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Abstract
Polarization modulation and multichannel beam generation are crucial in multichannel communication and high-resolution imaging at THz frequency. In this work, we present a polarization-reprogrammable coding metasurface composed of VO2/Au composite concentric rings (CCRs). Owing to the phase-change property of VO2, the CCR is designed as a digital coding element for the polarization conversion. When VO2 remains insulator state at room temperature, the y-polarized incident wave is transformed into x-polarized wave, which can be regarded as digital state 0. When VO2 converts into metal state at critical temperature (68 °C), the polarization of reflected wave stays unchanged, corresponding to digital state 1. Any desired linear polarization state of reflected beam is achieved by taking advantage of different coding sequences in a programmable manner. Furthermore, by combining phase gradient with polarization coding states, we propose an anisotropic programmable metasurface to control the multi-channel reflected beams dynamically. By arranging distinct coding sequences, we show that the EM reflected beams can be manipulated flexibly. The proposed programmable metasurface paves new ways towards THz polarization manipulation, signal detection and information communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
THz waves are playing an important role in sensing, wireless communication and imaging [1,2]. At present, as a sort of ultra-thin artificial structures, metasurfaces are considered as an ideal carrier for terahertz device. THz metasurfaces have been reported to achieve a series of functions, such as invisibility cloak [3], wave plate [4], absorber [5] and optical illusion [6], attributing to the lower profile and less processing difficulties compared to 3D metamaterials.
Recently, Cui et al. proposed the concept of coding metasurfaces to connect the physical world with the digital world. From the perspective of information science, they managed to manipulate the electromagnetic (EM) wave with different functionalities by controlling the sequence of digital coding states “0” and “1”, which matches phase 0 and π [7]. Compared with traditional wave manipulation, coding metasurfaces have achieved a variety of gorgeous physical phenomena and novel EM devices [8–11]. Nevertheless, there exists a major obstacle to practical application due to the lack of tunability. To overcome the problem, programmable metasurfaces are proposed to generate reprogrammable holographic image [12], develop harmonic information transition [13] and single-frequency EM imaging [14]. Meanwhile, space-time-coding [15] and smart metasurfaces [16] with self-adaptive capabilities are brought out to fulfill more complicated and customized functionalities. However, most proposed digital coding and programmable metasurfaces concentrate on the phase coding rather than polarization coding.
Polarization modulation is desirable in multichannel communication [17] and high-resolution imaging [18]. Series of polarization converters have been proposed to achieve polarization manipulation from microwave to terahertz (THz) [19,20] based on metamaterials or metasurfaces. Nevertheless, majority of polarization metasurfaces are function-fixed [21,22], which limits their further applications. Besides, two orthogonally polarized incident THz waves are required to implement multifunction via metasurfaces [23–26]. In order to realize multifunctional metasurfaces, it is wise to adopt active component, such as PIN diodes [27], to realize adjustable polarization converting. More recently, Cui et al. have achieved arbitrarily linear-polarization editing of reflected EM waves at microwave frequency [28]. Simultaneous controlling of phase and polarization can’t be implemented yet due to the scale restriction of PIN diode. In addition, PIN diode is not applicable to THz frequency. Therefore, it is still a challenge to design a reprogrammable metasurface in THz band.
For tunable THz wave manipulation, phase-change materials (PCM) such as liquid crystal [29], Ge3Sb2Te6 (GST) [30], graphene [31] and vanadium dioxide (VO2) [32–36] are widely used in active metasurfaces. Here, we choose VO2 as a constructing component of metasurface because of its phase transition characteristics near room temperature, which is different from the method based on large Pockels effect of BaTiO3 film [37,38]. VO2 is an excellent material which supports an ultrafast and strong reversible phase transition from the insulator state to the metal state when temperature reaches a crucial value TC = 68 °C [39]. Methods such as thermal excitation [40,41], electrical stimuli [42] or optical incentive [43] are adopted to achieve metal-insulator transition (MIT) which occurs in nanoseconds or even femtoseconds [44]. The electrical conductivity of VO2 changes rapidly (4–5 orders of magnitude) when MIT occurs, which has great influence on electrical and optical properties. Owing to the ultrafast and abundant phase transition behaviors, VO2 is of vital importance in tunable metasurface at THz frequencies for reconfigurable filter [45], absorber [46], and antenna [47].
