Full-State Controls of Terahertz Waves Using Tensor Coding

Subscriber access provided by Nanyang Technological Univ

Article

Full-State Controls of Terahertz Waves Using Tensor Coding Metasurfaces Shuo Liu, Hao Chi Zhang, Lei Zhang, Quan Long Yang, Quan Xu, Jian Qiang Gu, Yan Yang, XiaoYang Zhou, Jiaguang Han, Qiang Cheng, Weili Zhang, and Tie Jun Cui ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 05 Jun 2017 Downloaded from http://pubs.acs.org on June 5, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Applied Materials & Interfaces is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

Full-state controls of terahertz waves using tensor coding metasurfaces Shuo Liu1,2, Hao Chi Zhang1,2, Lei Zhang1,2, Quan Long Yang3, Quan Xu3, Jianqiang Gu3, Yan Yang1,2, Xiao Yang Zhou4, Jiaguang Han3, Qiang Cheng1,5, Weili Zhang3,5, and Tie Jun Cui1,5,* 1

State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China Synergetic Innovation Center of Wireless Communication Technology, Southeast University, Nanjing 210096, China 3 Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China 4 Jiangsu Xuantu Technology Co., Ltd., 12 Mozhou East Road, Nanjing 211111, China 2

5

Cooperative Innovation Centre of Terahertz Science, No.4, Section 2, North Jianshe Road, Chengdu 610054, China

*

Corresponding author.

E-mail: [email protected]. Tel: 008683790295 Fax: 008683790295

Keywords: Metasurface, coding metasurfaces, tensor, terahertz frequencies, surface wave

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Coding metasurfaces allow us to study metamaterials from a fully-digital perspective, enabling many exotic functionalities such as anomalous reflections, broadband diffusions, and polarization conversion. Here, we propose a tensor coding metasurface at terahertz frequency that could take full-state controls of electromagnetic wave in terms of its polarization state, phase and amplitude distributions, and wave-vector mode. Due to the off-diagonal elements that dominant in the reflection matrix, each coding particle could reflects the normally incident wave to its cross polarization with controllable phases, resulting in different coding digits. A 3-bit tensor coding metasurface with three coding sequences is taken as example to show its full-state controls in reflecting normally incident terahertz beam to anomalous directions with cross polarizations, and making a spatially propagating wave (PW) to surface wave (SW) conversion at the terahertz frequency. We show that the proposed PW-SW convertor based on tensor coding metasurface supports both x and y-polarized normal incidences, producing cross-polarized transverse- magnetic (TM) and transverse-electric (TE) modes of terahertz SWs, respectively.


Page 2 of 37

Page 3 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


INTRODUCTION

Metamaterials have been continuously attracting enormous interests both in physics and engineering communities since the past decade, owing to their unique ability in manipulating electromagnetic (EM) waves that cannot be obtained with natural materials.1 The conventional metamaterials are usually constructed by periodically arranging subwavelength scatterers or drilling air holes in a bulk volume, manipulating wavefronts of EM waves in the designed way through the phase accumulation in a three-dimensional (3D) space.2-5 However, the inherent thickness of such metamaterials results in significant loss and fabrication challenge, especially in the terahertz (THz) and infrared regimes.6-9 Fortunately, two-dimensional (2D) versions of metamaterials, termed as metafilms or metasurfaces,10 have overcome such limitations and undergone a rapid development in the past a few years. Owing to its flat and ultrathin features, many metasurface-based devices have been designed and fabricated in the THz frequency using the current micro-fabrication techniques to manipulate THz waves with high degree of freedom and low loss, such as propagating wave filters,11-13 absorbers,14,

15

polarization convertors,16, 17 modulators,8, 18 and holography.19-21

In 2011, Yu et al. proposed a metasurface possessing interfacial phase discontinuities at infrared wavelength by designing an array of V-shaped antennas on the substrate surface, which exhibits new phenomena of anomalous reflections and refractions, described by the generalized Snell’s law.22, 23 In this approach, 2π phase variation is readily achieved by adjusting the angle and orientation of the V-shaped antenna, offering us a great convenience to tailor the EM wavefronts using an ultrathin film instead of bulky 3D metamaterials. It was further reported that this idea could be used to design interesting devices such as beam deflectors,24,

