Abstract

Abstract: Pancharatnam–Berry (PB) metasurfaces have intrigued a great deal of interest in recent years for anomalous reflection/refraction, vortex plate, orbital angular momentum, flat lens, photonic spin hall effect (PSHE), holograms and reflect/transmit arrays. However, almost all designs are restricted to fixed electrical performance/functionality once the design is finished. Here, we report for the first time a strategy for PB metasurface with agile working frequency by involving each meta-atom with tunable PIN diodes. For verification, a tunable PB metasurface with frequency reconfigurability is designed and numerically characterized across C and X band. By controlling the external voltages imposed on the diodes, numerical results show that the operation band with 180° phase difference between orthogonal reflection coefficients can be dynamically controlled. As such, the resulting PB metasurface composed of these orderly rotated meta-atoms exhibits a broadband PSHE with nearly 100% conversion efficiency in the “On” state while switches to dual well-separated bands in the “Off” state. Our proposal, not confined to PHSE, set a solid platform for PB phase control and can be populated to any dual-functional and/or multifunctional devices with high integrity, stability and low cost.

© 2016 Optical Society of America

1. Introduction

In recent years, controlling phase discontinuities along metasurfaces has intrigued an utmost interest in both science and engineering community due to unprecedented capability of metasurfaces in modulating wavefronts of electromagnetic (EM) waves or light [1–7]. The agile phases of these metasurfaces were engineered by varying structure parameters of meta-atoms under illumination of linearly-polarized (LP) EM wave. These metasurfaces are termed broadband when large phase tolerances and deteriorative operation performance are allowed. In addition to aforementioned metasurfaces, Pancharatnam–Berry (PB) metasurface is another type of specific planar artificial structures with rotational orientations under circularly-polarized (CP) stimulations [8–27]. Along with the success of ushering PB metasurfaces in anomalous reflection/refraction [8], the vast potential applications to novel devices are also evidenced due to their broad operation band and versatile features, such as vortex plate [9,10], orbital angular momentum [11], ultrathin flat lens [12,13], photonic spin hall effect (PSHE) [14,15], contoured beam synthesis [16,17], beam steering antenna [19], high-gain lens array [20–25], holograms [26,27] and so on.

Unfortunately, above PB metasurfaces or devices are confined to fixed electrical performance/functionality once the design is accomplished, indicating somewhat a limited freedom, low reusability and integrity, and a waste of resources. Moreover, their functionality cannot be dynamically modulated with versatile performances despite a broadband dispersionless phase gradient. Such two issues would hamper the applications of PB metasurfaces in practice. Tunable approaches have been investigated recently to control the EM response of metasurfaces in different frequency domains, however, they are mostly confined to homogenous metasurfaces without geometry rotation [28–35]. To date, tunable inhomogeneous PB metasurface with frequency and/or functionality reconfigurability is rarely seen due to the lack of efficient feeding technique for rotated structures. Moreover, tunable metasurface typically features limited phase and frequency tuning range [30], sharp resonant dips and a small phase shift less than 180°. This is because tunable diodes commonly introduce LC elements and undesired resistive loss, which enhance considerably the quality (Q) factor and absorptions. As a result, sharp dips and swift phase shift are observed for reflection magnitude and phase response, yielding identical phases (asymptotic behavior) near below and near above the resonance.

The goal of this work is to implement a highly-integrated frequency-agile high-efficiency PSHE device with dual-band response in the “Off” state while a broadband behavior in the “On” state by using PIN-loaded tunable metasurface. In the interval of the dual bands, the functionality can be switched from normal reflector in the “Off” state to a PSHE device with nearly 100% efficiency in the “On” state under LP excitation. To bridge the gap between flexible functionality and dynamical phase control, we conceived an efficient feeding strategy by proposing a new topology of slip ring brush. Such strategy enables the active feeding of every rotated meta-atoms by involving each of them with a PIN diode. Of particular relevance is the mechanism studied for suppression of normal reflection modes.

2. Unit cell topology and EM behavior

To accomplish our target, the basic meta-atom should exhibit dual-mode operations in the “Off” state while a broadband single-mode operation in the “On” state. One easy and straightforward way is to design dual-mode meta-atom in the “Off” state and then close up one of the dual modes by biasing PIN diodes to “On” state.

Figure 1 depicts the topology of proposed meta-atom as a basic building block of the tunable PB metasurface. As can be seen, the meta-atom is composed of three metallic layers sandwiched by two dielectric spacers: the top composite metallic pattern, middle ground plane and the bottom feeding network. This configuration enables a completely reflective system without transmissions. In practice, the two dielectric spacers can be bonded together by adhesives and reinforced by hot press. To break the asymptotic behavior and thus facilitate an active design, the meta-atom is required with sufficiently large phase and frequency tuning range. In this regard, the top metallic pattern is purposely designed as a composite of “I” structure and a pair of symmetric patches. When illuminated by normally incident y-polarized transverse EM wave along z direction, the electric and magnetic fields drive the “I” structure and patch, and each couples to the ground and generates an independent magnetic resonance around f1(y) and f2(y), respectively. Our dual-mode strategy is analogous to the V-antenna by combining its two eigenmodes [1] but is with additional degree of freedom for individual control of f1(y) and f2(y). Such multi-resonant element feature relaxes the high Q of a resonant circuit and thus efficiently resolves the issues of sharp resonance and limited phase/frequency tuning range in previous tunable work. Note that two different “I” structures kept side by side also enable similar dual magnetic resonances, however, the simultaneous control of them requires two diodes and two different biasing lines. Our strategy enables this target through the coupling between the patch and “I” structure which will be discussed later.

 

Fig. 1 Topology of the proposed tunable PB meta-atom. (a) Perspective view. (b) Simulation setup. (c) Slot in ground. (d) Side view. (e) Top view. (f) Bottom view.