In this work, we propose a programmable metasurface, composed of composite concentric rings (CCRs) with gold and VO2, to tune the arbitrary linearly polarized state of THz wave. Linearly polarized THz wave is converted into either x or y polarization depending on the state of VO2, which matches the digital ‘0’ and ‘1’ states. By arranging the CCRs under different digital coding sequences, any linear polarization state including x/y polarization and transition states between them can be realized. Furthermore, by adjusting the CCR’s geometric parameters such as radius, opening angle and orientation angle to obtain phase gradient, the proposed anisotropic-reprogrammable metasurface is capable of controlling multi-channel reflected beam actively. We demonstrate the concept of tunable multifunctional programmable metasurface through numerical simulation and theoretical explanation. Such a metasurface provides potential applications for real-time manipulation of THz polarization, tunable THz wavefront engineering and so on.
2. Theoretical analysis and structural design
As shown in Fig. 1(a) and (b), the meta-atom consists of three layers: the CCR, dielectric substrate, and a gold reflective layer from top to bottom. The periodicity of meta-atom is p = 100 µm. We select polyimide as the suitable substrate (ɛr = 3, tan δ = 0.001) with the thickness of td = 20 µm, in which tan δ represents the heat dissipation. The schematic of CCR composed of Au and VO2 is shown in Fig. 1(c), the parameters R1, α, β and w of the structure are outer radius, orientation angle, opening angle and width of the ring, respectively. The properties of VO2 can be described by the Bruggeman effective-medium in the THz ranges [48]:
Fig. 1. The schematic of unit cell designed with (a) insulator state (b) metal state of VO2. td=20 µm is the thickness of substrate, p=100 µm is the period of meta-atom. (c)The geometry of the CCR. R1 is the outer radius and w=20 µm is the width of the CCR, α is the orientation angle while β is the opening angle.
At room temperature, the dielectric constant of VO2 is about 11 in the insulator state. Because of the relatively low loss of VO2, it is regarded as a dielectric gap, and the CCR could work as a split ring resonator in this case. Symmetric mode or asymmetric mode occur when the polarization of the incident light is parallel or perpendicular to the symmetric axis of the CRR. When the y-polarized wave incidents, for example, the scattering filed is described as [49]:
In the metal state, the CCR is considered as a concentric metal ring shown in Fig. 1(b). The y-polarized reflected wave occurs when y-polarized plane wave incidents normally. The amplitude could remain almost unchanged due to the gold reflector, while the phase is able to be changed by altering outer radius R1 of the CCR. Therefore, attributing to the phase-change property of VO2, the CCR is designed as a digital coding element for the polarization conversion, which is encoded as the digital 0 and 1 in the following discussion.
3. Results and discussion
3.1 Design of the polarization-reprogrammable coding metasurface
In order to generate arbitrary linearly polarized reflected beam, as illustrated in Fig. 2(a), the specific parameters of the CCR are as follows: outer radius R1=48 µm, the opening angle β=29° and the orientation angle α=−45°. Herein, the reflected information is numerically calculated by utilizing the commercial software (CST Microwave Studio). We adopt a y-polarized wave to illuminate the structure normally. The boundary conditions are periodic in x- and y-directions and open for z-direction in free space. The conductivity of VO2 is set as σ=10 S/m [48]and σ=105 S/m in the insulating and metallic phase, respectively [39]. As shown in Fig. 2(b), when VO2 is in insulator state, the incident y-polarized wave entirely transforms to x-polarized wave and the reflection coefficient ryx is 0.912 at 1.3 THz. As the temperature increases to 68 °C, VO2 is in the metal state, and the reflection coefficient ryy of y-polarized wave is 0.978 at the same frequency, as shown in Fig. 2(c), which means the heat dissipation has little influence on the metasurface. As the reflection phase responses are almost the same before and after polarization conversion, more polarization deflection angles can be realized by applying the polarization synthesis. It can be observed in Fig. 2(d) that the phases of x-polarized and y-polarized reflection are identical at 1.3THz, which is perfect for polarization synthesis and further tuning of the polarizations. Thus, operating frequency of the proposed polarization-reprogrammable coding metasurface is 1.3THz. Based on the far field scattering function of the coding metasurface [7], the electric field of N×N element metasurface can be expressed as follow:
Fig. 2. (a) The schematic of meta-atom designed with metal state and insulator state of VO2. R1 = 48 µm, β = 29°, α = −45°. With y-polarized plane wave illuminating normally, the amplitude of reflected y- and x-polarized beam while VO2 is in insulator (b) and metal (c) state, respectively. (d) The phase of the reflected y-polarized beam while VO2 is in metal state and the reflected x-polarized beam while VO2 is in insulator state.
