Abstract

Recent advances of space-time-coding digital metasurfaces demonstrate powerful capabilities in the generation of nonlinear harmonics and the accurate control of the corresponding wavefronts. However, to date the near field manipulation and the experiment characterization are still not explored. In this paper, we propose a space-time-digital coding metasurface to realize accurate manipulation of the near fields at the fundamental and +1st (1st) harmonics simultaneously, by properly controlling the initial phase and time delay of the time varying reflectivity. A novel mapping system is established to measure the nonlinear near field distributions of multiharmonics. Both the simulation and experimental results demonstrate the validity of the proposed method.

© 2021 Chinese Laser Press

1. INTRODUCTION

Metasurfaces have attracted enormous interest due to their intriguing electromagnetic (EM) responses, which bring us many fascinating physical phenomena including negative refraction [1,2], perfect lensing [3], and invisibility cloaking [46]. The metasurfaces usually consist of the resonant or nonresonant subwavelength elements, whose reflection/transmission coefficients can be customized at will by changing the size, shape [7], or orientation of unit cells [810]. Due to the elaborate arrangement of the metaatoms across the whole metasurface, the phase discontinuities can be introduced to control the propagation direction [11], polarization state [1214], and wavefront [1519] of EM waves. To simplify the complexity of metasurface design, coding metasurfaces [20,21] were proposed to facilitate accurate control of the EM waves based on the coding sequences of binary metaatoms. Hence, versatile functionalities of the coding metasurfaces have been demonstrated, including ultrathin planar lenses [22,23], vortex beam generations [2426], and metasurface holograms [2730].

However, most of these metasurfaces are passive, and their functions are fixed once they have been fabricated. To overcome these limitations, dynamic control of the EM waves was proposed based on programmable/tunable metasurfaces. These metasurfaces are usually integrated with active devices, such as positive-intrinsic-negative (PIN) diodes [3135], varactors [3639], and microelectro-mechanical systems [40]. However, most of the aforementioned programmable metasurfaces only focus on the control of the incident carrier wave, but seldom realize accurate manipulations of nonlinear amplitudes and phases.

In the THz and visible regimes, plenty of metasurfaces were proposed to control nonlinear wave responses, including the intensity, phase, and the polarization state [4145]. However, the simultaneous control of the harmonic amplitudes and phases still remains a great challenge. Recently, space-time-digital metasurfaces [4650] were proposed to solve this problem. By dynamically altering the local amplitude or phase of the surface reflectivity in a periodic manner, the metasurfaces showed powerful capabilities in the generation and manipulation of a specific order harmonic [4650]. Furthermore, Dai et al. proposed a method to realize independent control of two harmonics [51]. However, these works did not explore the simultaneous manipulation of the fundamental and high-order harmonics. Furthermore, recent studies on space-time digital metasurfaces were restricted to their far-field characteristics, but the nonlinear near-field manipulation is seldom investigated experimentally.

On this basis, we propose a scheme to realize the manipulation of the fundamental and high-order harmonics simultaneously via the space-time digital metasurface. A novel experimental platform for nonlinear field mapping is developed to monitor the harmonic near field distributions. As an example, we show the feasibility of achieving two symmetric beams at the fundamental frequency, and the orbital angular momentum (OAM) beams with different topological numbers at ±1st order harmonics. The space-time digital metasurface is designed, fabricated, and measured at different harmonics. The experimental results validate the effectiveness of the theoretical analyses.

2. THEORY AND DESIGN

As shown in Fig. 1, the proposed space-time digital metasurface is composed of periodic metaatoms loaded with PIN diodes. By introducing initial phase φA and time delay t1, the reflectivity Γpq(t) of the element (p, q) in the metasurface can be defined as

Γpq(t)=m=0M1AΓmg(tt1mτ),0<|t|<T,
where g(t) is basic pulse function with the modulation period T=M×τ. τ is the pulse width. M is the pulse number in a period. Γm is the reflectivity at the interval (m1)τ<t<mτ. A is a constant with A=|A|exp(jφA).
 

Fig. 1. Schematic of the space-time digital coding metasurface, which can independently control the wavefronts of the fundamental and high-order harmonics by adjusting the phase φA, and the time delay t1 of the periodic reflectivity.

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Under the monochromatic wave incidence Ei(t)=exp(jωct), the reflected spectrum is composed of many harmonics [46]. cpqk is defined as the complex Fourier coefficient of the periodic reflectivity Γpq(t) at the kth order harmonic ω=kω0+ωc, where ω0=2π/T, k=0, ±1, ±2, ±3,. ω0 and ωc are the modulation frequency and the carrier frequency, respectively. cpqk can be written as

cpqk=|A|exp[j(kω0t1φA)](apqk).
Here, apqk is presented as
apqk=1MSa(kπM)ejkπMm=0M1Γnexp(jkω0mτ).
The phase of the kth order harmonic can be
φpqk=arg(cpqk)=(kω0t1φA)+φpq*k,
where φpq*k=arg(apqk). It depends on the pulse number and pulse amplitude simultaneously from Eq. (3).