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Here, tunability is actualized with the central “I” structure broken and then connected by M/A-COM MA4PBL027 PIN diodes with small junction capacitance Cj [36]. The external voltages are imposed to the diodes through two metallic vias which penetrated the two dielectric spacers and terminated with the back feeding network. To avoid an electrical DC short, two circular slots each with a central plate are etched on the ground. The functions of metallic ground are twofold. First, the effect of parasitic radiation of feeding lines to the PSHE is inhibited. Second, the fixed biasing line with respect to the top metallic structure does not destroy the two orthogonal axes with dynamically rotated angles. Otherwise, the orthogonal axes disappear and the PB phase does not preserve anymore. To guarantee the electrical connection of DC source to the top rotated composite pattern, an electrical slip ring brush is proposed as the bottom feeding network since the via always located on the slip ring no matter how it rotated. To provide an RF choke and thus reliable performance of the PB metasurface, Murata chip inductors in surface mount technology (SMT) with inductance of Lj = 10 nH are introduced in biasing lines. Moreover, symmetric LCP and RCP beams with equal amplitude will be restored, for which the mechanism will be explained later through field/current distributions. The required extremely small Cj was determined by the metallic via which introduces undesired loss and large inductance.

The widely available F4B substrate board with dielectric constant of εr = 2.65 + 0.00265i is utilized as the spacers. The periodicity of the subwavelength square element is px = py = 12 mm which approaches λ0/3 at center working frequency of 10 GHz. Since the nonuniform orthogonal reflection magnitudes would decrease the PSHE efficiency, the top substrate (h1 = 3 mm) is selected relatively thick to engineer a low Q of the system. In this regard, near-unity amplitude of two orthogonal reflection coefficients is guaranteed, and thus large frequency and phase tuning range are expected. The bottom substrate for supporting the biasing circuit poses little effect to the EM response due to the shielding of ground and is designed as h2 = 0.5 mm for the sake of a thin structure.

In the equivalent circuit model (CM) under y polarization, see Figs. 2(a)-2(d), the single magnetic resonance at f(y) in the “Off” state is modeled by L2, C2 and R2, whereas in the “On” state the two magnetic resonances at f1(y) and f2(y) are associated with I structure and patch and are modeled by two series resonant tanks formed of L1, C1, R1 (resonant loss), and L2, C2, R2 (resonant loss), respectively. The middle metallic layer was represented by the ground while the reflection through the dielectric was modeled by a transmission line (TL) with effective impedance Zc=Z0/εr and electrical length ho=2h1λ0/(2εr), where Z0 and λ0 are the wave impedance and wavelength in vacuum. For x polarization (Fig. 2(e)), the magnetic resonance originated from the coupling between patch and ground is modelled by a resonant tank formed of L3, C3 and R3 in both states. Such magnetic response for both orthogonal polarizations is determined by the line inductor Lp1 (Lp2) and parallel-plate capacitor Cp1 (Cp2) of the patch. By controlling the voltages imposed on the diodes, the working state of the PIN diode can be switched between “On” and “Off” state which corresponds to a series of lead inductance Ls and resistance Rs, and a series of Ls and Cj, respectively in Fig. 2(f) [36]. The association of various lumped elements with circuit parameters in “On”/“Off” state under x/y polarizations is now clear: L1Lw + Ls, L2Lp1, L3Lp2, R2 = R2+RS, C1 = Cs + Cj, C2Cp1 + kα*(Cs + Cj), C2 = Cp2, and C3Cp2, where Lw is bar inductor, Cs is package capacitance, and kα measures the coupling between the patch and I. Therefore, the resonances of the meta-atom under y polarization and thus the phase response at a fixed frequency can be arbitrarily tuned in terms of varied LC values. Note that a progressive control can be implemented by utilizing varactor diodes with a significant tuning range of Cj. However, such a progressive control is hard to realize by the high-impedance meta-atom with metallic vias. This is because such element topology requires extremely small Cj which typically exhibits small variation and cannot be afforded by commercially available tuning varactors.

 

Fig. 2 The equivalent circuit model of the (a-e) proposed meta-atom for (a-d) y polarization and (e) for x polarization at f(x) and (f) microwave model of PIN diodes. The (a, c) general and (b, d)detailed model and of the meta-atom at (a, b) f(y)in the “On” state and at (c, d) f1(y),f2(y) in the “Off” state.

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For characterization, the unique EM behavior of the meta-atom in the “Off” state (Ls = 0.11 nH, Cj = 0.03 pF) is evaluated in CST Microwave Studio where the unit cell boundary is assigned to four walls along x and y directions to mimic an infinite array, see Fig. 1(b). For comprehensive study, five cases are considered. As shown in Figs. 3(a) and 3(b), there is only a single resonant mode identified from the reflection dip and sharply changed phase in either bare I structure or bare patch case. However, with both patch and I structure involved, two magnetic resonances are observed at the lower (f1(y) = 5.8 GHz) and upper (f2(y) = 8.7 GHz) frequencies when h3 = 9 mm, where the phase changes rapidly across 0° twice. The reflection response calculated from EM and CM simulations coincides well, revealing the rationality of the model. The f2(y) shifts upwards as h3 decreases and therefore we do not observe the high-frequency resonance within available band when h3 is 3 and 6 mm. The dual-mode resonances are in much proximity in reflection spectra when h3 is sufficiently large. As a result, the dual-mode operation breaks asymptotic phase at edge frequencies, yielding a large phase tuning range and a near-unity reflection amplitude. Moreover, the coupling between the patch and I induced slightly lower f1(y) and higherf2(y) in the composite meta-atom. The origin of f1(y) from I structure while f2(y) from patch is further illustrated from the surface current distributions shown in the insets to Fig. 3(b), where strong current intensity is observed on I structure and patch at f1 and f2, respectively. Although strong current intensity is also observed on I structure at f2, it is in reversed phase with that on patch due to the parasitic coupling from the patch.