25

focusing lenses,26-29 and background-free

circular-polarization converters.30



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Recently, Giovampaola and Engheta have proposed digital metamaterials to design the medium parameters in a digital way.31 In the meantime, Cui et al. have introduced the concept of coding metamaterials by arranging a number of reflective coding particles with different digital states on a 2D surface.32 Since each coding particle is pre-designed with a discrete phase response in the 2π range within a certain frequency band, the manipulation to the EM wavefronts is totally determined by the coding sequences. Such a new concept allows us to design radiation and scattering patterns from a fully digital perspective, and has enabled the design of programmable metamaterial,32 on which the state of each coding particle is digitally controlled in real time using a field programmable gate array (FPGA). This idea was further extended to the terahertz range to realize ultralow specular reflections through scattering diffusion on flat33, 34 and curved35 substrates. Lately, the concept of anisotropic coding metamaterial,36 with the digital states of each coding particle represented by a tensor, has been proposed at terahertz frequencies, which could realize dual functionalities using a single coding matrix under orthogonal polarizations.

All previous works on the coding metasurfaces are designed to manipulate the phase front of the incoming wave, instead of the polarization state and wave-vector mode. In this work, we propose a tensor coding metasurface at terahertz frequencies using a rectangular split-ring resonator (RSRR) to provide full-state controls of the EM waves, namely, the polarization state and wave vector. Previous studies are designed to redirect the co-polarized component of the normal incidence to desired directions. In this study, RSRR is employed as the coding particle to convert the incident wave to its cross polarization with controllable reflection phases, as shown in Figure 1a. As the reflection response of the RSRR structure can be described by a tensor, we call it tensor coding metasurface. Such a tensor coding metasurface could work either in spatial wave mode or surface wave mode,


Page 4 of 37

Page 5 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


depending on different coding sequences. For the spatial wave mode, a y-polarized normal incidence is reflected to an anomalous direction with cross polarization using a gradient coding sequence, as schematically illustrated in Figure 1b. Similarly, an x-polarized incidence will be anomalously reflected to the same direction with y-polarization. For the surface wave mode, the normally incident spatial propagating wave containing both x- and y-polarizations is converted to surface waves in different modes, as illustrated in Figures 1c and d. This function can be realized by reducing the period of the coding sequence down to a free-space wavelength. For example, the y-polarized normally incident propagating wave is converted to TM-mode surface wave propagating on the quartz substrate (Figure 1c); while the x-polarized normally incident propagating wave is converted to TE-mode surface wave (Figure 1d). The red and blue arrows indicate the y- and x-polarized propagating waves in free-space, respectively, and the purple arrows represent the surface waves on the quartz substrate.

RESUTLS AND DISCUSSION 3-bit chiral coding metasurfaces

Figure 1a shows the structure of the building block of the tensor coding metasurface, which consists of a metallic RSRR and a metallic sheet, separated by a dielectric spacer (polyimide) with thickness d=20 µm and period p=50 µm. The length L and width w of RSRR are 45 and 5µm, respectively. The permittivity of polyimide is set as ε=3.0+0.09i in simulations. Because the electric field is polarized 45º (either x- or y-direction) with respect to the symmetry axis of the structure (see the red arrow in Figure 1a), both symmetric and antisymmetric eigenmodes are excited and contribute to the reflection with cross-polarization,22, 37 making the coding particle function as a reflection-type 90º linear polarizer. To distinguish the current structure from our previous structures in a mathematical



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 37

perspective, 32, 33, 35, 36 we describe the reflection matrix of a coding particle in the following form, ܴ௫௫ ܴത = ൤ ܴ௬௫