In this study, we consider a high-efficiency reflective metasurface with |Γm|=1. Two states, namely 0 and 1 states, are found with the reflection phases of Γpq(t) to be 0° and 180°, respectively. From Eqs. (2) and (3), the duty cycle of the reflection phases of Γpq(t) is very important for the energy conversion from the fundamental wave into the different harmonics. As an example, altogether 12 time slots with the duty cycle of 1/3 are selected to get the larger amplitudes for the 0th, 1st, 1st order harmonics. For simplicity, the basic coding sequence is chosen as 000011111111, implying that the reflection phases are 0° in the first four time slots, and 180° in the last eight time slots. The corresponding reflection amplitude and phase spectra can be found in Fig. 2(a), with φA=0° and t1=0. However, as demonstrated in Figs. 2(b) and 2(c), the phases φA and time delays t1 also show great influence on the harmonic phase distributions, which is consistent with the prediction from Eq. (4).

 

Fig. 2. Reflection amplitudes and phases of Γpq(t) in each period (left column) and the calculated reflection spectra (right column) under different combinations of φA and t1, when the coding sequence 000011111111 is employed. (a) φA=0°, t1=0, (b) φA=180°, t1=0, (c) φA=0°, t1=T/2.

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From Eq. (4), the harmonic phases for the fundamental and ±1st order harmonics are obtained as

φpq0=φA+φpq*0,φpq1=φAω0t1+φpq*1,φpq1=φA+ω0t1+φpq*1.

According to Eqs. (2)–(4) when the coding sequence Γm and period T are determined, φpq*0, φpq*1, and φpq*1 are fixed. Thus, we control the phases of any two harmonics independently by choosing the proper sets of (φA, t1), which enables us to design and realize various functionalities at different harmonics.

To validate the concepts illustrated in Fig. 1, a metaatom in Fig. 3 is designed to achieve the time-varying reflectivity by switching the embedded PIN diode between the on and off states. It consists of two dielectric substrates. Two symmetrical metallic patches are connected by a PIN diode on the top of the upper substrate. A perfect electric conductor (PEC) ground is attached to the bottom of the upper substrate to serve as the ground. A glue layer is used to combine the two substrates, and a biasing circuit is printed on the back of the lower substrate. Both substrates are F4B with the dielectric constant of 2.65 and the loss tangent of 0.001. The thicknesses of the two substrates are 4 and 0.7 mm, respectively. The glue has a dielectric constant of 3.54, a loss tangent of 0.001, and a thickness of 0.1 mm. A PIN diode (Skyworks SMP1320-040LF) [52] is chosen in the element design for the excellent broadband property. When the biasing voltage is above 0.7 V, the PIN diode is switched on and behaves like a small resistor. On the contrary, when the biasing voltage falls to 0 V, the diode is switched off like a capacitor to isolate the DC current. The left patch is connected to the PEC ground, while the right patch is connected to the bottom biasing circuit. The mender lines are used to filter RF signal. The diameter of the metallic vias is 0.4 mm, and the mender lines have a width of 0.2 mm.

 

Fig. 3. (a) Perspective view, (b) top view, and (c) bottom view of the metaatom. (d) The simulated reflection spectra of the metaatom under the normal incidence. (e) The scattering patterns of the metaatom for the on and off states. The geometric parameters of the metaatom are p=14, h1=0.8, h2=4, d0=0.7, x1=2, y1=4, x2=0.4, y2=0.6, x3=0.15, and x4=0.8mm.

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The commercial software CST Microwave Studio 2019 is used to investigate the reflection spectrum of the metaatom under different working states of the PIN diode. During the simulation, the unit-cell boundaries are applied in both the x and y directions to incorporate the mutual coupling effect between adjacent elements. Two Floquet ports for x-polarized waves are applied in the +z and z directions.

The simulated reflection amplitudes/phases and the corresponding far-field scattering patterns are given in Figs. 2(d) and 2(e), respectively. When the PIN diode is turned from on to off, the phase difference is approximately 180° from 6.5 to 8.5 GHz, and the corresponding amplitudes are over 0.9, which means the element can work in both the 0 and 1 states under different biasing voltages. No matter the PIN diode is switched on or off, the scattering wave from the metaatom under normal incidence is always restricted on both sides of the normal direction as illustrated in Fig. 3(e), and the total scattering waves from the metasurface are the superposition of those from the composing elements. Therefore, it is easy to find that the field intensity along the normal direction of the metasurface is the largest.

To illustrate the independent manipulations of the EM waves at both the fundamental and higher-order harmonics, a space-time digital metasurface is encoded to realize the two symmetric beams at the fundamental frequency, and an OAM beam at the ±1st order harmonics. Here, we need to remark that if we want to get an OAM beam with the topological number l=+1 for the 1st order harmonic, another OAM beam with the topological number l=1 is also achieved at the 1st order harmonic, which can be explained from Eq. (5). When the initial phase φA and the parameter φpq*k are fixed, it will cause different influences on the ±1st order harmonics by changing the time delay t1. In other words, if the time delay t1 is increased, the 1 st harmonic phase is increased as well, while the 1st harmonic phase is decreased with the same degree, giving rise to the opposite topological number as a result.

The space-time digital metasurface consists of 24×24 metaatoms, which are specifically divided into the eight regions [marked from 1# to 8#, in Fig. 4(a)] with the same coding sequences Γm, but different combination values (ω0t1, φA). For the fixed coding sequences Γm 000011111111, φpq*k can be calculated as 180°, 60°, and 60° for the 0th, 1st and 1st order harmonics, respectively, from Eq. (3) and Fig. 2(a). From Eq. (5), the phase at the fundamental frequency can be adjusted by the initial phase φA, and the different harmonic phases can be obtained by changing the time delay t1 at the ±1st order harmonics.

