in Figs. 3(a) and 3(d), the localized electric field ($|{E_z}|$) and surface current are mainly concentered on the outer MDCSR structure, and flowing directions of current inside and outside the structure are inverse. At the same time, the electric field ($|{E_z}|$) and surface current on other resonator structures are very weak. Similarly, as shown in Figs. 3(b), 3(e) and 3(c), 3(f), the localized electric field ($|{E_z}|$) and surface current are focused on inner MDCSR and CER structures at the second and third frequencies of 1.143 THz and 1.82 THz, respectively. The coupling interference between any two resonators is weak at different resonance frequencies, as has been demonstrated. Obviously, the excitation of local coupling is a key aspect of manipulating the wavefront easily by rotating the three resonators independently at three different resonance frequencies.
Fig. 3. Simulated distributions of the (a)–(c) electric field ($|{E_z}|$) and (d)–(f) surface current of unit-cell structure at (a), (d) 0.706 THz; (b), (e) 1.143 THz; and (c), (f) 1.82 THz.
Fig. 4. Simulated geometric phase shift by rotating ${\theta _1}$ with a fixed (a) ${\theta _2}$ and (b) ${\theta _3}$ at 0.706 THz; by rotating ${\theta _2}$ with a fixed (c) ${\theta _1}$ and (d) ${\theta _3}$ at 1.143 THz; by rotating ${\theta _3}$ with a fixed (e) ${\theta _1}$ and (f) ${\theta _2}$ at 1.82 THz.
The phase and amplitude of the reflected orthogonal CP wave of the unit-cell structure have been simulated numerically. Figures 4 and 5 present the phase and amplitude of the reflected orthogonal CP wave of the unit-cell structure for a normally incident THz wave when rotating the orientation angle $\theta \;({\theta _1},\;{\theta _2},\;{\theta _3})$ of one resonator and fixing the other two resonators at ${f_{1}} = {0.706}\;{\rm{THz}}$, ${f_{2}} = {1.143}\;{\rm{THz}}$, and ${f_{3}} = {1.82}\;{\rm{THz}}$. Figures 4(a) and 4(b) show that the full ${{2}}\pi$ phase coverage can be achieved by changing rotation angles of the outer MDCSR structure (${\theta _1}$) from 0 to $\pi$ with a $\pi /{{8}}$ phase interval with fixed ${\theta _2}$ and ${\theta _3}$ at 0.706 THz. It can be seen that the phase variation is distinctly equivalent to twice the rotation angle, and the phase difference between adjacent elements is $\pi /{{4}}$. It also can be observed that phase variation is nearly negligible at 0.706 THz by varying ${\theta _2}$ or ${\theta _3}$ with fixed ${\theta _1}$. Similarly, Figs. 4(c), 4(d) and 4(e), 4(f) show the reflection phases of unit-cell structures with different rotation angles (${\theta _2},\;{\theta _3}$) of inner MDCSR and CER structures (the other two resonators have been fixed) for RCP incidence at 1.143 THz and 1.82 THz, respectively. Obviously, the phase variation is also nearly negligible by varying ${\theta _1}$ and ${\theta _3},\;{\theta _1}$ and ${\theta _2}$ with fixed ${\theta _2}$ and ${\theta _3}$ at 1.143 THz and 1.82 THz, respectively.
Fig. 5. Cross-polarized reflection coefficient at (a), (b) 0.706 THz; (c), (d) 1.143 THz; and (e), (f) 1.82 THz.
In addition, as shown in Figs. 5(a)–5(f), the corresponding reflection coefficients of the orthogonal CP wave are always greater than 0.7 in all conditions, revealing the efficient CP conversion coefficients of the proposed reflection MS at three different resonance frequencies.