 

Fig. 3 Effects of the (a, b, g, h) patch height h3 and (c-f) junction capacitance Cj on reflection response of the tunable meta-atom under y polarization. EM calculated reflection response in the (a-d)“Off” and (g, h) “On” state. (e, f) CM calculated reflection response in the “Off” state. (a, c, e, g) Reflection amplitude. (b, d, f, h) Reflection phase. For general purpose, we plot here the results for meta-atom without lumped inductors in the bias line since they are the same as those for meta-atom with lumped inductors when self-resonance of the lumped inductors does not occur. Note that h3 = 9 mm was used for the “only patch” case. The geometrical parameters are designed as (unit: mm) px = py = 12, d1 = 0.4, d2 = 0.5, d3 = 0.3, w1 = 3, w2 = 0.4, R1 = 3, R2 = 2.5, h1 = 3, h2 = 0.5, h3 = 9, h4 = 2.5, h5 = 1 and h6 = 1. In full-wave simulations, Ls = 0.115 nH, Cj = 0.03 pF and Rs = 2.8 Ω. The circuit parameters are retrieved as L1 = 13 nH, C1 = 0.04 pF, L2 = 1 nH, C2 = 0.081 pF, R1 = 0.9 Ω, R2 = 0.8 Ω, Zc = 109.3 Ω and ho = 60.5°.

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Figures 3(c) and 3(d) depict the reflection coefficients of the tunable meta-atom for different Cj when other geometrical parameters are kept constant while Figs. 3(e) and 3(f) depict those for different C1 obtained from CM simulations. As is expected, the trends predicted from CM are in good consistency with those from EM results. Both f1(y) and f2(y) undergo a red-shift when Cj increases from 0.03 to 0.12 pF or C1 from 0.06 to 0.12 pF. The capacitive coupling between the patch and I structure enables such a simultaneous control. Moreover, the reflection dip at f1(y) reduces remarkably with Cj and C1. This is because the increase of capacitance enhances the energy stored in the circuit and thus reduces the wave intensity scattered in free space. The non-uniform amplitude would induce undesired scattering modes of PB metasurface and thus degrade the PSHE efficiency. This EM feature makes the progressive control through varactors inappropriate but the discrete control through PIN diodes more suitable. To validate this proposal, we also calculate the reflection spectrum in the “On” state (Ls = 0.11 nH, Rs = 2.8 Ω), see Figs. 3(g) and 3(h). As can be seen, the resonant response of the “I” structure dies off and a new resonance f(y) occurs between f1(y) and f2(y). The origin of f(y) from the patch can be validated from the progressive red shift with h3, and the almost identical f(y) in patch only case. The changed and shifted resonances in both states afford considerable phase agile which is the key to implement phase-dependent devices with dynamically switched functionality. This can be implemented by engineering the biasing circuit forward or zero biased through imparted DC voltages, so that the PIN diodes work in the “On” or “Off” state.

3. Design, numerical results and discussion

With all fundamentals and EM behavior of the meta-atom known, we now describe our strategy to design a functionality switchable PB metasurface utilizing these basic building blocks. Figure 4 portrays the layout of the designed PB metasurface. As is shown, the metasurface is composed of several super cells periodically arranged along x and y direction, respectively. The super cell consists of six (N = 6) sequentially rotated meta-atoms with identical geometrical parameters in a rotation angle step of Δφ = 30° along x direction, such that they provide an incremental phase shift of π/3 and exhibit desired phase gradient following the relationship ξ=±2π/(Npx). To guarantee an efficient biasing for meta-atoms rotated by 90°, the splits introduced in the ring are purposely rotated by 15° in the initial element, see Fig. 1(f). According to generalized Snell’s law [1], the scattered patterns from the normally incident CP wave will be directed toward off broadside by θr=arcsin(λξ/2π) with respect to the normal. Therefore, two splitted EM beams are expected traveling along inverse directions if the metasurface is illuminated by a normally incident LP wave which can be represented by the sum of a RHCP wave and a LHCP wave. Note that there are also other scattered modes (normal reflections) which will inevitably decrease the PSHE efficiency [15]. Here, we will briefly analyze the mechanism below from the scattering matrix method [23]. Moreover, the approximate ray-optical design which does not take into account the required variation of the wave impedance may also induce specular reflections [37–41]. This is because wave impedance mismatch does not guarantee 100%-efficiency coupling to the desirable modes whose reflection amplitude cannot be predicted by generalized Snell's law. Further discussion of it is beyond the scope of our concentration.

 

Fig. 4 Layout of the designed tunable PB metasurface with zoom-in view of a super cell shown in the dashed. The geometrical parameters of the meta-atoms are the same as those shown in Fig. 3 except for different rotation angles and introduced chip inductors.

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For a reflection meta-atom under Cartesian coordinate system, the Jones matrix in reflection scheme after a rotation angle φ can be written as

RφXY=[cosφsinφsinφcosφ]1[rxxrxyryxryy][cosφsinφsinφcosφ]
where the superscripts x and y denote the polarization of incidence. Then we can immediately obtain the reflection matrix under CP basis.

RφLR=12[1j1j]RφXY[1j1j]1

By substituting Eq. (1) into (2) we derive the following scattering matrix under CP incidence after some algebraic manipulations.

rll=12[(rxxryy)j(rxy+ryx)]ej2φ
rrr=12[(rxxryy)+j(rxy+ryx)]e+j2φ
rlr=12[(rxx+ryy)+j(rxyryx)]
rlr=12[(rxx+ryy)j(rxyryx)]
Equations (3) show that for rotated meta-atoms, only two components rll and rrr carry the PB phase information, which is twice the rotation angle [42], while the other two components rlr and rrl do not supply any PB phase and contribute to normal reflections. To ease the design, we design our system without chirality and thus without cross-polarization conversion under LP illumination (|rxy||ryx|0). To eliminate the undesired scattering modes, we only require rxx+ryy = 0. In a reflection scheme, we can easily obtain two orthogonal near-unity reflection amplitudes (|rxx||ryy|1). Therefore, we only need φxx-φyy180o to guarantee a high PSHE efficiency of our system. Such phase relation has been successfully utilized for polarization control and highly-directive subwavelenth cavity [35]. Here, we follow the developed dispersion engineering method (engineering the phase versus frequency) to design our meta-atom with broadband 180° phase difference between two orthogonal reflections in the “On” state. To achieve such a goal, we require that the reflection phases for two orthogonal polarizations exhibit similar slopes at several test frequencies, so that their difference can remain nearly a constant within broadband. Generally speaking, these test frequencies can be arbitrarily selected and are chosen as f=(f(y)+f(x))/2 and f=f(x) for easy design without loss of generality.
φxx(f)f=φyy(f)f
In the implementation, the structure parameters of w1 and h3 are chosen to optimize the dispersion curve through iterative full-wave simulations.