ܴ௫௬ ൨ ܴ௬௬

(1)

where the diagonal elements Rxx and Ryy are the co-polarized components of reflection, while the off-diagonal elements Rxy and Ryx represent the cross-polarized components of reflection. For isotropic coding particle,32, 33, 35 ܴ௫௫ = ܴ௬௬ ; while for anisotropic coding particle,36 ܴ௫௫ ≠ ܴ௬௬ . For both isotropic and anisotropic coding particles, we aim to manipulate the co-polarized components, and thus the off-diagonal elements should approach to zero. Whereas for the RSRR coding particle proposed in this work, the diagonal elements should be close to zero and the off-diagonal elements should approach to unity, which is the origin of the polarization conversion effect possessed by the tensor coding metasurface. We note that similar structures have been reported for the manipulation of cross-polarization in previous works, including the V-shaped antenna22 and C-shaped resonator.24, 25

However, under the presence of opaque metallic ground, the RSRR structure proposed here

provides much higher reflection amplitude.

Eight coding particles labeled with digital states ‘000’, ‘001’, ‘010’, ‘011’, ‘100’, ‘101’, ‘110’ and ‘111’ are required to build a 3-bit tensor coding metasurface, and the corresponding structures are shown at the bottom of Figure 1e. The lengths s of the first four coding particles (‘000’, ‘001’, ‘010’, ‘011’) are optimized using commercial software, the CST Microwave Studio (Computer Simulation Technology AG, Framingham, Massachusetts, United States), as 0, 7, 17, and 24.75 µm, respectively. Because the symmetry axis of RSRR has 45º tilt angle with respect to the incidence polarization (x- or y-axis), the last four coding particles (‘100’, ‘101’, ‘110’ and ‘111’) can be simply obtained by rotating the first four structures by 90º along the z-axis. Figure 1e gives the simulated


Page 7 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


amplitudes and phases of the cross-polarized electric fields for the eight coding particles at the designed frequency 0.93 THz. It can be seen that the eight coding particles (from left to right) reflect the THz waves with phases 122º, 76º, 32º, -12º, -57º, -103º, -147º, and 167º, respectively, forming a 2π phase coverage with π/4 interval. The reflection amplitudes for the eight coding particles are all above 0.8 at the designed frequency. To evaluate the performance of the eight coding particles in a broader bandwidth, we further provide the amplitudes and phases of reflections from 0.8 to 1.2 THz in Figures S1a and b, respectively.

Anomalous reflection with polarization conversion

As a proof of principle, we first take a gradient coding sequence ‘001 011 101 111 001 011 101 111 …’ as example to demonstrate the performance of the tensor coding metasurface in controlling the polarization state of the impinging wave. Figure 2a displays the coding pattern which consists of 48×48 coding particles. To minimize the couplings between neighboring coding particles with different geometries, each coding digit in the gradient coding sequence represents a super unit cell comprising of 3×3 identical coding particles. In spite of this, undesired EM couplings still exist between coding particles with different geometries, which are particularly significant in the RSRR structure due to the magnetic coupling among metallic loops. Please refer to Ref. 38 for detailed explanation on advantages of the super unit cell. Although each coding particle is originally designed to work at 0.93THz, we obtain the best performance of the encoded metasurface at a slightly higher frequency of 1 THz, as shown in Figure 2b for the 3D scattering pattern under the y-polarized normal incidence. A scattering beam is obviously observed at 30º with respect to the z-axis in the x-z plane, as displayed in Figure S1c for the 2D scattering pattern, which is in excellent agreement with the theoretical calculation result (30º) governed by the generalized Snell’s law:



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λ θ = sin −1   Γ 



Page 8 of 37

(2)

in which λ and Γ represent the free-space wavelength (300 µm at 1THz) and the gradient period (600 µm), respectively. Please refer to Figure S2 for the detailed derivation of the above anomalous reflection angle. A smaller beam representing the co-polarized scattering is also observed at 0º from both 3D and 2D scattering patterns in Figure 2b and Figure S1c, due to the non-ideal reflection of the coding particle. To better visualize the cross-polarized anomalous reflection, we provide the electric-field distributions (Ex component) in the x-z plane in Figure 2c. We clearly see that, under the y-polarized normal incidence (marked by red arrow), the cross-polarized scattered wave (marked by blue arrow) propagates like a plane wave in the direction of 30º with respect to the z-axis. We remark that the proposed tensor coding metasurface could work in a relatively broad bandwidth, as can be observed in Figure S1e.