To realize arbitrary linearly polarized reflected beam, we arrange 40×40 CCRs to construct a reprogrammable metasurface, the states of VO2 in the elements along x direction stay the same, and the different coding sequences are imposing in y direction by applying external modulated voltage to the structure, as shown in Fig. 3(a). Figure 3(b)-(f) present the 2D normalized far electric field results of the coding metasurface. The energy is almost totally transformed into the x / y polarization, corresponding to coding sequence ‘0000….0000’ / ‘1111….1111’, which can be observed in Fig. 3(b) and (f). Coding sequence ‘0000….0000’ means that the reprogrammable metasurface is at room temperature and all VO2 stay in insulator state. The normalized amplitude is 0.957, which indicates that the reflected EM wave is totally transformed into x polarization. Meanwhile, coding sequence ‘1111….1111’ means that the reprogrammable metasurface is applied external voltage and all VO2 are changed into the metal state. The EM wave is totally reflected with the same y-polarization as the normalized amplitude of y-polarized reflected wave is 0.985. In addition to the orthogonal x/y polarization, the transition polarization states can be realized as well. As shown in Fig. 3(c)-(e), for different coding sequences ‘1000….1000’, ‘1100….1100’, and ‘1110….1110’, (ryy, rxy) are (0.324, 0.656), (0.617, 0.358) and (0.761, 0.172), respectively. According to the Eq. (5), the corresponding polarization angle η of the synthetic linear electric field is 26.28°, 59.88° and 77.26°. As y-x polarization ratio increase, polarization angle η changes from 0° to 90°. Thus, any linearly polarized state is realized by taking advantage of the proposed reprogrammable metasurface.
Fig. 3. (a) The scheme of proposed reprogrammable coding metasurface with coding sequence being 0101 $\cdots $ 0101. (b)-(f) Simulated 2D far-field results and y/x polarization conversion rate (ryy, rxy) with different coding sequences ‘0000….0000’, ‘1000….1000’, ‘1100….1100’, ‘1110….1110’ and ‘1111….1111’.
3.2 Design of the anisotropic programmable metasurface
Multi-channel beams are mainly realized by combining active component with two orthogonally polarized incident THz waves [19–26], which may have some limitations. In this work, CCRs encoding arrays are designed to realize dynamic multi-channel beams by single polarized incident wave.
Anisotropic dynamic reprogrammable coding metasurface is constructed by combining phase gradient with polarization coding states. Polarization conversion is achieved by using the two states of VO2.Then, we focus on the geometric design of CCR for phase discretization. When VO2 is in metal state, CCR could be regarded as a concentric metal ring, under which y polarization is almost totally reflected. From Figs. 4(a) and (b), we can see that the reflection coefficient ryy of y polarization is nearly the same while the phase of y polarization φyy is varied by the outer radius R1 of the CCR. CCR1(R1=48 µm) and CCR2(R1=29.2 µm) are chosen as basic phase discrete elements between which the phase difference is 180° at 1.3THz. When VO2 is in insulator state, CCR could be regarded as a split ring, under which y polarization is almost totally transformed to x polarization. In order to design appropriate x-polarized phase discrete elements while keeping y-polarized phase gradient unchanged, the outer radius R1 remain 48 µm and 29.2 µm. When R1 is fixed, the reflection coefficient rxy and phase φxy of x polarization is mainly determined by the orientation angle α and the opening angle β, respectively. As shown in Figs. 4(c) and (e), the reflection coefficient rxy get the maximum value when the orientation angle of CCR1 and CCR2 is set as α=±45°, and the amplitude are 0.87 and 0.89 at 1.3 THz. From Figs. 4(d) and (f), it should be noted that the x-polarized phase difference is always 180° as orientation angle α changes from 45° to −45°. Meanwhile, the opening angle of CCR1 and CCR2 is set as β=18°and β=38° to ensure the same reflection phase (φxy=119.26°) at 1.3 THz. Another two units CCR3 and CCR4 are obtained by rotating the orientation angle α of CCR1 and CCR2 by 90°. The geometry parameters and reflected information of four kinds of coding units are shown in Table 1 and Table 2.
Fig. 4. (a) The amplitude ryy and (b) the phase φyy of CCR1 (β1=38°, α1=−45°, R1=48 µm) and CCR2 (β2=18°, α2=45°, R2=29.2 µm) as VO2 is in metal state. (c), (e)The amplitude rxy and (d), (f) the phase φxy of CCR1 (α1=±45°) and CCR2 (α2 = ±45°) as VO2 is in insulator state.