Figures 5(a) and 5(b) show the two orthogonal reflection coefficients of our finally designed meta-atom in both “On” and “Off” states. As is expected, two well-separated resonant dips are clearly observed around f1(y)≈5.62 and f2(y) = 8.45 GHz where the phases reach zero degree in the “Off” state from |ryy| spectrum. The |ryy| is more than 0.97 at most observed frequencies of 5~12.5 GHz except for that around 10.5 GHz where a parasitic resonance of I structure through the feeding network occurred. However, there is only a resonant dip around f(y) = 7.01 GHz in the “On” state where the phase reaches 0°. Moreover, the band for |ryy|>0.9 ranges from 5 to 12 GHz. The self-resonance of lumped inductors and parasitic resonances of I structure and feeding network give rise to three shallow dips after 10 GHz. In both “On” and “Off” state, only a weak resonant dip occurs around f(x) = 11.2 GHz from |rxx| spectrum. The out-of-phase difference (φyy-φxx) with a tolerances of −180° ± 40° is obtained within 5.67~6.08 GHz (Band I) and 9~10.55 GHz (Band II) in the “Off” state, whereas it is observed within 7.5~12.2 GHz (Band II) in the “On” state. Therefore, a dual-band and a broadband high-efficiency PSHE is expected in the former and latter case, respectively.

 

Fig. 5 Simulated (a, b) LP and (c, d) CP reflection coefficients of the designed PB metasurface in the (a, c) “Off” and (b, d) “On” states.

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Figures 5(c) and 5(d) further depict the CP reflection coefficients of the PB metasurface under RCP wave illumination. As is expected, slight ripples observed at high frequencies of the spectrum are attributable to the parasitic resonances for both orthogonal polarizations. The nonuniform reflection amplitude and fluctuated reflection phases give rise to the shallow dips in rrr spectrum at 10.5 GHz in the “Off” state while at 9.9 and 10.6 GHz in the “On” state. Nevertheless, the variation is in an acceptable level such that the broad band was not divided into two in the “On” state. The bandwidth characterized by |rlr|<0.3 (−10 dB) and |rrr|>0.9 is 7.6~12.1 GHz in the “On” state while is 5.7~6.05 GHz and 9.15~10.5 GHz in the “Off” state.

For demonstration, we have performed extensive characterizations on far-field scattering patterns of the PB metasurface with five super cells along x direction, whereas periodic boundary is assigned to the walls along y direction to mimic an infinite array. Figure 6 depicts the 2D contour of scattering power intensity of the PB metasurface in both working states under y-polarized incident EM wave. It is learned that the metasurface can split the incident LP beam into a LCP and a RCP beam traveling along two distinct directions in both “On” and “Off” states. However, the operation band identified from completely suppressed normal reflections and equal amplitudes of LCP and RCP beam dynamically switched from 8.1~12.2 GHz (a fractional bandwidth of 40.4%) in the “On” state to dual bands of 5.7~6.05 GHz and 9.15~10.5 GHz in the “Off” state. Outside these working bands, significant specular reflections appear which lower the PSHE efficiencies. The switched functionality of our PSHE device can be further inspected from Figs. 6(c) and 6(f) where the far-field scattering patterns for the “On” and “Off” state are plotted at a frequency around 8 GHz. In the former case the incident LP beam was split and deflected to near ± 30.8°, while in the latter case it was specularly reflected.

 

Fig. 6 Simulated and theoretically calculated (symbols) normalized far-field scattering power intensity P(θr, λ) of the PB metasurface under y-polarized normal incidence for −90°<θr<90°. The P(θr, λ) is normalized to the maximum intensity. The (a, d) LCP and (b, e) RCP wave for (a-c) “On” state and (d-f) “Off” state. The 3D scattering pattern at 8 GHz in the (c) “On” state and (f) “Off” state.

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Though normal reflections were suppressed to some extent within 10.6~11.4 GHz in the “Off” state, the asymmetric LCP and RCP amplitudes and hybrid beams with degraded polarization extinct ratio deteriorate the PSHE efficiency even below 50%. In both cases, the simulated steering angles coincide well with those predicted from generalized Snell’s law. The slight weak power intensity around 10.6 GHz in both “On” and “Off” states is attributed to the absorption loss of parasitic resonances illustrated in Fig. 5.

To further quantitatively study the PSHE performance, Fig. 7 shows the scattered intensity curve versus the elevation angle. To illustrate the advantage of our design, we also show here the results of PB metasurface without chip inductors introduced in biasing lines for reference. As is shown, very symmetric scattering patterns with equal amplitude are inspected for our designed PB metasurface in both states. However, asymmetric patterns with unequal amplitude is observed for reference metasurface. The flowing current in the bottom plane gives rise to the asymmetric LCP and RCP patterns, see Fig. 8. The current density decreases significantly on both ring and feeding line when chip inductors are introduced. Therefore, the leakage of RF signal through the bias line and ring is considerably prevented using chip inductors. The PSHE efficiency, calculated as the ratio between anomalously reflected power and the totally reflected power calculated by integrating power over the angle regions spanned by reflection modes, is obtained more than 89% at 5.95 GHz in the “On” state and 93% in the “Off” state within the operation band revealed in Fig. 6. At most frequency studied, the PSHE efficiency is achieved almost 100% such as at 8.7 and 10.8 GHz shown in Figs. 7(c) and 7(d) whose efficiency is obtained as 98%. The possibility of completely suppressing one polarization while maximizing the other can be implemented by loading asymmetric resistance along gradient (x) direction. This strategy has been validated from the results shown in Figs. 7(g) and 7(h) where almost completely suppressed RCP wave was inspected by setting Rs = 200 Ω in the last three PIN diodes along + x direction while Rs = 2 Ω in all residual ones.