 

Fig. 4. (a) Required phase distributions of the different harmonics. (b) The corresponding far-field scattering patterns. (c), (d) Near-field amplitude and phase distributions for the 1st, 0th, and 1st order harmonics.

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As shown in Fig. 4(a), to achieve two split beams [1921] at the fundamental frequency, the element phases φpq0 are 0° in the left half part (regions 1#4#), but 180° in the right half (regions 5#8#). In addition, to realize an OAM beam with the topological number l=1 at the 1st order harmonic, the phase distribution of φpq1 is shown in Fig. 4(a), which is gradually increased by a step of 45° from region 1# to the region 8#. Substituting φpq0, φpq1, φpq*0, φpq*1, and φpq*1 into Eq. (5), the values of ω0t1 and φpq1 in the eight regions are obtained, as listed in Table 1. Note that the phase profile of the 1st order harmonic is just opposite to that of the 1st order harmonic, as demonstrated in Table 1, leading to the OAM beams with the opposite topological numbers.

Tables Icon

Table 1. Combination Values (ω0t1, φA) and Calculated Harmonic Phases in the Eight Zones of the Metasurface

The far-field scattering pattern of the space-time digital metasurface at the mth order harmonic can be written as [47]

Fm(θ,φ)=p=1Nq=1McpqmEpq(θ,φ)exp(j2πλc)exp[(p1)dxsinθcosφ+(q1)dysinθsinφ],
where Epq(θ,φ) is the far-field scattering pattern of the element (p, q) at the fundamental frequency. θ and φ are the elevation and azimuth angles, respectively. dx and dy are the element periods along the x and y directions, respectively. λc is the wavelength of the fundamental frequency. cpqm is the complex Fourier coefficient of the periodic reflectivity Γpq(t) at the mth order harmonic. In the ideal theoretical model, the mutual coupling between the coding elements is ignored, and the coding elements are isotropic [i.e., Epq(θ,φ)=1]. The fundamental and modulation frequencies are fc=7GHz and f0=10kHz, respectively.

From the phase distributions listed in Table 1, the far-field scattering patterns under normal incidence are calculated by Eq. (6) for the different harmonics, as shown in Fig. 4(b). In Fig. 4(b), two symmetric beams at the fundamental frequency, and the vortex beams with hollow intensity at the ±1st order harmonics are generated. To show more details of the harmonic wavefronts, the near-field distributions at the observation plane (located at 1200 mm in front of the metasurface) are calculated and shown in Figs. 4(c) and 4(d). Typical intensity profiles with a hollow center, and spiral phase profiles with different rotation directions can be clearly recognized at the ±1st order harmonics. Besides this, the characteristics of dual beams at the fundamental frequency can also be observed. The calculated profiles for both far and near fields again demonstrate the great potential of the metasurface for nonlinear wavefront controls.

3. EXPERIMENT AND DISCUSSION

To validate the theoretical model, the proposed space-time digital metasurface is fabricated as shown in Figs. 5(a) and 5(b), which is divided into eight regions. The biasing voltages of the eight regions are independently supplied, where the metaatoms in each region share the same voltage during the experiment. An FPGA control board (Artix-7) is employed to provide dynamic biasing voltages for the PIN diodes of the metaatoms. At first, the reflection coefficients of the metasurface are measured via the vector network analyzer (VNA, Agilent N5230C) in an anechoic chamber.

 

Fig. 5. (a) Front view and (b) back view of the proposed space-time digital coding metasurface. (c) Measured reflection spectra for the on and off states of the PIN diodes. (d) Measured harmonic amplitude distributions under two coding sequences 111100000000 and 000011111111, respectively.

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In the first experiment, all the metaatoms are turned on or off simultaneously to measure the reflection amplitudes and phases of 0 and 1 states, as shown in Fig. 5(c). At 7 GHz, the measured amplitudes and phases of the metasurface are approximately 0.7 and 100°, and 0.84 and 260° for the on and off states of the PIN diodes, respectively. The measured phase difference between the two states is 200°, which is slightly greater than the desired 180° in theory.

In the second experiment, the reflection spectra under the periodic phase modulation are measured, where two standard horn antennas are employed to transmit and receive signals. One antenna is connected to a microwave signal generator (Keysight E8267D), which provides the excitation signal at 7 GHz. Another horn antenna is used to receive the harmonic scattered signals via a spectrum analyzer (Keysight E4447A). The control circuit is programmed to generate square-wave control signals with the desired biasing voltages, periods, and time delays. The modulation period T of the coding sequences is 100 μs with the modulation frequency f0=10kHz.

Two cases are considered in the experiment, in which the basic coding sequence is 000011111111. The initial phase φA is selected as 0° for the case 1, and 180° for the case 2, leading to the changed coding sequence 111100000000 in the case 2. The measured amplitude spectra in the two cases are shown in Fig. 5(d). From Eq. (2), the amplitude spectra should not be affected by the change of φA. In Fig. 5(d), the harmonic amplitudes are nearly equal except at the fundamental frequency. This can be ascribed to phase deviations of the metaatoms from their ideal values under different biasing voltages, stemming primarily from the parasitic parameters of the PIN diode, the fabrication tolerance, and the distortion of the control signal.