Table 1. The structural parameters of coding units
Table 2. Amplitude and phase of coding units
The anisotropic metasurface designed with four types of coding units is illustrated in Fig. 5(a). The presented metasurface is composed of 40×40 meta-atoms, and 8 phase discrete meta-atoms are regarded as a supercell with CCR1, CCR1, CCR2, CCR2, CCR3, CCR3, CCR4 and CCR4 along x direction. To more clearly, the enlarged part of Fig. 5(a) distinguishes the insulator/metal state of VO2 (encoded as 0/1) with red/blue. For coding state 1, there only exists y-polarized reflection and the phase φyy of the supercell is −60.34°, −60.34°, 119.26°, 119.26°, −60.34°, −60.34°, 119.26° and 119.26°, respectively. For coding state 0, there only exists x-polarized reflection and the phase φxy of the supercell is 90°, 90°, 90°, 90°, −90°, −90°, −90° and −90°, respectively. Based on the designed gradient phase, the anomalous reflection angle of anisotropic metasurface [9] is given by:
where D is the periodicity of the gradient phase, λ is the wavelength of the y-polarized incident wave. Owing to different distribution of the gradient phase φxy and φyy, Dxy is 800 µm and Dyy is 400 µm. The theoretically calculated anomalous reflection angles of the x-polarized wave and y-polarized wave are ±16.76° and ±35.23° at 1.3 THz. In order to realize dynamic control of the multi-channel reflected beam, 2D far-field scattering results of the metasurface with different coding sequence are calculated numerically, as shown in Fig. 5(b)-(d). When coding sequence is ‘0000….0000’, that is, VO2 is all in the insulator state, the reflected beam is almost totally transformed into the x polarized wave and the reflection angles are ±17°, which is highly consistent with the calculated results ±16.76°. When the coding sequence is ‘0101….0101’, the two states of VO2 in the metasurface are alternately distributed along the y direction as shown in Fig. 5(a). Both x and y polarized wave are reflected, due to the difference in the phase gradient, the anomalous reflection angles of x-polarized and y-polarized reflected wave are ±17° and ±36°, and the number of reflected beams is changed from double to quatary. When the coding sequence is ‘1111….1111’, that is, VO2 is all in the metal state, only the y-polarized reflected beam exists and the reflection angles are ±36°, which is highly consistent with the calculated result ±35.23°. Therefore, the proposed anisotropic programmable metasurface is capable of controlling the number of channels, polarization, amplitude, as well as the anomalous reflection angle of the reflected beam dynamically.Fig. 5. (a)The diagrammatic sketch of anisotropic reprogrammable metasurface that coding sequence is 0101….0101 and the top view of supercell composed of CCR1, CCR2, CCR3 and CCR4. (b)-(f) Simulated far-field 2D results in x-polarized and y-polarized beam with different coding sequences ‘0000….0000’, ‘0101….0101’ and ‘1111….1111.
Owing to the repeatable and ultrafast phase transition of VO2 with applied voltage, it is hopeful to combine coding metasurface with FPGA to achieve anisotropic reprogrammable metasurface with ultra-fast response. The presented metasurface can be developed into an information encoder, the polarization and amplitude of two and four reflected beams can be detected and decoded modules. Therefore, the reprogrammable metasurface would also serve as a carrier of encrypted information.
Here we demonstrate the experimental feasibility of the design. On the current fabrication technologies [50,51], the unit structure is fabricated by a standard lift-off process and electron-beam evaporation. By applying external bias voltage directly to CCR with Au reflective layers serving as ground wire, VO2 can be changed from the insulator state into the metal state. Thus, we can use FPGA and CCR structures to construct reprogrammable metasurface, and the proposed reprogrammable metasurface is manipulated by different coding sequences.
4. Conclusion
In summary, we presented a polarization-reprogrammable metasurface to yield arbitrary linearly polarized EM wave and obtained an anisotropic programmable metasurface to dynamic control multi-channel beam at terahertz frequency. We theoretically analyzed the reflection information of the VO2/ Au composite concentric rings when VO2 is in the metal state and the insulator state, respectively, and encode them as digital coding elements 0 and 1. Moreover, polarization-reprogrammable metasurface is designed to realize arbitrary linear polarization including x/y polarization and the transition polarization states between them under specific coding sequences. Then, we proposed a novel idea of constructing anisotropic programmable metasurface by combining phase gradient with polarization coding states. Both simulation and calculation results confirmed its capability of controlling number of channels, polarization, amplitude, as well as the anomalous reflection angles of the reflected beam dynamically. The repeatable and ultrafast phase transition of VO2 with applied voltage may offer a unique possibility to achieve anisotropic reprogrammable metasurface with ultra-fast response by combining metasurface with FPGA. Our scheme may open up an extensive platform to realize a new class of ultra-fast THz polarization modulator, multichannel beam generation and THz information transmission system.
Funding
National Natural Science Foundation of China (62075048); Innovation Research of Science in Harbin Institute of Technology (2019KYCXJJZD01).
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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