When the same coding metasurface is illuminated with the x-polarized normal incidence, an obvious reflection appears at 35º in the x-z plane at 0.87 THz, which can be observed from the 3D and 2D scattering patterns in Figure 2d and Figure S1d, respectively. Similarly, the scattered electric-field distribution (Ey component) is given in Figure 2e on the x-z plane, where the x-polarized THz beam is efficiently converted to the y-polarized beam and anomalously reflected to the upper-half space at 35º with respected to the z-axis. The larger reflection angle is due to the larger observing wavelength, as predicted from Eq. (2). The slight disturbance observed in the electric-field distributions in both cases are attributed to the presence of EM couplings between adjacent coding particles having different geometries. We should note that, except for ‘all zero’ or ‘all one’ coding pattern, such EM coupling will always exist in all other coding patterns and leads to unpredictable


Page 9 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


wave fronts. Similar broadband performance is maintained for this case, which can be observed from the broadband reflection curves at 0.8, 0.87, 0.9, 1.0, and 1.1 THz in Figure S1f.

Since the plots in Figures S1c and d have been normalized to the maximum value of the bare perfect electric conductor (PEC), the conversion efficiencies (please refer to Supporting Information Note S1 for definition) from the normal incidence to anomalous reflection with cross polarization under the y- and x-polarized incident waves can be directly read as 73% and 63%, respectively. The slightly lower efficiency for the x-polarized incidence is attributed to larger scan angle, which results in smaller effective antenna aperture.39 Note that the efficiencies listed above include both the polarization conversion efficiency reported in Refs. 40-42 and the conversion efficiency from the normal incidence to anomalous reflection defined in our previous work.36 The optimum anomalous reflections occur at different frequencies for the two cases, because the obliquely reflected waves in Figures 2b and c belong to TM and TE modes, respectively, which inevitably result in a slight difference in EM responses of the coding particle.

One may notice that the proposed structure resembles reflectarray that has been widely studied in the microwave regime,43-45 which possess different coverages for the x and y polarizations. We remark that the proposed tensor coding metasurface differs from the reflectarray in the following aspects. Firstly, the proposed structure could make a 90° linear polarization conversion to the incident wave while controlling their wavefront distribution. Secondly, the unit cell of coding metasurfaces is typically in subwavelength scale (1/8 to 1/4 free-space wavelengths). This is in contrast to that of the conventional array antenna, in which the unit cell is normally larger than 1/2 wavelength. Smaller unit cell could provide more versatile functions. For example, a 2-bit coding



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

metasurface could be used to realize the conversion from PWs to SWs with a gradient coding sequence ‘01230123…’, by setting the coding period smaller than a free-space wavelength. However, such PW-SW conversions cannot be realized using the reflectarrays because the 2π gradient phase period is always longer than a free-space wavelength, which cannot provide the required wave momentum for the PW-SW conversion. Thirdly, coding metasurfaces not only generate single or multiple scattering beam patterns with controllable shape and direction, but also establish a bridge between the physical metasurface and digital information. Owning to the Fourier transform relation between the coding pattern and far-field pattern, the digital characterization of coding metasurface provides the possibility to study metasurfaces and their scattering patterns from digital perspective. We could therefore apply many existing theorems from information theory directly to design coding metasurfaces and realize more versatile controls of EM waves. For example, we used Shannon entropy to estimate the information capacity carried by coding metasurface by analyzing the entropy of the coding pattern,46 revealing the proportional relationship between the geometrical entropy (the entropy of coding pattern) and physical entropy (the entropy of the radiation pattern). We also proposed convolution operations to coding metasurfaces to steer the scattering beam to arbitrary directions with negligible beam distortion.47 A continuous scan of the single-beam radiation in the upper-half space is allowed using a 2-bit coding metasurface which consists of only four coding states.

