Anomalous Refraction and Nondiffractive Bessel-Beam Generation of

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Anomalous refraction and non-diffractive Bessel beam generation of terahertz waves through transmission-type coding metasurfaces Shuo Liu, Ahsan Noor, Liang Liang Du, Lei Zhang, Quan Xu, Kang Luan, Tian Qi Wang, Zhen Tian, WenXuan Tang, Jiaguang Han, Weili Zhang, XiaoYang Zhou, Qiang Cheng, and Tie Jun Cui ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00515 • Publication Date (Web): 28 Sep 2016 Downloaded from http://pubs.acs.org on October 1, 2016

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Anomalous refraction and non-diffractive Bessel beam generation of terahertz waves through transmission-type coding metasurfaces Shuo Liu1,2, Ahsan Noor1,2, Liang Liang Du 4, Lei Zhang1,2, Quan Xu4, Kang Luan1,2, Tian Qi Wang4, Zhen Tian1,2, Wen Xuan Tang1,2, Jia Guang Han4, Wei Li Zhang3,4, Xiao Yang Zhou5, and Qiang Cheng1,3, Tie Jun Cui1,3,* 1

State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

2

Synergetic Innovation Center of Wireless Communication Technology, Southeast University, Nanjing 210096, China 3 Cooperative Innovation Centre of Terahertz Science, No.4, Section 2, North Jianshe Road, Chengdu 610054, China 4 Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China 5 Jiangsu Xuantu Technology Co., Ltd., 12 Mozhou East Road, Nanjing 211111, China * Corresponding author: E-mail: [email protected].

ABSTRACT Coding metasurfaces, composed of an array of coding particles with discrete phase responses, are encoded with pre-designed coding sequences to manipulate wavefronts of electromagnetic (EM) waves and realize novel functionalities such as the anomalous beam deflection, broadband diffusion, and polarization conversion. Such a new concept can be viewed as a bridge linking metamaterial and digital codes, yielding the investigation of metamaterials from a digital perspective, and eventually the realization of real-time controls of EM waves. Here, we propose and experimentally demonstrate a transmission-type coding metasurface to bend normally incident terahertz beam to anomalous directions and generate non-diffractive Bessel beams at normal and oblique directions. To overcome the larger reflection and strong Fabry-Perot resonance that are usually originated from the thick silicon substrate, a freestanding design is presented for the coding particle, which is formed by stacking three metallic layers with four polyimide spacers alternately. Experimental results show that the fabricated sample could bend the normally incident terahertz wave to anomalous refraction angles at 26º and 58º with 58% and 40% efficiencies, respectively. Owing to the excellent mechanical and chemical properties of polyimide, the fabricated sample is extremely flexible and endurable, implying promising applications in terahertz imaging and communication. Keywords: Terahertz, transmitarray, metasurface, free-standing, Bessel beam

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In the past twenty years, metamaterial has gradually cemented its place as an area of exciting research and drawn broad attention from the physics and engineering communities, owing to its exotic electromagnetic (EM) behaviors [1-11]. By periodically or non-periodically distributing subwavelength structures or drilling air holes on the dielectric substrate, unprecedented EM behaviors such as negative refraction [1-3], subwavelength focusing [4-6], and cloaking [7-11]can be achieved. Since both permittivity and permeability of metamaterials are artificially engineered, the contrast and distribution of refractive index are no longer limited by those attained from the natural materials, enabling the emergence of metamaterial lens antennas in both microwave and optical frequencies [12-14]. However, the wavefront control of these metamaterial-based devices still rely on the gradient phase accumulations accomplished by varying the spatial profile of the refractive index, posing serious fabrication challenges in the terahertz and optical spectra using the existing cuttingedge three-dimensional microfabrication techniques [15, 16]. Fortunately, the wavefront manipulation can also be realized by introducing abrupt phase discontinuities on an ultrathin surface, which is characterized as two-dimensional (2D) metamaterial, formally known as metasurface [17]. Due to their flat profiles and convenience of fabrication, metasurfaces have led to many practical devices such as perfect absorbers [18, 19], polarization convertors [20, 21], modulators [26, 27], and holography [28, 29]. In 2011, Yu et al. introduced the concept of generalized Snell’s law to bend light to anomalous directions by designing a linear gradient phase at an interface using V-shaped antennas [30] whose flaring angles and orientations are adjusted to obtain the 2π interfacial phase profile. Based on the similar approach and configuration (metal, insulating spacer), several designs have been demonstrated at terahertz and optical regimes to bend or focus plane waves [31, 32], create vortex beams [33], and convert propagating waves to surface waves under the normal illuminations [34]. In the conventional EM community, the reflective array and transmittive array antennas have been proposed and are widely used in the manipulation of the far-field radiation patterns [35-40]. In the reflection arrays, continuous phase changes are designed to tailor the