 

Fig. 7 Scattering power intensity of the tunable PB metasurface (a-d) with (e, f) and without chip inductors in biasing lines at (a) 5.95, (b) 9.6, (e) 6 and (f) 10 GHz in the “Off” state, and at (c) 8.7 and (d) 10.8 GHz in the “On” state. Scattering (g) power intensity and (h) far-field pattern of the tunable PB metasurface at 8 GHz in the “On” state with Rs = 200 Ω in the last three PIN diodes along + x direction and Rs = 2 Ω in all residual ones.

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Fig. 8 Surface current distributions on bottom plane for PB metasurface (a) without and (b) with chip inductors introduced in feeding lines. Each plot shows 2 × 2 meta-atoms.

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4. Conclusions

To sum up, we have proposed a tunable strategy to dynamically control the working frequencies of PB metasurface by combining electrical slip ring brush feeding network and dual-mode meta-atoms. For demonstration, a tunable PB device is designed and numerically demonstrated with frequency-agile and high-efficiency PSHE. Our tunable approach engineered for rotated meta-atom provides additional degree of freedom for phase and wave front control in addition to geometrical and orientation modulations. Moreover, it can be readily populated to design/realize other phase-related functional devices in high integration and broad bandwidth. Finally, the tunable PB phase control in reflection scheme can be directly extended to a transmission scheme by utilizing multilayer composite structure whose multi-mode response is realized through Fabry-Perot resonance. Although the much-cost varactor with extremely small Cj hinders back the realization, a proof-of-concept prototype fabrication is now considered by designing novel micro-electromechanical system (MEMS) meta-atoms without metallic vias and high-loss varactors. In this case, large frequency tuning range and higher efficiency can be realized without much cost.

Funding

National Natural Science Foundation China (NSFC) Grant Nos. 61501499 and 61372034; China Postdoctoral Science Foundation Grant No. 2015M570323; special financial grant from the China Postdoctoral Science Foundation Grant No. 2016T90337; and Natural Science Foundation of Shaanxi Province Grant 2016JQ6001.

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11. E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014). [CrossRef]  

12. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012). [CrossRef]   [PubMed]  

13. X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015). [CrossRef]  

14. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013). [CrossRef]   [PubMed]  

15. W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3(8), 1102–1108 (2015). [CrossRef]  

16. M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, O. Breinbjerg, and G. Toso, “The generalized direct optimization technique for printed reflectarrays,” IEEE Trans. Antenn. Propag. 62(4), 1690–1700 (2014). [CrossRef]  

17. M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013). [CrossRef]  

18. E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015). [CrossRef]  

19. M. Euler and V. F. Fusco, “Frequency selective surface using nested split ring slot elements as a lens with mechanically reconfigurable beam steering capability,” IEEE Trans. Antenn. Propag. 58(10), 3417–3421 (2010). [CrossRef]  

20. J. Huang and R. J. Pogorzelski, “A ka-band microstrip reflectarray with elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 46(5), 650–656 (1998). [CrossRef]  

21. A. E. Martynyuk, J. I. Martinez-Lopez, and N. A. Martynyuk, “Spiraphase-type reflectarrays based on loaded ring slot resonators,” IEEE Trans. Antenn. Propag. 52(1), 142–153 (2004). [CrossRef]  

22. B. Strassner, C. Han, and K. Chang, “Circularly polarized reflectarray with microstrip ring elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 52(4), 1122–1125 (2004). [CrossRef]  

23. R. H. Phillion and M. Okoniewski, “Lenses for circular polarization using planar arrays of rotated passive elements,” IEEE Trans. Antenn. Propag. 59(4), 1217–1227 (2011). [CrossRef]  

24. A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012). [CrossRef]  

25. J. Rodriguez-Zamudio, J. I. Martinez-Lopez, J. Rodriguez-Cuevas, and A. E. Martynyuk, “Reconfigurable reflectarrays based on optimized spiraphase-type elements,” IEEE Trans. Antenn. Propag. 60(4), 1821–1830 (2012). [CrossRef]  

26. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). [CrossRef]  

27. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]   [PubMed]  

28. D. F. Sievenpiper, J. H. Schaffner, H. J. Song, R. Y. Loo, and G. Tangonan, “Two-dimensional beam steering using an electrically tunable impedance surface,” IEEE Trans. Antenn. Propag. 51(10), 2713–2722 (2003). [CrossRef]  

29. P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013). [CrossRef]  

30. B. O. Zhu, J. Zhao, and Y. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3, 3059 (2013). [CrossRef]   [PubMed]  

31. J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014). [CrossRef]  

32. T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014). [CrossRef]  

33. Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015). [CrossRef]  

34. C. P. Scarborough, D. H. Werner, and D. E. Wolfe, “Compact low-profile tunable metasurface-enabled antenna with near-arbitrary polarization,” IEEE Trans. Antenn. Propag. 64(7), 2775–2783 (2016). [CrossRef]  

35. H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016). [CrossRef]   [PubMed]  

36. MA4PBL027, HMICTM Silicon Beam-Lead PIN Diodes, www.macomtech.com for data sheets and product information, M/A-COM Technology Solutions Inc.