3. REFLECTIVE MS FOR VORTEX BEAM GENERATION
By arranging the proposed unit-cell structure suitably, vortex beam generators with same/different topological charges at three different resonance frequencies are demonstrated numerically. At the horizontal plane, the vortex beam carrying OAM mode has a phase distribution of ${e^{{il\varphi}}}$, where $l$ and $\varphi$ are the topological charge and azimuthal angle, respectively. To satisfy the desired vortex beams with the prospective topological charge, the required phase distribution at each coordinate ($x,y$) should match the corresponding relationship with the azimuthal angle around the center as [46]
where ${l_i}$ is the OAM mode number, also called topological charge.Figure 6 illustrates the digitized phase distributions for $l = + {{1}},\;{{- 1}},\;{{- 2}}$, and ${-}{{3}}$ along the azimuthal direction. To address whether the phases ${{2}}\pi l$ of OAM range from 0 to ${{2}}\pi$, 0 to ${{4}}\pi$, or 0 to ${{6}}\pi$, the reflective MS has been divided into ${{8}} \times l$ areas of adjacent regions with a phase gradient of $\pi /{{4}}$. It is worth noting that counterclockwise and clockwise along the azimuthal direction for the normally incident RCP wave correspond to the increase in distributed phase for $l\gt {{0}}$ and $l \lt {{0}}$, respectively. The direction of phase distribution increases along the azimuthal, which is indicated by the creamy white dashed line arrows in Fig. 6.
Fig. 6. Schematic of the calculated phase distributions of the proposed reflective MS under a normally incident RCP wave for vortex beam generation with topological charges of (a) $l = + {{1}}$, (b) $l = - {{1}}$, (c) $l = - {{2}}$, and (d) $l = - {{3}}$.
To eliminate the truncation effect caused by the edges of the reflection-type MS, a Gaussian beam is a priority choice as an excitation source. We first consider the designed MS to generate vortex waves with the same topological charge $l = + {{1}}$ at three different THz resonance frequencies. The designed MS consists of ${{14}} \times {{12}}$ unit-cell structure along $x$ and $y$ axes directions, and an area of ${1.61} \times {1.38}\;{\rm{mm}}^2$. In the simulation, the RCP Gaussian beam is used to illuminate the MS along the ${-}z$-axis direction, and the electric fields of the reflected LCP waves are recorded in the $xoy$ plane at $z = {{2}}\;{\rm{mm}}$ above the designed MS. We can see from Fig. 7 that the incident RCP plane wave is transformed to a reflected LCP vortex wave, and the corresponding spiral phase and amplitude can be clearly observed at three different THz resonance frequencies. As shown in Figs. 7(a)–7(c), the phase distribution feature exhibits a clear spiral shape that is very consistent with the topological charge $l = + {{1}}$ at three different resonance frequencies. The phase change is only once from 0° to 360°. It is worth noting that the center of intensity distribution is equal to zero, caused by the phase singularity as shown in Figs. 7(d)–7(f). The results reveal that designed MS can convert incident plane CP waves into reflected vortex waves. We also observe that the apparent sizes of doughnut shapes are different at three different resonance frequencies, which could be caused by different interferences occurring among the three resonators. Therefore, vortex behavior has a high feasibility because the magnitude and phase distributions of reflective vortex waves at three different resonance frequencies can be controlled independently.
Fig. 7. Simulated distributions of (a)–(c) phase and (d)–(f) electric field intensity of a reflected vortex beam with topological charge of $l = + {{1}}$ at (a), (d) 0.706 THz; (b), (e) 1.143 THz; and (c), (f)1.82 THz for a normally incident RCP Gaussian beam.
To further verify, we change the topological charge number $l$ equal to ${-}{{1}},\;{{- 2}}$, or ${-}{{3}}$ at three different frequencies separately. The reflective MS arrays have 45° phase intervals between adjacent regions. Figure 8 presents the simulated distributions of the phase and electric field intensity of the reflective vortex waves with topological charges of $l = - {{1}}$ at 0.706 THz, $l = - {{2}}$ at 1.143 THz, and $l = - {{3}}$ at 1.82 THz for a normally incident RCP Gaussian beam. The rotation direction and number of spiral arms of the electric field distributions of the vortex wave are usually determined by topological charge. As shown in Figs. 8(a)–8(c), it can be observed clearly that there is one spiral arm for phase distribution of the reflective vortex beams with $l = - {{1}}$ at ${f_{1}} = {0.706}\;{\rm{THz}}$, and two and three spiral arms for $l = - {{2}}$ and ${-}{{3}}$ at ${f_{2}} = {1.143}\;{\rm{THz}}$ and ${f_{3}} = {1.82}\;{\rm{THz}}$, respectively. In contrast to Figs. 7(a)–7(c), the rotatory orientations of the spiral arms are inverse due to the topological charge sign “${-}$.” In general, due to the restriction of the arrangement of the MS, the generated vortex wave with order $l = {{\pm n}}$ has an $n$ intensity null. It can be clearly seen in Figs. 8(d)–8(f) that there is a null area of electrical amplitude in the center region of the reflective vortex waves for $l = - {{1}}$ at 0.706 THz, and two and three null areas in the center regions for $l = - {{2}}$ and $l = - {{3}}$ at 1.143 THz and 1.82 THz, respectively. As the topological charge increases, the vortex waves [Fig. 8(c)] have much more distorted intensity distributions similar to the doughnut shape. The irregular shape is caused by an error of the theoretical and simulated phase and amplitude of the reflected electric field. This might decrease the resolution caused by the limited unit-cell structure. This is a key question that we need to improve in the future. The proposed MS can generate the reflected THz vortex wave with different topological charges at three different frequencies for the normally incident RCP Gaussian beam without disturbing each other, as shown in Fig. 8.