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reflection-type far-field patterns [31,32]. Whereas in the transmission arrays, the transmitted far fields are controlled by arranging different amplitude and phase distributions of array elements [37, 38]. The notable difference between metasurfaces and reflective/transmittive array antennas is that metasurfaces have more deeply subwavelength-scale elements and can be used to control near fields. While the the unit cell in traditional reflective/transmittive arrays have comparatively larger dimensions (over one-half of the wavelength), and are usually used for controlling the far-field radiations [35-40]. Because the aforementioned metamaterials/metasurfaces or reflection/transmission arrays are described by continuous values of effective medium parameters or phases, they can be compared to the analog circuits. Interestingly, the concept of

digital circuits was

introduced to the design of coding metamaterials, enabling coding metamaterials and digital metamaterials [41, 42]. They have led to the exploration of phenomenon like anomalous beam reflection, random diffusion and polarization conversion, etc, which were simply realized by distributing the coding particles with discrete reflection phases on a 2D surface by predesigned coding sequences [41, 43-46]. One of the benefits of coding metasurface is the digital characterization of its reflection responses, making it possible for the design of programmable metasurfaces, whose functionality are digitally controlled by the input coding sequences [41]. The other benefit is that the coding characterization of metamaterials and metasurfaces allows us to study them from a fully-digital perspective so that many existing theorems from the information science can be directly applied. Recently, coding metasurfaces have been implemented in the terahertz frequencies to realize anomalous reflections and broadband diffusions of terahertz waves [43- 45]. Furthermore, the concept of anisotropic coding metasurfaces has been proposed this year, exhibiting dual-functionalities to terahertz waves under orthogonal polarizations [47]. Here, we propose a transmission-type coding metasurface at the terahertz frequency to bend the terahertz waves anomalously and create non-diffractive Bessel beams in both normal and oblique directions. As conceptually illustrated in Figure 1a, the y-polarized normally incident terahertz wave is converted to its cross polarization and deflected to anomalous


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directions in the x-z plane. Using the coding metasurface, we can also generate the diffractionfree Bessel beams. To increase the transmission efficiency, the coding particle is designed to have three metallic layers (see Figure 1b), with each layer comprising a split-ring resonator (SRR) having different opening angles and orientations [31, 32]. The phase of transmission ranging from 0 to 2π can be obtained by adjusting the opening angle and orientation of SRRs. Although such SRRs have been reported for the anomalous refraction in previous literatures [31, 32], they are always associated with significant reflections and strong Fabry-Perot resonance because of the large thickness of the substrate [31, 32]. Therefore, it would be extremely beneficial to design a low-profile, high-efficiency, and flexible coding metasurface at terahertz frequencies that could manipulate the wavefronts of transmitted waves as effectively as the metamaterial lenses at microwave frequency. RESULTS AND DISCUSSIONS For the reflection-type coding metasurfaces proposed in previous works [41, 43-46], unity reflection was readily achieved across the 2π phase coverage by a single metallic layer due to the presence of the metallic ground sheet. However, for the gradient-phase transmit-arrays reported at terahertz and optical spectra using only a single metallic layer [30-32], it is impossible for them to obtain the 2π phase coverage together with the sufficient transmittance. Consequently, the beam bending and focusing devices implemented by such structures are typically inefficient. This limitation has been theoretically clarified in Ref. 48 stressing that the attainable amplitude of the cross-polarization is physically limited to 0.5 for a singlelayered non-magnetic metasurface. They note that by cascading three layers of metasurface, each equivalent to a sheet impedance with certain surface reactance, it is possible to realize 2π phase coverage without sacrificing the amplitude for the co-polarized transmission. Ref. 49 presents another approach for realizing arbitrary control of co-polarized wavefront using a two-layered metamaterial Huygen’s surface. However, the plane of structure has to be perpendicular to the polarization of the incident wave, which poses great challenges on fabrication at THz and optical frequencies.