In the third experiment, the near-field distributions of harmonic waves are monitored with a home-built platform in the microwave anechoic chamber. This is a huge challenge because the traditional mapping apparatus has difficulty acquiring the near fields when the transmitting and receiving frequencies are different. To solve this problem, a novel experimental platform was developed in this work, as depicted in Fig. 6(a). In contrast to the traditional method, two coaxial probes were used to obtain the relative values of the phase and amplitude simultaneously. One was used as the reference probe to provide a reference electric field at the fixed position of the detection plane. The other one can scan the near fields at different positions of the detection plane, whose movement was controlled by a stepping motor. The excitation signal is emitted from a horn antenna connected to the signal generator. Meanwhile, the receiving ends of the two probes are connected to a two-port VNA. Moreover, a phase-locked loop is used to ensure that the VNA and the signal generator are synchronized. The VNA can compare the signals from the two probes. Hence, the near-field distributions can be extracted directly from the amplitude and phase ratios.

 

Fig. 6. (a) Schematic of the experimental setup for measuring the harmonic near-field distributions. (b) Photograph of the nonlinear near-field experiment environment. (c) The coaxial probe for near-field detection. (d) The waveguide antenna as the excitation of the metasurface. (e), (f) Measured amplitude and phase distributions of the fundamental and ±1st order harmonics.

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The experiment configuration of the nonlinear near field mapping system is shown in Fig. 6(b). The excitation antenna is placed at a distance of 700 mm above the metasurface. The coaxial probe is shown in Fig. 6(c). The scanning plane is located at 1200 mm away from the metasurface, with a scan range of 800mm×400mm (scanning step: 20 mm). The eight regions of the metasurface can be independently controlled by the FPGA control board. The initial coding sequence was 000011111111 with the modulation frequency f0=10kHz, which corresponds to the combination of values ω0t1=0° and φA=0°. When ω0t1=0° and φA=180°, the coding sequence is changed to 111100000000.

Figures 6(e) and 6(f) illustrate the measured harmonic magnitude/phase distributions of the electric fields where φA and ω0t1 are listed in Table 1. As expected by the theoretical analysis, the typical intensity profiles with a hollow center, and the spiral phase profiles with different rotation directions can be clearly observed in Figs. 6(e) and 6(f), indicating the generation of OAM beams with the topological number l=±1 for ±1st order harmonics. The measured distributions at fundamental frequency are different from the calculated results, which can be ascribed to the huge gap of intensity between the case 1 and case 2 in Fig. 5(d).

There are two main factors responsible for the deviation between the calculated and measured results. (1) The calculated near-field patterns in Figs. 4(c) and 4(d) are obtained under the incidence of plane wave, and the harmonic phases along the metasurface can be accurately determined. However, in the experiment, the feeding source is a waveguide antenna, and it is not a strictly plane wave when arriving at the metasurface. Therefore, the harmonic phase profile is disturbed which may cause the opposite influence on the generations of OAM beams at different harmonics. (2) The measurement of harmonic amplitudes and phases is a great challenge in our experiment. First, the harmonic amplitudes are minimal, and they cannot be directly measured by the VNA. The amplitude/phase comparison method is adopted to solve this problem where a comparing probe is introduced near the detection plane. The coaxial probe with omnidirectional pattern has low efficiency to obtain the harmonic energies. Besides, the slight vibration of the probe during the movement can also affect the measurement accuracy. (3) Other factors, including parasitic parameters of the PIN diodes, the distortions of the control signals, the fabrication tolerances can also lead to the deviations of the harmonic intensities and phase distributions under the time-varying reflectivity. Nevertheless, from the measured and simulated results, we can still conclude that the time-domain metasurface can manipulate the wavefronts at the fundamental and high-order harmonics independently.

4. CONCLUSIONS

In this paper, we propose a space-time digital metasurface to realize near-field manipulations of the fundamental and ±1st order harmonics. Under the normal incidence of a plane wave, the metasurface can generate two symmetric beams at fundamental frequency, and two OAM beams with the topological number l=±1 at the ±1st order harmonics simultaneously. A novel experimental platform for nonlinear field mapping is developed to measure the harmonic near fields of the space-time digital metasurface. Although our experiments are conducted at microwave frequencies, the approach can be further extended into the THz and visible regimes by incorporating advanced modulation technologies.

Funding

111 Project (111-2-05); National Natural Science Foundation of China (11227904, 61722106, 61731010); National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700203, 2018YFA0701904).

Disclosures

The authors declare no conflicts of interest.

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35. M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019). [CrossRef]  

36. J. Zhao, Q. Cheng, J. Chen, M. Q. Qi, W. X. Jiang, and T. J. Cui, “A tunable metamaterial absorber using varactor diodes,” New J. Phys. 15, 043049 (2013). [CrossRef]  

37. Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019). [CrossRef]  

38. Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019). [CrossRef]  

39. G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018). [CrossRef]  

40. S. V. Hum and J. Carrier, “Reconfigurable reflectarrays and array lenses for dynamic antenna beam control: a review,” IEEE Trans. Antennas Propag. 62, 183–198 (2014). [CrossRef]  

41. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012). [CrossRef]  

42. A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015). [CrossRef]  

43. G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015). [CrossRef]  

44. E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016). [CrossRef]  

45. G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017). [CrossRef]  

46. J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018). [CrossRef]  

47. L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018). [CrossRef]  

48. L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019). [CrossRef]  

49. J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018). [CrossRef]  

50. J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021). [CrossRef]  

51. J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020). [CrossRef]  

52. https://www.skyworksinc.com.