Fig. 8. Simulated distributions of (a)–(c) phase and (d)–(f) electric intensity of a reflected vortex beam with topological charges (a), (d) $l = - {{1}}$ at 0.706 THz; (b), (e) $l = - {{2}}$ at 1.143 THz; and (c), (f) $l = - {{3}}$ at 1.82 THz for a normally incident RCP Gaussian beam.
We further illustrate the vortex wave with different topologies for the normally incident LCP Gaussian beam, and set different topological charges at three different frequencies: $l = - {{3}}$ at 0.706 THz; $l = - {{2}}$ at 1.143 THz; $l = - {{3}}$ at 1.82 THz. The distributions of phase and electrical field intensity of the reflected vortex waves with topological charges of $l = - {{3}},\;{{- 2}}$, and ${-}{{1}}$ at 0.706 THz, 1.143 THz, and 1.82 THz, respectively, are shown in Fig. 9. From Figs. 9(a)–9(c), it is obvious that similar spiral phase distributions of the reflected vortex beams with topological charges of $l = - {{3}},\;{{- 2}}$, and ${-}{{1}}$ exist at 0.706 THz, 1.143 THz, and 1.82 THz, respectively. However, for the normally incident LCP Gaussian beam, as shown in Figs. 9(d)–9(f), the directions of phase profiles of reflected vortex waves with topological charges of $l = - {{1}},\;{{- 2}}$, and ${-}{{3}}$ are reversed with respect to those for the normally incident RCP Gaussian beam [see Figs. 8(a)–8(c)]. The number of spiral arms of the phase distributions remains unchanged. Furthermore, by changing the helicity of the incident CP wave, the helical direction of the reflected vortex wave will be changed, implying the birefringent nature of the unit-cell structure. To analyze the aforementioned vortex wave generation, the proposed reflective MS has been verified to be capable of manipulating a wavefront independently for the normally incident LCP wave at three distinct THz frequencies. Thus, it can be imagined that the proposed reflective MS can create a series of vortex beams with more spiral arms and electrical null area distributions in the center region when increasing the topological charge (e.g., ${{l}} = - {{4}},\;{{- 5}},\;{{- 6 \ldots.}}$) for the normally incident CP wave at any of the three different frequencies. It should be noticed that besides vortex beam generation, anomalous reflection, planar focusing, and other wavefront manipulation phenomena also can be realized for our proposed reflective MS at three independent THz frequencies for the normally incident CP wave (not shown).
Fig. 9. Simulated distributions of (a)–(c) phase and (d)–(f) electric intensity of a reflected vortex beam with topological charges (a), (d) $l = - {{3}}$ at 0.706 THz; (b), (e) $l = - {{2}}$ at 1.143 THz; and (c), (f) $l = - {{1}}$ at 1.82 THz for a normally incident LCP Gaussian beam.
4. MODE PURITY
To further characterize the efficiency of the generated vortex waves with various topological charge numbers at three different THz resonance frequencies, we have calculated the mode purity of the generated vortex beams based on the analysis of simulation result phase profiles in Figs. 7–9. The OAM modes can be counted by disassembling their complex fields on a complete basis set of Laguerre–Gaussian modes [16,47].