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The reason for why the three-layered metasurface can be used to manipulate the copolarized transmission with arbitrary phase and amplitude [48] is because it is no longer restricted by the EM boundary condition 1+S11=S12, which foundamentally limits the attainable phase range with acceptable amplitude. Therefore, the three-layered metasurface with each metallic layer indepdendently designed can also be utilized to control the crosspolarized tranmission with a 2π phase coverage and acceptable amplitude. Here, a threemetallic-layer structure sandwiched between polyimide spacers is designed as the coding particle for the transmission-type coding metasurfaces, as presented in Figure 1b. A SRR displayed in Figure 1c with an inner radius r=40 µm and width w=10 µm is designed as the structure on each metallic layer. SRRs located on the top and bottom metallic layers are aligned along the x- and y- axes (i.e. φ=90º and 0º), respectively, while the opening of SRR on the middle layer is orientated to 45º with respected to the x- or y-axis. Similar to the mechanism of the chiral structure reported in Refs. 20 and 21, the rotational twist of three SRRs from the bottom to the top layer provides 90º linear polarization rotations for the incoming wave through the magneto-electric coupling between neighbouring metallic layers [21]. To obtain the eight distinct coding particles required by the 3-bit transmission-type coding metasurface, numerical simulations were carried out using commercial software, CST Microwave Studio, with the periodic boundary condition (PBC) and Floquet-port excitation. Figure 1d presents the phases and amplitudes of transmissions at the designed frequency 0.97 THz, in which all transmission phases are obtained on the top and bottom surfaces of the cover layer. Note that the last four coding particles having 180º phase delay to the first four coding particles are obtained by simply rotating the middle SRRs of the first four coding particles by 90º around the z-axis. It is clear from Figure 1d that the eight coding particles labeled with number ‘0’ to ‘7’ fully cover the 360º phase range with a 45º interval. The transmission amplitudes range from 0.65 to 0.76 for the eight coding particles, which exceed the theoretical upper-bound 0.5 owning to the three-metallic-layer structure. One may notice that the opening angles α of the last four coding particles are not exactly the same as the first


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four, and the amplitudes of the last four coding particles (See Figure 1f) are also different from the first four. We remark that, for the V-shaped antenna [30] and C-shaped resonator [32] proposed in previous works, the last four unit cells are obtained by rotating the entire structure of the first four unit cells by 90º. Thus, the new reflection matrix R2 can be expressed by ܴଶ = ‫ݎ‬ሺ−ߠ ሻܴଵ ‫ݎ‬ሺߠ ሻ, in which R1 is the reflection matrix for the first four unit cells, and ܿ‫ߠ ݏ݋‬ ‫ݎ‬ሺߠሻ = ቀ − ‫ߠ ݊݅ݏ‬

‫ߠ ݊݅ݏ‬ ቁ ܿ‫ߠ ݏ݋‬

(1)

is a standard 2 × 2 rotation matrix. When the rotation angle θ equals 90º, we have ܴଶ = −ܴଵ , which implies that their phases are exactly opposite and the amplitudes are equal. However, this theory should not be applied directly to our structure because only SRR in the middle layer is rotated. Here, we note that the polarization conversion originates from the chirality of the structure. Similar to the broadband circular polarizer reported in Ref. 21, the sequential rotation of the three SRRs provides a magneto-electric coupling responsible for the 90° polarization conversion. To evaluate the transmission property of the eight coding particles in broadband, we further provide the phases and amplitudes from 0.8 to 1.2THz in Figures 1e and f, respectively. It can be observed from Figure 1e that the phase difference between adjacent coding particles remains around 45º from 0.8 to 1.02THz. However, the amplitudes of coding particles ‘3’ and ‘7’ drop to 0.6 when the frequency is smaller than 0.91THz. The light-yellow area outlines the working bandwidth of the 3-bit transmission-type coding metasurface from 0.91 to 1.05THz (equivalent to 14% relative bandwidth), where the amplitudes of transmission are larger than 0.6 and phase difference between adjacent coding particles is larger than 30º. Note that a metasurface capable of controlling both amplitude and phase of terahertz wavefronts using the single-layered C-shaped structure was demonstrated previously [31]. However, the measured transmittance 0.43 was not obtained directly from the structure itself but had been normalized to the reference of a bare silicon substrate. This is primarily due to the fact that the sample was fabricated on a silicon wafer with large permittivity, which