37. N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21 (2016). [CrossRef]  

38. N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6(4), 041008 (2016). [CrossRef]  

39. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016). [CrossRef]  

40. A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Trans. Antenn. Propag. 64(9), 3880–3895 (2016). [CrossRef]  

41. V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016). [CrossRef]  

42. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002). [CrossRef]   [PubMed]  

References

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  1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  2. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [Crossref] [PubMed]
  3. L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
    [Crossref]
  4. S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
    [Crossref]
  5. S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
    [Crossref] [PubMed]
  6. H.-X. Xu, S. Tang, G.-M. Wang, T. Cai, W. Huang, Q. He, S. Sun, and L. Zhou, “Multifunctional microstrip array combining a linear polarizer and focusing metasurface,” IEEE Trans. Antenn. Propag. 64(8), 3676–3682 (2016).
    [Crossref]
  7. S. Liu, L. Zhang, Q. L. Yanga, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Optical Mater., http://onlinelibrary.wiley.com/doi/10.1002/adom.201600471/full (2016).
  8. X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
    [Crossref] [PubMed]
  9. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
    [Crossref]
  10. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
    [Crossref] [PubMed]
  11. E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
    [Crossref]
  12. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
    [Crossref] [PubMed]
  13. X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
    [Crossref]
  14. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
    [Crossref] [PubMed]
  15. W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3(8), 1102–1108 (2015).
    [Crossref]
  16. M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, O. Breinbjerg, and G. Toso, “The generalized direct optimization technique for printed reflectarrays,” IEEE Trans. Antenn. Propag. 62(4), 1690–1700 (2014).
    [Crossref]
  17. M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
    [Crossref]
  18. E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015).
    [Crossref]
  19. M. Euler and V. F. Fusco, “Frequency selective surface using nested split ring slot elements as a lens with mechanically reconfigurable beam steering capability,” IEEE Trans. Antenn. Propag. 58(10), 3417–3421 (2010).
    [Crossref]
  20. J. Huang and R. J. Pogorzelski, “A ka-band microstrip reflectarray with elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 46(5), 650–656 (1998).
    [Crossref]
  21. A. E. Martynyuk, J. I. Martinez-Lopez, and N. A. Martynyuk, “Spiraphase-type reflectarrays based on loaded ring slot resonators,” IEEE Trans. Antenn. Propag. 52(1), 142–153 (2004).
    [Crossref]
  22. B. Strassner, C. Han, and K. Chang, “Circularly polarized reflectarray with microstrip ring elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 52(4), 1122–1125 (2004).
    [Crossref]
  23. R. H. Phillion and M. Okoniewski, “Lenses for circular polarization using planar arrays of rotated passive elements,” IEEE Trans. Antenn. Propag. 59(4), 1217–1227 (2011).
    [Crossref]
  24. A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012).
    [Crossref]
  25. J. Rodriguez-Zamudio, J. I. Martinez-Lopez, J. Rodriguez-Cuevas, and A. E. Martynyuk, “Reconfigurable reflectarrays based on optimized spiraphase-type elements,” IEEE Trans. Antenn. Propag. 60(4), 1821–1830 (2012).
    [Crossref]
  26. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
    [Crossref]
  27. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
    [Crossref] [PubMed]
  28. D. F. Sievenpiper, J. H. Schaffner, H. J. Song, R. Y. Loo, and G. Tangonan, “Two-dimensional beam steering using an electrically tunable impedance surface,” IEEE Trans. Antenn. Propag. 51(10), 2713–2722 (2003).
    [Crossref]
  29. P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
    [Crossref]
  30. B. O. Zhu, J. Zhao, and Y. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3, 3059 (2013).
    [Crossref] [PubMed]
  31. J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
    [Crossref]
  32. T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
    [Crossref]
  33. Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
    [Crossref]
  34. C. P. Scarborough, D. H. Werner, and D. E. Wolfe, “Compact low-profile tunable metasurface-enabled antenna with near-arbitrary polarization,” IEEE Trans. Antenn. Propag. 64(7), 2775–2783 (2016).
    [Crossref]
  35. H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
    [Crossref] [PubMed]
  36. MA4PBL027, HMICTM Silicon Beam-Lead PIN Diodes, www.macomtech.com for data sheets and product information, M/A-COM Technology Solutions Inc.
  37. N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21 (2016).
    [Crossref]
  38. N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6(4), 041008 (2016).
    [Crossref]
  39. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
    [Crossref]
  40. A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Trans. Antenn. Propag. 64(9), 3880–3895 (2016).
    [Crossref]
  41. V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
    [Crossref]
  42. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
    [Crossref] [PubMed]

2016 (10)

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
[Crossref] [PubMed]

H.-X. Xu, S. Tang, G.-M. Wang, T. Cai, W. Huang, Q. He, S. Sun, and L. Zhou, “Multifunctional microstrip array combining a linear polarizer and focusing metasurface,” IEEE Trans. Antenn. Propag. 64(8), 3676–3682 (2016).
[Crossref]

C. P. Scarborough, D. H. Werner, and D. E. Wolfe, “Compact low-profile tunable metasurface-enabled antenna with near-arbitrary polarization,” IEEE Trans. Antenn. Propag. 64(7), 2775–2783 (2016).
[Crossref]

H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
[Crossref] [PubMed]

N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21 (2016).
[Crossref]

N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6(4), 041008 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Trans. Antenn. Propag. 64(9), 3880–3895 (2016).
[Crossref]

V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

2015 (7)

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3(8), 1102–1108 (2015).
[Crossref]

E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015).
[Crossref]

Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

2014 (6)

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, O. Breinbjerg, and G. Toso, “The generalized direct optimization technique for printed reflectarrays,” IEEE Trans. Antenn. Propag. 62(4), 1690–1700 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

2013 (5)

M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
[Crossref]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

B. O. Zhu, J. Zhao, and Y. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3, 3059 (2013).
[Crossref] [PubMed]

L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

2012 (4)

A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012).
[Crossref]

J. Rodriguez-Zamudio, J. I. Martinez-Lopez, J. Rodriguez-Cuevas, and A. E. Martynyuk, “Reconfigurable reflectarrays based on optimized spiraphase-type elements,” IEEE Trans. Antenn. Propag. 60(4), 1821–1830 (2012).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

2011 (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

R. H. Phillion and M. Okoniewski, “Lenses for circular polarization using planar arrays of rotated passive elements,” IEEE Trans. Antenn. Propag. 59(4), 1217–1227 (2011).
[Crossref]

2010 (1)

M. Euler and V. F. Fusco, “Frequency selective surface using nested split ring slot elements as a lens with mechanically reconfigurable beam steering capability,” IEEE Trans. Antenn. Propag. 58(10), 3417–3421 (2010).
[Crossref]

2004 (2)

A. E. Martynyuk, J. I. Martinez-Lopez, and N. A. Martynyuk, “Spiraphase-type reflectarrays based on loaded ring slot resonators,” IEEE Trans. Antenn. Propag. 52(1), 142–153 (2004).
[Crossref]

B. Strassner, C. Han, and K. Chang, “Circularly polarized reflectarray with microstrip ring elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 52(4), 1122–1125 (2004).
[Crossref]

2003 (1)

D. F. Sievenpiper, J. H. Schaffner, H. J. Song, R. Y. Loo, and G. Tangonan, “Two-dimensional beam steering using an electrically tunable impedance surface,” IEEE Trans. Antenn. Propag. 51(10), 2713–2722 (2003).
[Crossref]

2002 (1)

1998 (1)

J. Huang and R. J. Pogorzelski, “A ka-band microstrip reflectarray with elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 46(5), 650–656 (1998).
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Aieta, F.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Albooyeh, M.