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    [Crossref]
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    [Crossref]
  50. J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
    [Crossref]
  51. J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
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  52. https://www.skyworksinc.com .

2021 (2)

J. W. Wu, Z. X. Wang, Q. Cheng, and T. J. Cui, “Anisotropic metasurface holography in 3D space with high resolution and efficiency,” IEEE Trans. Antennas Propag. 69, 302–316 (2021).
[Crossref]

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

2020 (3)

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
[Crossref]

C. Zhang, J. Gao, X. Cao, S. J. Li, H. H. Yang, and L. Li, “Multifunction tunable metasurface for entire-space electromagnetic wave manipulation,” IEEE Trans. Antennas Propag. 68, 3301–3306 (2020).
[Crossref]

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

2019 (6)

J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
[Crossref]

T. J. Cui, S. Liu, G. D. Bai, and Q. Ma, “Direct transmission of digital message via programmable coding metasurface,” Research 2019, 2584509 (2019).
[Crossref]

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019).
[Crossref]

2018 (8)

G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
[Crossref]

J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018).
[Crossref]

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

F. Ding, R. Deshpande, and S. I. Bozhevolnyi, “Bifunctional gap-plasmon metasurfaces for visible light: polarization-controlled unidirectional surface plasmon excitation and beam steering at normal incidence,” Light Sci. Appl. 7, 17178 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
[Crossref]

2017 (7)

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
[Crossref]

J. Ding, S. S. An, B. W. Zhang, and H. L. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta‐atoms:toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1700079 (2017).
[Crossref]

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

Z. Tao, X. Wan, B. C. Pan, and T. J. Cui, “Reconfigurable conversions of reflection, transmission, and polarization states using active metasurface,” Appl. Phys. Lett. 110, 121901 (2017).
[Crossref]

C. Huang, C. L. Zhang, J. Yang, B. Sun, B. Zhao, and X. G. Luo, “Reconfigurable metasurface for multifunctional control of electromagnetic waves,” Adv. Opt. Mater. 5, 1700485 (2017).
[Crossref]

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

2016 (2)

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[Crossref]

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (2016).
[Crossref]

2015 (6)

G. Rosenblatt and O. Meir, “Perfect lensing by a single interface: defying loss and bandwidth limitations of metamaterials,” Phys. Rev. Lett. 115, 195504 (2015).
[Crossref]

A. Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[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, e324 (2015).
[Crossref]

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
[Crossref]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

2014 (5)

S. V. Hum and J. Carrier, “Reconfigurable reflectarrays and array lenses for dynamic antenna beam control: a review,” IEEE Trans. Antennas Propag. 62, 183–198 (2014).
[Crossref]

C. D. Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (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, e218 (2014).
[Crossref]

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photon. Rev. 8, 757–765 (2014).
[Crossref]

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

2013 (5)

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61, 4615–4623 (2013).
[Crossref]

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).
[Crossref]

J. Zhao, Q. Cheng, J. Chen, M. Q. Qi, W. X. Jiang, and T. J. Cui, “A tunable metamaterial absorber using varactor diodes,” New J. Phys. 15, 043049 (2013).
[Crossref]

2012 (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

2011 (1)

N. F. 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, 333–337 (2011).
[Crossref]

2010 (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[Crossref]

2009 (1)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

2008 (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

Aieta, F.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

N. F. 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, 333–337 (2011).
[Crossref]

Almeida, E.

E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
[Crossref]

Alu, A.

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

An, S. S.

J. Ding, S. S. An, B. W. Zhang, and H. L. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta‐atoms:toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1700079 (2017).
[Crossref]

Bagheri, M.

A. Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref]

Bai, B. F.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]

Bai, G. D.

M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019).
[Crossref]

T. J. Cui, S. Liu, G. D. Bai, and Q. Ma, “Direct transmission of digital message via programmable coding metasurface,” Research 2019, 2584509 (2019).
[Crossref]

G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
[Crossref]

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

Bai, L.

G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
[Crossref]

Bao, D.

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref]

Bo, X. C.

J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
[Crossref]

Bo Li, Y.

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

Bozhevolnyi, S. I.

F. Ding, R. Deshpande, and S. I. Bozhevolnyi, “Bifunctional gap-plasmon metasurfaces for visible light: polarization-controlled unidirectional surface plasmon excitation and beam steering at normal incidence,” Light Sci. Appl. 7, 17178 (2018).
[Crossref]

Bykov, A. Y.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
[Crossref]

Cao, J.

D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
[Crossref]

Cao, X.

C. Zhang, J. Gao, X. Cao, S. J. Li, H. H. Yang, and L. Li, “Multifunction tunable metasurface for entire-space electromagnetic wave manipulation,” IEEE Trans. Antennas Propag. 68, 3301–3306 (2020).
[Crossref]

Capasso, F.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
[Crossref]

N. F. 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, 333–337 (2011).
[Crossref]

Carrier, J.

S. V. Hum and J. Carrier, “Reconfigurable reflectarrays and array lenses for dynamic antenna beam control: a review,” IEEE Trans. Antennas Propag. 62, 183–198 (2014).
[Crossref]

Castaldi, G.

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

Cheah, K. W.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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.