Fig. 10. (a) Calculated OAM mode purity of reflected vortex beams with topological charge ($l = + {{1}}$) at 0.706 THz, 1.143 THz, and 1.82 THz for normally incident RCP wave; (b) at 0.706 THz ($l = - {{1}}$), 1.143 THz ($l = - {{2}}$), and 1.82 THz ($l = - {{3}}$) for normally incident RCP wave, and (c) at 0.706 THz ($l = - {{3}}$), 1.143 THz ($l = - {{2}}$), and 1.82 THz ($l = - {{1}}$) for normally incident LCP wave.
According to the discrete Fourier transform (DFT) algorithm, the Fourier relationship between OAM spectrum ${A_l}$ and corresponding sampling phase $\psi (\varphi)$ can be described as [48]
where $\psi (\varphi)$ represents the phase value in the sampling plane, and ${e^{- jl\phi}}$ is the harmonic related to the spiral phase front. Based on Eq. (5) and Eq. (6), we calculated the OAM mode purity of the reflected vortex waves (topological charges $l = + {{1}},\;{{- 1}},\;{{- 2}}$, and ${-}{{3}}$), as shown in Figs. 10(a)–10(c). For the normally incident RCP Gaussian beam, as shown in Fig. 10(a), the mode purities of reflected vortex waves with a topological charge of $l = + {{1}}$ are up to 79%, 74.8%, and 74.7% at 0.706 THz, 1.143 THz, and 1.82 THz, respectively. As shown in Fig. 10(b), for the normally incident RCP Gaussian beam, the mode purities of reflected vortex beams with topological charges of $l = - {{1}},\;{{- 2}}$, and ${-}{{3}}$ are up to 84.8%, 84.3%, and 60% at 0.706 THz, 1.143 THz, and 1.82 THz, respectively. For a normally incident LCP Gaussian beam, as shown in Fig. 10(c), the dominant OAM mode purities of reflected vortex beams with topological charges of $l = - {{3}},\;{{- 2}}$, and ${-}{{1}}$ are up to 70.4%, 85.1%, and 71.4% at 0.706 THz, 1.143 THz, and 1.82 THz, respectively. The larger topological charge and quantization loss lead to some phase noise appearing at other modes at three different resonance frequencies. The theory and simulation results of all fully prove the ability that the proposed reflective MS can be adjusted at three different frequencies independently.5. CONCLUSION
In conclusion, a novel reflection-type MS has been proposed to generate vortex waves with high efficiency for normally incident CP waves at three different THz resonance frequencies by rotating the orientation angles of three different resonators independently. The patterned metallic structure is composed of the outer MDCSR, inner MDCSR, and CER, which is used to control the phase shift at three different resonance frequencies (${f_{1}} = {0.706}\;{\rm{THz}}$, ${f_{2}} = {1.143}\;{\rm{THz}}$, and ${f_{3}} = {1.82}\;{\rm{THz}}$). The numerical simulation results pinpointed that the amplitudes of the reflected orthogonal CP waves are over 0.7, and the complete full phases have coverage from 0 to ${{2}}\pi$ by rotating the orientation angles of three different resonators independently. The further numerical simulation demonstrated that the proposed reflective MS has high-quality vortex waves with different topological charges of $l = {{\pm 1}}$, ${-}{{2}}$ and, ${-}{{3}}$ at 0.706 THz, 1.143 THz, and 1.82 THz for a normally incident RCP wave; the vortex beams with topological charges of $l = - {{3}},\;{{- 2}}$, and ${-}{{1}}$ at 0.706 THz, 1.143 THz, and 1.82 THz are for a normally incident LCP wave. In addition, the dominant OAM mode purities of vortex waves with different topological charges are all over 60% at three distinct THz resonance frequencies. The results show that the designed reflective MS can generate vortex waves with excellent fidelity in the propagation process. Without any complex feed network or structure change, vortex waves can be realized by only changing the corresponding frequency with predetermined topological charges. The design scheme could provide a new path to developing multiband modulations independently or attractive multi-functional meta-devices. If the MS is large enough and has an infinite number of alternating empty slots and metal resonators, it is theoretically possible to independently modulate EM waves at an infinite number of frequencies. However, with the increase in the number of empty slots and metal resonators, the effect of coupling interference in the unit-cell structure will increase accordingly. By adjusting the size or material type of the unit-cell structure, the MS may work in the infrared band or microwave band. These conjectures need further verification and improvement.
Funding
Natural Science Foundation Innovation Group Project of Hubei China (2020CFA0038); Key Research and Development Project of Hubei Province (2020BAA028).
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.
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