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always results in serious impedance mismatch and Fabry-Perot resonance [31]. We remark that the amplitudes of transmission given in Figures 1d-f are obtained from the multi-layer structure itself. Such a free-standing design featuring the enhanced transmission efficiency may provide the possibility for the transmission-type coding metasurfaces to be applied in practical applications. Similar to the anomalous reflections enabled by reflection-type coding metasurfaces in previous work [41], here we demonstrate the ability of the transmission-type coding metasurfaces to refract the normally incident terahertz waves to anomalous directions with two differently graded coding sequences. The first example is a coding metasurface comprising 32×32 particles and having a graded coding sequence S1: 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7…. Time-domain solver in CST Microwave Studio was employed to simulate the electric-field distribution of the encoded metasurface under the y-polarized plane-wave illumination. Figure 2a presents the Ex-component of the electric field on the x-z cutting-plane for this design. Note that the near-field result is presented at 1.04THz, which is slightly larger than the designed frequency of 1 THz. This frequency shift is resulted from the EM coupling between adjacent coding particles having different geometries, which are not considered in the simulation of the single unit cell under infinite PBC. We clearly see that the wavefront is propagating in an oblique direction with respect to the z-axis, indicating that the y-polarized incidence is converted to its cross polarization and deflected to the anomalous direction. The direction of anomalous refraction can be observed as 21º from the far-field radiation pattern in Figure 2b, which plots the far-field radiation pattern in the x-z plane for cross-polarized component (θ-component) of the transmitted electric field. This value is highly consistent with the theoretical result (21.13º) calculated by the following equation (please refer to Ref. 47 for the derivation) ఒ

ߠ = ‫ି݊݅ݏ‬ଵ ቀ௰ቁ

(1)

in which λ and Γ are the free-space wavelength (288 µm at 1.04THz) and the gradient periodicity (800 µm), respectively. Eq. (1) predicts that the smaller periodicity of the coding


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sequence generates larger anomalous scattering angle. To evaluate the performance of the transmission-type coding metasurface in bending the normal incident terahertz waves with a larger angle, we decrease the periodicity of the coding sequence to 400µm as S2: 1 3 5 7 1 3 5 7…. The electric-field (Ex-component) distribution is shown in Figure 2c. In this case, the wavefront bends away from the surface normal with a larger refraction angle. The deflection angle can be read from the scattering plot shown in Figure 2d as 46º, which is again in accurate accordance with the theoretical prediction (46.14º). Comparing Figures 2c and d, more perturbations are inspected from the wavefront in Figure 2c, which could be attributed to the following reason. The geometrical differences between adjacent coding particles of coding sequence S2 are bigger than coding sequence S1, leading to more undesired EM couplings. Such deteriorations of the electric fields can also be verified from the radiation patterns presented in Figure 2d, where the width is broadened and transmittance is lowered, implying a smaller directivity of the refracted beam. We define the maximum amplitude of normalized transmission as the efficiency from the normal incidence to anomalous refraction, which is obtained by normalizing the transmission spectra of the coding metasurface to that of a perfect electric conductor (PEC) slab with the same dimension. It is observed from the normalized scattering patterns in Figures 2b and 2d as 72% and 58% for S1 and S2 coding sequences, respectively. The relatively lower efficiency for the S2 case is caused by the wider beam width (see the far-field scattering pattern in Figure 2d), and is essentially due to the undesired EM coupling between adjacent coding particles with different geometries. In the future work, we will focus on the suppression of such EM coupling by designing new types of coding particles to confine the electric field inside the structure instead of letting them oscillate between two neighboring structures. For the square patch coding particle proposed in the previous work [41], an effective solution is to add a metallic frame at the edge of each coding particle, which could function as a common ground for all the inside structures . Such a metallic frame will serve as an isolator for each coding particle, and could let them resonant independently without affect their neighboring ones. Furthermore, we demonstrate another important feature of the transmission-type coding


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metasurface in generating non-diffractive Bessel beams of terahertz waves in the near-field region by simply arranging the coding particles gradiently along the radial direction while constantly along the azimuthal direction, which is analytically determined by the following function: ߮ሺ‫ݔ‬, ‫ݕ‬ሻ = ݇଴ ඥ‫ ݔ‬ଶ + ‫ ݕ‬ଶ ‫ ߠ ݊݅ݏ‬+ ܽ · ‫ݔ‬