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (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, e324 (2015).
[Crossref]

Chen, J.

J. Zhao, Q. Cheng, J. Chen, M. Q. Qi, W. X. Jiang, and T. J. Cui, “A tunable metamaterial absorber using varactor diodes,” New J. Phys. 15, 043049 (2013).
[Crossref]

Chen, M. Z.

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
[Crossref]

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

Chen, S.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

Chen, S. M.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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. Q.

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

Chen, X. Z.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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, Z. H.

D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
[Crossref]

Cheng, Q.

J. W. Wu, Z. X. Wang, Q. Cheng, and T. J. Cui, “Anisotropic metasurface holography in 3D space with high resolution and efficiency,” IEEE Trans. Antennas Propag. 69, 302–316 (2021).
[Crossref]

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
[Crossref]

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
[Crossref]

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (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, 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, e218 (2014).
[Crossref]

J. Zhao, Q. Cheng, J. Chen, M. Q. Qi, W. X. Jiang, and T. J. Cui, “A tunable metamaterial absorber using varactor diodes,” New J. Phys. 15, 043049 (2013).
[Crossref]

Cheung, S. W.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61, 4615–4623 (2013).
[Crossref]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Chung, K. L.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61, 4615–4623 (2013).
[Crossref]

Cui, T. J.

J. W. Wu, Z. X. Wang, Q. Cheng, and T. J. Cui, “Anisotropic metasurface holography in 3D space with high resolution and efficiency,” IEEE Trans. Antennas Propag. 69, 302–316 (2021).
[Crossref]

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
[Crossref]

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
[Crossref]

T. J. Cui, S. Liu, G. D. Bai, and Q. Ma, “Direct transmission of digital message via programmable coding metasurface,” Research 2019, 2584509 (2019).
[Crossref]

M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019).
[Crossref]

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

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J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
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J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

Li, Y. B.

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

Liang, J. C.

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[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, e324 (2015).
[Crossref]

Liu, J. F.

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

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L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Liu, S.

T. J. Cui, S. Liu, G. D. Bai, and Q. Ma, “Direct transmission of digital message via programmable coding metasurface,” Research 2019, 2584509 (2019).
[Crossref]

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
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L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (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, e324 (2015).
[Crossref]

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J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[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, e324 (2015).
[Crossref]

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J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
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C. Huang, C. L. Zhang, J. Yang, B. Sun, B. Zhao, and X. G. Luo, “Reconfigurable metasurface for multifunctional control of electromagnetic waves,” Adv. Opt. Mater. 5, 1700485 (2017).
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X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photon. Rev. 8, 757–765 (2014).
[Crossref]

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Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
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Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
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Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
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J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
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J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
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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, e324 (2015).
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T. J. Cui, S. Liu, G. D. Bai, and Q. Ma, “Direct transmission of digital message via programmable coding metasurface,” Research 2019, 2584509 (2019).
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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, e324 (2015).
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J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
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J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
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G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).
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E. Almeida, G. Shalem, and Y. Prior, “Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” Nat. Commun. 7, 10367 (2016).
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L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
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X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photon. Rev. 8, 757–765 (2014).
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L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
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Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

Wen, Q. Y.

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, e324 (2015).
[Crossref]

Wong, P. W. H.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

Wu, H. T.

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Wu, J. W.

J. W. Wu, Z. X. Wang, Q. Cheng, and T. J. Cui, “Anisotropic metasurface holography in 3D space with high resolution and efficiency,” IEEE Trans. Antennas Propag. 69, 302–316 (2021).
[Crossref]

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
[Crossref]

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Wu, P. 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, e324 (2015).
[Crossref]

Wu, R. Y.

J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
[Crossref]

Wu, T. L.

D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
[Crossref]

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L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

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M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019).
[Crossref]

Yang, H. H.

C. Zhang, J. Gao, X. Cao, S. J. Li, H. H. Yang, and L. Li, “Multifunction tunable metasurface for entire-space electromagnetic wave manipulation,” IEEE Trans. Antennas Propag. 68, 3301–3306 (2020).
[Crossref]

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J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

C. Huang, C. L. Zhang, J. Yang, B. Sun, B. Zhao, and X. G. Luo, “Reconfigurable metasurface for multifunctional control of electromagnetic waves,” Adv. Opt. Mater. 5, 1700485 (2017).
[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, e324 (2015).
[Crossref]

Yang, L. X.

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

Yang, X.

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[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, e324 (2015).
[Crossref]

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D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

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N. F. 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, 333–337 (2011).
[Crossref]

Yuan, M. J.

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (2016).
[Crossref]

Yuan, W.

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

Yuk, T. I.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61, 4615–4623 (2013).
[Crossref]

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M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

Zentgraf, T.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref]

Zhang, B. W.

J. Ding, S. S. An, B. W. Zhang, and H. L. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta‐atoms:toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1700079 (2017).
[Crossref]

Zhang, C.

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
[Crossref]

C. Zhang, J. Gao, X. Cao, S. J. Li, H. H. Yang, and L. Li, “Multifunction tunable metasurface for entire-space electromagnetic wave manipulation,” IEEE Trans. Antennas Propag. 68, 3301–3306 (2020).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, W. Yuan, L. X. Yang, J. C. Ke, M. Z. Chen, A. Mahmoud, Q. Cheng, and T. J. Cui, “Tailoring polarization states of multiple beams that carry different topological charges of orbital angular momentums,” Opt. Express 26, 31664–31674 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
[Crossref]

Zhang, C. L.