THz PW-SW convertors supporting both TE and TM modes

We present the second function of the tensor coding metasurface in converting the wave vector mode, i.e., to realize the conversion from PWs to SWs, by scaling down the period of the coding sequence to around one free-space wavelength.48 Here, the same coding sequence ‘001 011 101 111 001 011


Page 10 of 37

Page 11 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


101 111 …’ with the super-unit-cell size of 2×2 is applied to the metasurface. The principle for selecting appropriate coding sequence for the PW-SW conversion is to make the period of gradient coding sequence be roughly equal to the working wavelength. Due to the non-ideal plane-wave illumination and unpredictable EM couplings between adjacent coding particles, the optimal frequency for PW-SW conversion may deviate from the theoretical value determined by Ref. 48, and can be obtained by numerical simulations. More discussions are given in Supporting Information Note S4. For detailed descriptions of the simulation configuration, please refer to the method section. We remark that the thickness 80 µm of the quartz is determined by considering the momentum matching between the PW-SW convertor and quartz substrate, as well as the fabrication feasibility, as discussed in Supporting Information Note S4. Figures 3a and b show the electric-field distributions for the Ex and Ey components at 0.75 THz in the x-z plane, respectively. In Figure 3a, strong Ex components are observed inside and in the vicinity of the quartz substrate; while in Figure 3b, very weak Ey components are observed, indicating that the y-polarized normally incident PW is efficiently converted to TM-mode SW. In Figure 3a, the remaining electric field below the waveguide port is actually the anomalous reflection resulted from mismatch of the impedance and momentum between the PW-SW convertor and free space.

In order to rigorously prove that the field on the quartz substrate is surface wave, we give the analytical dispersion relations in an infinitely large dielectric slab. Please refer to Supporting Information Note S4 for detailed derivations. For the TM-mode SW, we have

k x2 − k02 =

k02ε − k x2

ε

n   tan  k02ε − k x2 d / 2 + π  2  


(3)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 37

for the TE-mode SW, we have

n   k x2 − k02 = k02ε − k x2 tan  k02ε − k x2 d / 2 + π  2  

(4)

where k0 and kx are the wave numbers in free space and along the propagation direction, respectively; ε and d are the permittivity and thickness of the quartz substrate; and n represents the order of the SW mode. For the current simulations, the fundamental mode (n=0) is dominant for both TE and TM polarizations. It is clear from the above equations that the propagating wave number kx is larger than k0, leading to the slow-wave features such as the exponential decay in the z direction and the field confinement. As verification for above numerical simulations, we plot the theoretically calculated 2D (in the x-z plane) electric-field distributions on the quartz substrate for the TM- and TE-mode SWs in Figures 4a and b, respectively. Good agreements can be found between the numerical (Figures 3a and c) and theoretical (Figures 4a and b) results.

Figure 4c plots the amplitude of simulated electric field (Ex component) extracted on a straight line normal to the quartz substrate in Figure 3a. As expected from Eq. (3), the electric field decays exponentially once it leaves the surface of quartz substrate (marked by the green area), indicating that most EM energies are restricted in the vicinity of the substrate. In addition, the wavelength of the field in the quartz substrate is observed from Figure 3a as 328 µm, which is smaller than the propagating wavelength in free space at 0.75 THz (400 µm), implying again that the field is a slow wave and does not radiate to the free space. We further demonstrate the excellent field confinement feature on the quartz substrate in Figure S3b when the substrate is bent downward with a curvature of 1120µm.