(2)

where φ(x, y) (in degree unit) is the phase distribution on the coding metasurface which can be mapped to the discrete coding digits, x and y are the distances between each coding particle to the origin in the Cartesian coordinate system, k0 is the free space wavelength, θ is the tilt angle that determines the beam shape, and a is the offset value that controls the deviation angle of the Bessel beam away from the normal axis. Based on the above function, four different Bessel-beam formers are designed and simulated in CST Microwave Studio, each of which comprises 33×33 coding particles and is illuminated by a y-polarized plane wave. As we set θ=5º and 10º while keeping a=0 degree/µm, the y-polarized incidence is converted to the x-polarization and focused in the near-field region in front of the coding metasurface, exhibiting distinctive characteristics of a Bessel beam, as can be observed from the electric-field (Ex-component) in Figures 3a and b, respectively. Both plots are simulated at 1.03 THz on the x-z cutting plane. The length of non-diffractive beam in Figure 3a is longer than that in Figure 3b due to the smaller tilt angle θ in the former case. However, the intensity of the electric field inside the non-diffractive area in Figure 3b is larger than that in Figure 3a. It can be concluded that the non-diffractive length is determined by the tilt angle θ. A less steep phase variation (i.e. small θ) can lead to longer non-diffractive length. However, the non-diffractive length cannot be designed as infinite in practical applications due to the inevitable loss of material. When we add offset values a=0.1 and 0.2 degrees/µm to the coding pattern in Figure 3b, the non-diffractive beams are rotated by certain angles around the y-axis, while the beam shape are well kept, as shown in Figures 3c and 3d, respectively. Note that such a Bessel-beam former with controllable beam direction has not been reported in the terahertz domain yet.


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To confirm the focusing effect of the Bessel beam, we provide in Figures 3e-j the amplitudes of electric-field (Ex-component) distributions on six different cutting planes (x-y plane) at z=1000, 5000, 10000, 15000, 20000, and 25000µm, respectively. For the cutting plane closer to the Bessel-beam former (see Figure 3e), the electric-field distribution is still similar to the coding pattern. Bright spots representing the non-diffractive beams can be clearly observed around the optical axis on the cutting planes z=5000 and 10000 µm, and they gradually diffuse into larger spots as z further leaves the Bessel-beam former (see Figures 3hj). The shapes of the Bessel beams on the cross sections for cases c and d are similar to the first case but will shift to the x direction with different distances, which are not given in Figure 4 for the brevity of content. Although the phase discontinuities are designed to vary along the radial direction with the same gradient that forces the normally incident plane wave to bend towards the optical axis with the same tilt angle θ, we notice that the shape of the Bessel beam on the cutting plane is gradually stretched in the y-direction when z is equal or larger than 15000 µm (Figures 3h-j), which could be explained as follows. The refracted wave expriences both TM and TE modes when it pass through the coding metasurface, and the ratio between the TM-mode and TE-mode fields varies as a function of the azimuthal angle of the Bessel-beam former. The wave transmitting through the coding metasurface at exactly the x- or y-axis is strictly a TM or TE mode, respectively. It has been shown by numerical simulations (not shown in this manuscript) that there are some differences in the electric-field distributions as well as on the far-field radiations for these two modes, which could result in such asymmetrical beam shapes on the cross section. We should note that an all-dielectric metasurface was recently proposed at THz frequency to generate Bessel beams and vortex beams [50]. They have experimentally realized a high-efficiency all-dielectric single-layer metasurface which operates in reflection mode with the characteristics of a magnetic mirror in the THz band. Ownning to the silicon cube structure and the semi-infinite fused silica substrate with negligible loss, the all-dielectric metasurface can provide full range control by the simultaneous excitation of electric and magnetic dipoles. It is shown that the normal incidence, wtih either polarization, can be reflected to the direction of 15° with copoarlized reflectance of 0.75, and focused as a Bessel beam with a focal depth longer than 27λ,