C. Huang, C. L. Zhang, J. Yang, B. Sun, B. Zhao, and X. G. Luo, “Reconfigurable metasurface for multifunctional control of electromagnetic waves,” Adv. Opt. Mater. 5, 1700485 (2017).
[Crossref]

Zhang, G. X.

G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
[Crossref]

Zhang, H.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]

Zhang, H. C.

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Zhang, H. L.

J. Ding, S. S. An, B. W. Zhang, and H. L. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta‐atoms:toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1700079 (2017).
[Crossref]

Zhang, L.

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

Zhang, Q.

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

Zhang, S.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref]

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref]

Zhang, W. L.

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref]

Zhang, X. G.

Z. J. Luo, Q. Wang, X. G. Zhang, J. W. Wu, J. Y. Dai, L. Zhang, H. T. Wu, H. C. Zhang, H. F. Ma, Q. Cheng, and T. J. Cui, “Intensity-dependent metasurface with digitally reconfigurable distribution of nonlinearity,” Adv. Opt. Mater. 7, 1900792 (2019).
[Crossref]

Zhang, X. Q.

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

Zhang, Y.

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (2016).
[Crossref]

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013).
[Crossref]

Zhao, B.

C. Huang, C. L. Zhang, J. Yang, B. Sun, B. Zhao, and X. G. Luo, “Reconfigurable metasurface for multifunctional control of electromagnetic waves,” Adv. Opt. Mater. 5, 1700485 (2017).
[Crossref]

Zhao, J.

J. Zhao, X. Yang, J. Y. Dai, Q. Cheng, X. Li, N. H. Qi, J. C. Ke, G. D. Bai, S. Liu, S. Jin, A. Alu, and T. J. Cui, “Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems,” Natl. Sci. Rev. 6, 231–238 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
[Crossref]

J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
[Crossref]

L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9, 4334 (2018).
[Crossref]

J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018).
[Crossref]

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (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, 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, e218 (2014).
[Crossref]

J. Zhao, Q. Cheng, J. Chen, M. Q. Qi, W. X. Jiang, and T. J. Cui, “A tunable metamaterial absorber using varactor diodes,” New J. Phys. 15, 043049 (2013).
[Crossref]

Zhou, L.

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[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, e324 (2015).
[Crossref]

Zhou, X.

J. Zhao, Q. Cheng, X. K. Wang, M. J. Yuan, X. Zhou, X. J. Fu, M. Q. Qi, S. Liu, H. B. Chen, Y. Zhang, and T. J. Cui, “Controlling the bandwidth of terahertz low-scattering metasurfaces,” Adv. Opt. Mater. 4, 1773–1779 (2016).
[Crossref]

Zhou, X. Y.

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

Zhu, H. L.

H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antennas Propag. 61, 4615–4623 (2013).
[Crossref]

Adv. Funct. Mater. (2)

J. W. Wu, Z. X. Wang, Z. Q. Fang, J. C. Liang, X. Fu, J. F. Liu, H. T. Wu, D. Bao, L. Miao, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces,” Adv. Funct. Mater. 30, 2004144 (2020).
[Crossref]

Z. J. Luo, M. Z. Chen, Z. X. Wang, L. Zhou, Y. B. Li, Q. Cheng, H. F. Ma, and T. J. Cui, “Digital nonlinear metasurface with customizable nonreciprocity,” Adv. Funct. Mater. 29, 1906635 (2019).
[Crossref]

Adv. Mater. (2)

L. Zhang, X. Q. Chen, R. W. Shao, J. Y. Dai, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Breaking reciprocity with space‐time‐coding digital metasurfaces,” Adv. Mater. 31, 1904069 (2019).
[Crossref]

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

Adv. Opt. Mater. (6)

J. Ding, S. S. An, B. W. Zhang, and H. L. Zhang, “Multiwavelength metasurfaces based on single-layer dual-wavelength meta‐atoms:toward complete phase and amplitude modulations at two wavelengths,” Adv. Opt. Mater. 5, 1700079 (2017).
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D. W. Hu, J. Cao, W. Li, C. Zhang, T. L. Wu, Q. F. Li, Z. H. Chen, Y. L. Wang, and J. G. Guan, “Optically transparent broadband microwave absorption metamaterial by standing‐up closed‐ring resonators,” Adv. Opt. Mater. 5, 1700109 (2017).
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Adv. Sci. (1)

G. X. Zhang, W. X. Tang, W. X. Jiang, G. D. Bai, J. Tang, L. Bai, C. W. Qiu, and T. J. Cui, “Light‐controllable digital coding metasurfaces,” Adv. Sci. 5, 1801028 (2018).
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Appl. Phys. Lett. (3)

Z. Tao, X. Wan, B. C. Pan, and T. J. Cui, “Reconfigurable conversions of reflection, transmission, and polarization states using active metasurface,” Appl. Phys. Lett. 110, 121901 (2017).
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J. Yang, C. Zhang, H. F. Ma, J. Zhao, J. D. Dai, W. Yuan, L. X. Yang, Q. Cheng, and T. J. Cui, “Generation of radio vortex beams with designable polarization using anisotropic frequency selective surface,” Appl. Phys. Lett. 112, 203501 (2018).
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J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112, 073504 (2018).
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Appl. Phys. Rev. (1)