V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

Alu, A.

P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

Alù, A.

N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21 (2016).
[Crossref]

N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6(4), 041008 (2016).
[Crossref]

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

Amann, M.-C.

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

An, Z. H.

Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Asadchy, V. S.

V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

Bai, B.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref] [PubMed]

Bai, B. F.

L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Bao, D.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

Belkin, M. A.

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

Bernety, H. M.

P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

Biener, G.

Blanchard, R.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

Boehm, G.

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

Bomzon, Z.

Boyd, R. W.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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Breinbjerg, O.

M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, O. Breinbjerg, and G. Toso, “The generalized direct optimization technique for printed reflectarrays,” IEEE Trans. Antenn. Propag. 62(4), 1690–1700 (2014).
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M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
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Briggs, D. P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
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Burokur, S. N.

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
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Cai, T.

H.-X. Xu, S. Tang, G.-M. Wang, T. Cai, W. Huang, Q. He, S. Sun, and L. Zhou, “Multifunctional microstrip array combining a linear polarizer and focusing metasurface,” IEEE Trans. Antenn. Propag. 64(8), 3676–3682 (2016).
[Crossref]

H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
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Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Chang, K.

B. Strassner, C. Han, and K. Chang, “Circularly polarized reflectarray with microstrip ring elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 52(4), 1122–1125 (2004).
[Crossref]

Cheah, K. W.

L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, H. B.

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

Chen, M.

X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Chen, P.

P. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alu, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

Chen, P.-Y.

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

Chen, S. M.

L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, X.

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref] [PubMed]

Chen, X. Z.

X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Cheng, Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
[Crossref] [PubMed]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

Civi, O. A.

E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015).
[Crossref]

Cui, T. J.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
[Crossref] [PubMed]

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

De Leon, I.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

de Lustrac, A.

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

Demmerle, F.

J. Lee, S. Jung, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrafast electrically tunable polaritonic metasurfaces,” Adv. Opt. Mater. 2(11), 1057–1063 (2014).
[Crossref]

Díaz-Rubio, A.

V. S. Asadchy, M. Albooyeh, S. N. Tcvetkova, A. Díaz-Rubio, Y. Ra’di, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

Ding, K.

Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Ding, X.

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

Du, L.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

Eleftheriades, G. V.

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Trans. Antenn. Propag. 64(9), 3880–3895 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
[Crossref]

Elsherbeni, A. Z.

A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012).
[Crossref]

Epstein, A.

A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field transformations with passive lossless omega-type bianisotropic metasurfaces,” IEEE Trans. Antenn. Propag. 64(9), 3880–3895 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
[Crossref]

Erdil, E.

E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015).
[Crossref]

Esmaeilzad, N. S.

E. Erdil, K. Topalli, N. S. Esmaeilzad, Ö. Zorlu, H. Kulah, and O. A. Civi, “Reconfigurable nested ring-split ring transmitarray unit cell employing the element rotation method by microfluidics,” IEEE Trans. Antenn. Propag. 63(3), 1163–1167 (2015).
[Crossref]

Estakhri, N. M.

N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6(4), 041008 (2016).
[Crossref]

N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21 (2016).
[Crossref]

Euler, M.

M. Euler and V. F. Fusco, “Frequency selective surface using nested split ring slot elements as a lens with mechanically reconfigurable beam steering capability,” IEEE Trans. Antenn. Propag. 58(10), 3417–3421 (2010).
[Crossref]

Feng, Y.

B. O. Zhu, J. Zhao, and Y. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3, 3059 (2013).
[Crossref] [PubMed]

Fusco, V. F.

M. Euler and V. F. Fusco, “Frequency selective surface using nested split ring slot elements as a lens with mechanically reconfigurable beam steering capability,” IEEE Trans. Antenn. Propag. 58(10), 3417–3421 (2010).
[Crossref]

Gaburro, Z.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gao, D.

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

Gao, L. H.

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

Genevet, P.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gu, J. Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
[Crossref] [PubMed]

Han, C.

B. Strassner, C. Han, and K. Chang, “Circularly polarized reflectarray with microstrip ring elements having variable rotation angles,” IEEE Trans. Antenn. Propag. 52(4), 1122–1125 (2004).
[Crossref]

Han, J.

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M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
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A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012).
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H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
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H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
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M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
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Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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J. Rodriguez-Zamudio, J. I. Martinez-Lopez, J. Rodriguez-Cuevas, and A. E. Martynyuk, “Reconfigurable reflectarrays based on optimized spiraphase-type elements,” IEEE Trans. Antenn. Propag. 60(4), 1821–1830 (2012).
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H.-X. Xu, S. Tang, G.-M. Wang, T. Cai, W. Huang, Q. He, S. Sun, and L. Zhou, “Multifunctional microstrip array combining a linear polarizer and focusing metasurface,” IEEE Trans. Antenn. Propag. 64(8), 3676–3682 (2016).
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H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
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A. Yu, F. Yang, A. Z. Elsherbeni, J. Huang, and Y. Kim, “An offset-fed X-band reflectarray antenna using a modified element rotation technique,” IEEE Trans. Antenn. Propag. 60(3), 1619–1624 (2012).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

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X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

Zhang, L.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
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X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27(7), 1195–1200 (2015).
[Crossref] [PubMed]

Zhang, S.