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which is similar to the result in Figures 2b and 3b, respectively. Considering the fact that it is usually more difficult to design a tranmission-type structure with full-phase control and hightransmission amplitude, and it is more convenient to feed the transmission type coding metasurface than the reflection type, we believe our work can make a significant contribution to the THz field. To experimentally validate the proposed transmission-type coding metasurface, we fabricated two samples encoded with the same gradient coding sequences as those in Figures 2a and b. The photos of the samples fabricated on the flexible polyimide are presented in Figure 4a, in which each sample includes 96×96 coding particles, covering an area of 9.6×9.6 mm2. It is noteworthy that the fabricated sample can be bent, twisted and even conformed with the conventional lenses or other devices owning to the flexible nature of the polyimide. Hence the novel designs could tailor the terahertz wavefronts by both object geometry and abrupt phase changes induced on the coding metasurface. In addition, the cover polyimide layers could protect the outer metallic pattern against scratches and chemicals in practical applications. Figure 4b presents the microscopy photograph (VHX-5000, Keyence Company, Beijing, China) of the sample, in which the metallic structures on the middle and bottom layers are difficult to be identified because they overlap each other in the top view. To characterize the beam bending performance of the fabricated sample, we performed the farfield in-plane scanning measurement with a rotary terahertz time-domain system (THz-TDS), as illustrated in Figures 4c and d. Figures 5a and b present the measured amplitudes of transmission spectra from 0.4 to 1.8 THz, which are measured every 3° in the range from 0º to 78º for the samples encoded with coding sequences S1 and S2, respectively. Inspecting Figure 5a, we find an obvious transmission peak from 0.8 to 1.2THz in the angle range from 20º to 32º, which shifts to smaller angles as the frequency increases. The analytically predicted curves for the anomalous refraction angle at different frequencies are indicated by yellow dots in Figures 5a and b for coding sequences S1 and S2, respectively. It can be found that the measured transmission peak is about 5º larger than the theoretical prediction. We also notice that the transmission


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amplitude decreases dramatically outside the above frequency range because the coding particles no longer provide sufficient transmittances and the required phases at those frequencies. Figure 5c presents the transmission amplitudes extracted at different frequencies (marked by the green lines) in Figure 5a. At the designed frequency 1.04THz, the transmission rises to the maximum value 0.58 at the receiving angle 26º. The lower measured transmittance and the discrepancy between simulated and measured refracted angles could be attributed to the following reasons. First, the averaging effect of the electric field measured across the large aperture of the receiving antenna results in a wider beam width, and consequently lowers the intensity of the transmission peak. Second, we should note that the terahertz wave incident on the sample in the experiment should not be considered as an ideal plane wave. In fact, due to focusing effect by the lens mounted in front of the antenna, the shape of the wavefront was deformed to be either convex or concave when it reaches the surface of the sample. It can be theoretically predicted that the beam width of the main lobe will be broadened, and the intensity will be decreased, under the convex or concave wavefronts of the illumination. In addition, the fabrication tolerance on the dimension of metallic structure and higher loss of the polyimide might also contribute to the discrepancy between the measured and simulated transmittances. For the coding sequence S2 that has shorter periodicity, the transmission peak appears at a larger range of angles from 43º to 66º, which are about 8º larger than the theoretical value marked by the yellow dots. Similar to the S1 case, the transmittance plunges down for frequencies over 1.2 THz. There is also no anomalous transmission below 0.75THz because the wavelength for the said frequency range is larger than the periodicity of the gradient coding sequence, under which condition the normally incident propagating wave in free space be converted to a surface wave [34]. Figure 5d shows the curves of the transmission from 0º to 70º extracted from the five green lines in Figure 2b. At the designed frequency 1.04THz, the transmission amplitude can be read as 0.40 at the center of the peak 54º. Although the measured transmission amplitude is lower than the simulation, we remark that it is substantially higher than that in previous work [31].


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CONCLUSIONS We have experimentally demonstrated a transmission-type coding metasurface at terahertz frequency, which are capable of diffracting the normally incident waves to anomalous directions and generating Bessel beams. Two free-standing samples encoded with different gradient coding sequences were fabricated and measured using a rotary THz-TDS, and the measured results demonstrated that the normally incident terahertz waves were converted to cross-polarization and refracted to 26º and 54º directions with 58% and 40% efficiencies, respectively. We have also conducted the numerical simulations for the Bessel-beam former, which showed excellent performance in focusing the plane terahertz waves to non-diffractive beams to both normal and oblique directions. The free-standing design grants the proposed transmission-type coding metasurfaces with great potential in controlling EM fields without the disadvantages like excessive loss, bulky volume, and fabrication challenges that are commonly associated with threedimensional metamaterials. We remark that the free-standing samples are also free from the serious impedance mismatch and Fabry-Perot resonance, which have prevented those thick substrates samples from real applications. Moreover, the flexible and ultrathin natures of this design make it easy to be bent or twisted, and therefore extend its application scope in current terahertz systems. For instance, it will enable the dual manipulations of the phase front through both the spatial phase accumulation (curved shape) and abrupt phase change (coding metasurface). One of the most desireble devices for the current terahertz system is a spatial light modulator that could actively manipulate the wavefronts of transmitted terahertz waves. In the future work, we could design a transmission-type programmable metasurface by using doped silicon or GaAs [51] to implement the real-time beam steering, Bessel beam scanning, and other manipulations of terahertz radiation for applications such as imaging and communications. Furthermore, by designing a gradient coding sequence along the azimuthal direction, the transmission-type coding metasurface could be utilized to generate orbital angular momentum to enhance the transmission rate in wireless communication systems [52].