J. Y. Dai, J. Yang, W. Tang, M. Z. Chen, J. C. Ke, Q. Cheng, S. Jin, and T. J. Cui, “Arbitrary manipulations of dual harmonics and their wave behaviors based on space-time-coding digital metasurface,” Appl. Phys. Rev. 7, 041408 (2020).
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IEEE Trans. Antennas Propag. (5)

S. V. Hum and J. Carrier, “Reconfigurable reflectarrays and array lenses for dynamic antenna beam control: a review,” IEEE Trans. Antennas Propag. 62, 183–198 (2014).
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C. Zhang, J. Gao, X. Cao, S. J. Li, H. H. Yang, and L. Li, “Multifunction tunable metasurface for entire-space electromagnetic wave manipulation,” IEEE Trans. Antennas Propag. 68, 3301–3306 (2020).
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J. W. Wu, R. Y. Wu, X. C. Bo, X. J. Fu, and T. J. Cui, “Synthesis algorithm for near-field power pattern control and its experimental verification via metasurfaces,” IEEE Trans. Antennas Propag. 67, 1073–1083 (2019).
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J. W. Wu, Z. X. Wang, Q. Cheng, and T. J. Cui, “Anisotropic metasurface holography in 3D space with high resolution and efficiency,” IEEE Trans. Antennas Propag. 69, 302–316 (2021).
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Laser Photon. Rev. (2)

X. Wan, X. P. Shen, Y. Luo, and T. J. Cui, “Planar bifunctional Luneburg-fisheye lens made of an anisotropic metasurface,” Laser Photon. Rev. 8, 757–765 (2014).
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A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
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Light Sci. Appl. (5)

J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light Sci. Appl. 7, 90 (2018).
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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, e324 (2015).
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T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3, e218 (2014).
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M. Qian, G. D. Bai, H. B. Jing, C. Yang, L. L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light Sci. Appl. 8, 98 (2019).
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F. Ding, R. Deshpande, and S. I. Bozhevolnyi, “Bifunctional gap-plasmon metasurfaces for visible light: polarization-controlled unidirectional surface plasmon excitation and beam steering at normal incidence,” Light Sci. Appl. 7, 17178 (2018).
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Nano Lett. (1)

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
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Nat. Commun. (6)

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Small Struct. (1)

J. C. Ke, J. Y. Dai, M. Z. Chen, L. Wang, C. Zhang, W. Tang, J. Yang, W. Liu, X. Li, Y. F. Liu, Q. Cheng, S. Jin, and T. J. Cui, “Linear and nonlinear polarization syntheses and their programmable controls based on anisotropic time-domain digital coding metasurface,” Small Struct. 2, 2000060 (2021).
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Other (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the space-time digital coding metasurface, which can independently control the wavefronts of the fundamental and high-order harmonics by adjusting the phase φA, and the time delay t1 of the periodic reflectivity.
Fig. 2.
Fig. 2. Reflection amplitudes and phases of Γpq(t) in each period (left column) and the calculated reflection spectra (right column) under different combinations of φA and t1, when the coding sequence 000011111111 is employed. (a) φA=0°, t1=0, (b) φA=180°, t1=0, (c) φA=0°, t1=T/2.
Fig. 3.
Fig. 3. (a) Perspective view, (b) top view, and (c) bottom view of the metaatom. (d) The simulated reflection spectra of the metaatom under the normal incidence. (e) The scattering patterns of the metaatom for the on and off states. The geometric parameters of the metaatom are p=14, h1=0.8, h2=4, d0=0.7, x1=2, y1=4, x2=0.4, y2=0.6, x3=0.15, and x4=0.8mm.
Fig. 4.
Fig. 4. (a) Required phase distributions of the different harmonics. (b) The corresponding far-field scattering patterns. (c), (d) Near-field amplitude and phase distributions for the 1st, 0th, and 1st order harmonics.
Fig. 5.
Fig. 5. (a) Front view and (b) back view of the proposed space-time digital coding metasurface. (c) Measured reflection spectra for the on and off states of the PIN diodes. (d) Measured harmonic amplitude distributions under two coding sequences 111100000000 and 000011111111, respectively.
Fig. 6.
Fig. 6. (a) Schematic of the experimental setup for measuring the harmonic near-field distributions. (b) Photograph of the nonlinear near-field experiment environment. (c) The coaxial probe for near-field detection. (d) The waveguide antenna as the excitation of the metasurface. (e), (f) Measured amplitude and phase distributions of the fundamental and ±1st order harmonics.

Tables (1)

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Table 1. Combination Values (ω0t1, φA) and Calculated Harmonic Phases in the Eight Zones of the Metasurface

Equations (6)

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Γpq(t)=m=0M1AΓmg(tt1mτ),0<|t|<T,
cpqk=|A|exp[j(kω0t1φA)](apqk).
apqk=1MSa(kπM)ejkπMm=0M1Γnexp(jkω0mτ).
φpqk=arg(cpqk)=(kω0t1φA)+φpq*k,
φpq0=φA+φpq*0,φpq1=φAω0t1+φpq*1,φpq1=φA+ω0t1+φpq*1.
Fm(θ,φ)=p=1Nq=1McpqmEpq(θ,φ)exp(j2πλc)exp[(p1)dxsinθcosφ+(q1)dysinθsinφ],