X. Z. Chen, M. Chen, M. Q. Mehmood, D. D. Wen, F. Y. Yue, C. W. Qiu, and S. Zhang, “Longitudinal multifoci metalens for circularly polarized light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. Tan, G. Jin, K. W. Cheah, C.-W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref]

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S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
[Crossref] [PubMed]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhang, Y. B.

Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

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L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
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B. O. Zhu, J. Zhao, and Y. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3, 3059 (2013).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

Zhou, L.

H.-X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G.-M. Wang, T. Cai, H.-P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6, 27503 (2016).
[Crossref] [PubMed]

H.-X. Xu, S. Tang, G.-M. Wang, T. Cai, W. Huang, Q. He, S. Sun, and L. Zhou, “Multifunctional microstrip array combining a linear polarizer and focusing metasurface,” IEEE Trans. Antenn. Propag. 64(8), 3676–3682 (2016).
[Crossref]

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015).
[Crossref]

W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3(8), 1102–1108 (2015).
[Crossref]

Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Zhou, M.

M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, O. Breinbjerg, and G. Toso, “The generalized direct optimization technique for printed reflectarrays,” IEEE Trans. Antenn. Propag. 62(4), 1690–1700 (2014).
[Crossref]

M. Zhou, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, “Direct optimization of printed reflectarrays for contoured beam satellite antenna applications,” IEEE Trans. Antenn. Propag. 61(4), 1995–2004 (2013).
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Zhou, X. Y.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
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S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv Sci (Weinh) 3(10), 1600156 (2016).
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MA4PBL027, HMICTM Silicon Beam-Lead PIN Diodes, www.macomtech.com for data sheets and product information, M/A-COM Technology Solutions Inc.

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Figures (8)

Fig. 1
Fig. 1 Topology of the proposed tunable PB meta-atom. (a) Perspective view. (b) Simulation setup. (c) Slot in ground. (d) Side view. (e) Top view. (f) Bottom view.
Fig. 2
Fig. 2 The equivalent circuit model of the (a-e) proposed meta-atom for (a-d) y polarization and (e) for x polarization at f (x) and (f) microwave model of PIN diodes. The (a, c) general and (b, d)detailed model and of the meta-atom at (a, b) f (y) in the “On” state and at (c, d) f 1 (y) , f 2 (y) in the “Off” state.
Fig. 3
Fig. 3 Effects of the (a, b, g, h) patch height h3 and (c-f) junction capacitance Cj on reflection response of the tunable meta-atom under y polarization. EM calculated reflection response in the (a-d)“Off” and (g, h) “On” state. (e, f) CM calculated reflection response in the “Off” state. (a, c, e, g) Reflection amplitude. (b, d, f, h) Reflection phase. For general purpose, we plot here the results for meta-atom without lumped inductors in the bias line since they are the same as those for meta-atom with lumped inductors when self-resonance of the lumped inductors does not occur. Note that h3 = 9 mm was used for the “only patch” case. The geometrical parameters are designed as (unit: mm) px = py = 12, d1 = 0.4, d2 = 0.5, d3 = 0.3, w1 = 3, w2 = 0.4, R1 = 3, R2 = 2.5, h1 = 3, h2 = 0.5, h3 = 9, h4 = 2.5, h5 = 1 and h6 = 1. In full-wave simulations, Ls = 0.115 nH, Cj = 0.03 pF and Rs = 2.8 Ω. The circuit parameters are retrieved as L1 = 13 nH, C1 = 0.04 pF, L2 = 1 nH, C2 = 0.081 pF, R1 = 0.9 Ω, R2 = 0.8 Ω, Zc = 109.3 Ω and ho = 60.5°.
Fig. 4
Fig. 4 Layout of the designed tunable PB metasurface with zoom-in view of a super cell shown in the dashed. The geometrical parameters of the meta-atoms are the same as those shown in Fig. 3 except for different rotation angles and introduced chip inductors.
Fig. 5
Fig. 5 Simulated (a, b) LP and (c, d) CP reflection coefficients of the designed PB metasurface in the (a, c) “Off” and (b, d) “On” states.
Fig. 6
Fig. 6 Simulated and theoretically calculated (symbols) normalized far-field scattering power intensity P(θr, λ) of the PB metasurface under y-polarized normal incidence for −90°<θr<90°. The P(θr, λ) is normalized to the maximum intensity. The (a, d) LCP and (b, e) RCP wave for (a-c) “On” state and (d-f) “Off” state. The 3D scattering pattern at 8 GHz in the (c) “On” state and (f) “Off” state.
Fig. 7
Fig. 7 Scattering power intensity of the tunable PB metasurface (a-d) with (e, f) and without chip inductors in biasing lines at (a) 5.95, (b) 9.6, (e) 6 and (f) 10 GHz in the “Off” state, and at (c) 8.7 and (d) 10.8 GHz in the “On” state. Scattering (g) power intensity and (h) far-field pattern of the tunable PB metasurface at 8 GHz in the “On” state with Rs = 200 Ω in the last three PIN diodes along + x direction and Rs = 2 Ω in all residual ones.
Fig. 8
Fig. 8 Surface current distributions on bottom plane for PB metasurface (a) without and (b) with chip inductors introduced in feeding lines. Each plot shows 2 × 2 meta-atoms.

Equations (7)

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R φ XY = [ cosφ sinφ sinφ cosφ ] 1 [ r xx r xy r yx r yy ][ cosφ sinφ sinφ cosφ ]
R φ LR = 1 2 [ 1 j 1 j ] R φ XY [ 1 j 1 j ] 1
r ll = 1 2 [( r xx r yy )j( r xy + r yx )] e j2φ
r rr = 1 2 [( r xx r yy )+j( r xy + r yx ) ]e +j2φ
r lr = 1 2 [( r xx + r yy )+j( r xy r yx )]
r lr = 1 2 [( r xx + r yy )j( r xy r yx )]
φ xx (f) f = φ yy (f) f

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