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METHODS Sample fabrication. Two main procedures, the preparation of polyimide layers and a standard lift-off process, were included in the fabrication of the flexible sample of the transmission-type coding metasurface. The first step was to spin-coat a 5µm-thick polyimide layer (the bottom cover) on a 2-inch silicon wafer (400µm thick, n-type, resistivity ρ=36Ω·cm), served as a temporary carrier substrate, followed by a curing process on a hot plate at 80, 120, 180, and 250ºC for 5, 5, 5, and 20 minutes, respectively, to help solidify the liquid polyimide (Yi Dun New Materials Co. Ltd, Suzhou) into the thin film. The second step was to define the metallic pattern on the polyimide layer by a standard lift-off process, which mainly includes a photolithography process to generate the photoresist pattern, a deposition of Ti/Au layer (10/180nm) by electron-beam evaporation and a lift-off operation in acetone to enable the final metallic pattern (bottom layer). The rest of the polyimide layers and metallic patterns were created by repeating the aforementioned steps in sequence. Note that in each spincoating process, the maximum thickness we could make was about 13.3µm. Therefore, it had to be repeated three times to generate the middle polyimide spacer with 40µm thickness. After finishing all the required polyimide layers and metallic patterns, we immerse the sample in pure hydrofluoric acid (HF concentration>40%) solvent for about 1 hour and the free-standing sample was mechanically scored around its edge with a knife to aid in the release from the silicon substrate. Note that a total number of nine different samples were fabricated on the 2inch silicon wafer (See Figure 4a), which includes the Bessel-beam former. However, because current measurement condition does not support the near-field measurement to map the shape of Bessel beam, only the two samples encoded with gradient cooing sequences were measured. Experimental setup. The experimental setup of the 4-f fiber-based rotary THz-TDS for the measurement of anomalous transmission is schematically illustrated in Figure 4c. Here, a fiber-based terahertz photoconductive antenna (TR4100-RX1, API Advanced Photonix, Inc.), optically excited by a commercial ultrafast erbium fiber laser system (T-Gauge, API Advanced Photonix, Inc.), was fixed on the optical stabilization platform to generate a vertically polarized terahertz wave. The effective aperture radius of the terahertz wave


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focused at the sample was roughly measured to be 5 mm at 1 THz. Another same antenna was mounted on a rotary stage that could rotate around the holder where the sample was attached (See Figure 4d), from 0º to 78º with high precision to receive the horizontal polarized THz wave refracted by the sample. Note that the position of the round hole on the sample holder where the sample was attached was designed at the exact center of the rotary stage. We record the direction transmission (at 0º receiving angle) as the reference signal when both the transmitting and receiving antennas were vertically polarized. The 2D plots of the transmission amplitude in Figures 5a and b were obtained by making a data smooth treatment and a data interpolation to the originally measured data at discrete angles. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Note The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (61138001, 61302018, 61401089, 61401091, 61571117, 61501112, 61501117), National Instrumentation Program (2013YQ200647), and 111 Project (111-2-05).

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Figure 1 The designed transmission-type coding metasurface and transmission coefficients of each constituent particles. (a) Conceptual illustration of the transmission-type coding metasurface to refract the normal incidence to anomalous direction with cross-polarization conversion. (b) Perspective view of the coding particle composed by staking three metallic layers and four polyimide layers alternately. The thickness of the two inner polyimide layers (spacer layer) and two outer polyimide layers (cover layers) are d1=40 µm and d2=5 µm, respectively. (c) The structure of SRR on each metallic layer with lattice constant L= 100 µm. The geometrical parameters α/φ for the coding particle from ‘0’ to ‘7’ are optimized as 30º/45º, 50º/45º, 68º/45º, 90º/45º, 30º/135º, 49.5º/135º, 67.5º/135º and 87º/135º respectively. (d) The simulated amplitudes and phases of transmission for the eight coding particles at 0.97 THz. (e,f) The broadband performance of the phases and amplitudes of transmission for the eight coding particles from 0.8 to 1.2 THz, respectively. The yellow area in each plot outlines the frequency range where the amplitudes are larger than 0.6 and phase differences between adjacent coding particles are larger than 30º.

Figure 2 Simulated electric-field distributions and far-field radiation patterns for the beam bending performance. (a, c) The electric field distributions in the x-z plane for the coding metasurfaces encoded with coding sequences S1 and S2, respectively, under the y-polarized normal incidence. (b, d) The 2D farfield radiation patterns in the x-z plane that correspond to (a) and (c), respectively.


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Figure 3 Simulated electric-field distributions for the Bessel-beam formers. (a, b) The electric-field distributions in the x-z plane of the non-diffractive beams generated at normal direction with tilt angle θ set as 5º and 10º (keeping a as 0 degree/µm), respectively. (c, d) The electric-field distributions in the x-z plane of the non-diffractive beams generated at oblique directions as we set a as 0.1 degrees/µm and 0.2 degreesµm (θ=10º), respectively. (e-j) The amplitude of electric-field distributions on the cross sections of the Bessel beam at z=1000, 5000, 10000, 15000, 20000 and 25000µm, respectively. The obvious black circle in each plot represents the first zero of Bessel beam.

Figure 4 The fabricated samples and experimental setup. (a) The photograph of the free-standing samples including nine different coding patterns. (b) The microscopy image of the fabricated sample. Only a small part of the metallic structures on the bottom and middle layers are visible in the image due to the blockage of the first metallic layer. (c, d) The schematic and photograph of the rotary THz-TDS to measure the refracted terahertz wave from 0º to 78º in the horizontal plane. Since the coding metasurface converts the vertically polarized incidence to anomalous refraction with horizontal polarization, the polarizations of the transmitting and receiving antennas were adjusted accordingly in the experiment.

Figure 5

Experimentally obtained amplitudes of refraction for two samples encoded with different

gradient coding sequences. (a,b) The amplitudes of transmission spectra measured from 0º to 78º, for samples S1 and S2, respectively. The yellows dots mark the theoretically calculated directions of the refracted beam. (c,d) The measured amplitudes of transmission with respect to receiving angles extracted at five different frequencies (the green lines) from (a) and (b), respectively. For (c) and (d) at the designed frequency 1.04 THz, the normal incidences are converted to cross-polarization and refracted to 26º and 54º directions with 58% and 40% efficiencies, respectively.


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For Table of Contents Use Only Anomalous refraction and non-diffractive Bessel beam generation of terahertz waves through transmission-type coding metasurfaces Shuo Liu1,2, Ahsan Noor1,2, Liang Liang Du 4, Lei Zhang1,2, Quan Xu4, Kang Luan1,2, Tian Qi Wang4, Zhen Tian1,2, Wen Xuan Tang1,2, Jia Guang Han4, Wei Li Zhang3,4, Xiao Yang Zhou5, and Qiang Cheng1,3, Tie Jun Cui1,3,*

Brief synopsis: A transmission-type coding metamaterial composed of three layers of metallic split-rings with different orientations is presented in the terahertz frequency to realize anomalous refractions and Bessel beam generations with cross polarizations. Experimental results show that the normally incident terahertz wave is bent to 26º and 54º directions with efficiencies of 58% and 40%, respectively. The free-standing design makes it possible to realize high-efficiency and flexible devices for controlling terahertz waves without the disadvantages of excessive loss, Fabry-Perot resonance, and fragility, which are commonly associated with the previous designs fabricated on thick silicon or sapphire substrates. Moreover, the inner metallic structures are fully protected from mechanical scratches and chemical corrosion due to the insulation of polyimide layers covering on the bottom and top sides


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Figure 1 The designed transmission-type coding metasurface and transmission coefficients of each constituent particles. 169x213mm (300 x 300 DPI)


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Figure 2 Simulated electric-field distributions and far-field radiation patterns for the beam bending performance. 189x126mm (300 x 300 DPI)


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Figure 3 Simulated electric-field distributions for the Bessel-beam formers. 193x214mm (300 x 300 DPI)


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Figure 4 The fabricated samples and experimental setup. (a) The photograph of the free-standing samples including nine different coding patterns. 269x208mm (300 x 300 DPI)


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Figure 5 Experimentally obtained amplitudes of refraction for two samples encoded with different gradient coding sequences. 248x187mm (300 x 300 DPI)


Anomalous Refraction and Nondiffractive Bessel-Beam Generation of

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