Page 13 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


To evaluate the performance of the PW-SW convertor at higher frequency under the x-polarized normal incidence, we keep compressing the period of the coding sequence down to 200 µm, in which each coding digit is composed of only one coding particle (corresponding to super-unit size of 1×1). All other parameters for the convertor and quartz substrate are kept the same with the above TM case. The simulated electric-field distributions (Ey and Ex components) at 1.05 THz are given in Figures 3c and d, respectively. In this case, the x-polarized normally incident plane wave is converted to TE-mode SW, in which the electric field is polarized along the y-axis, as can be observed from the amplitudes of Ey and Ex in Figures 3c and d. For the TE case, the electric field is mostly confined in the quartz substrate, as clearly shown in Figure 4d for the plot of electric-field (Ey) distribution on the line normal to the surface. The lower intensity of SW in the TE case might be caused by the lack of super unit cells. In this condition, the real reflection from each coding particle may deviate from the design value due to the EM couplings between adjacent coding particles with different geometries. As theoretical verification, we have provided in Figures 4e and f the intensities of the electric fields below and inside the substrate in a broad bandwidth, in which excellent agreements are observed by comparing with Figures 4c and d.

Although conventional devices like prism, gratings, and dipole antenna have been used to convert spatial PWs to SWs, the conversion efficiencies are quite low. To solve the problem, an efficient PW-SW convertor has been proposed in Ref. 48 using gradient metasurface. But it can only support the x-polarized incidence to produce TM-mode SWs with the same polarization. The tensor coding metasurface presented in this work, however, supports both x- and y-polarized normal incidences and is able to convert spatial PWs to SWs with cross polarizations in both TE and TM modes efficiently. We remark that the proposed compact PW-SW convertor could be utilized as a



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

high-performance device in real applications to convert THz signals propagating in free space to SWs in both TE and TM modes transmitted in flexible substrate such as a fiber.

Experimental verification

Two different samples are fabricated using the standard photolithography process to experimentally validate the performance of the tensor coding metasurface. Figures 5a and b show the photograph and microscopy image of the first sample, respectively, which has the same coding pattern as in Figure 2a. In order to accommodate the plane-wave like incident beam with diameter around 5 mm at 1 THz, we fabricate a large sample that covers an area of 35×35 mm2 (see Figure 5a). A rotary THz-TDS was employed to measure the anomalously reflected THz fields at different angles, as illustrated in Figures 5c and d.

Figure 5e shows the dependence of the measured reflection amplitude for the first sample on the receiving angle and frequency, which has been normalized to the reference signal measured under the direct transmission (see Supporting Information Note S5 for the data post-processing). An obvious scattering peak is found in the 2D plot, which shifts to larger angles as the frequency decreases, as expected from the generalized Snell’s law. To compare the amplitudes of the anomalous reflections at different frequencies, the reflections extracted at 0.7, 0.8, 0.9, and 1.0THz from Figure 5e (see the blue lines) are replotted in Figure 5f. At the designed frequency 1.0 THz, the efficiency reaches the maximum value of 0.64 at the receiving angle 30º. However, the efficiency drops to 0.32 as frequency decreases to 0.7 THz because the coding particles far from the designed frequency no longer provide the required gradient phase and unity amplitude responses. The lower measured efficiency could be attributed to the average effect of electric field on the aperture of the


Page 14 of 37

Page 15 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


receiving antenna, which is not taken into account in simulations. In addition, inevitable fabrication tolerance on the dimension of structure as well as the shift in the permittivity of polyimide may also contribute to such discrepancy.

Figures 6a and b show the schematic and photo of THz time-domain near-field scanning system, which was used to measure surface THz waves propagating on the quartz substrate. The 80-µm thick quartz substrate was fabricated by reducing the thickness of a 500µm-thick crystal quartz wafer (Crystal Orientation 0001, KJMT, Hefei, China) to 80 µm. A microprobe, driven by a 2D translation stage, could automatically move in the x- and y-directions on the horizontal plane with high precision. Since most electric fields of TE-mode SWs are restricted inside the quartz substrate, only the sample supporting TM-mode SWs was measured in the experiment.

Figure 6c provides the time-domain signals (amplitudes of Ez components) measured every 0.4 mm from 2 to 8 mm along the middle line of the crystal quartz substrate in the time period from 0 to 80 ps. At the nearest point (2 mm), the oscillating waveform appearing in the time period from 7 to 26 ps represents the signal of surface wave. As the probe moves away from the PW-SW convertor, the wave packet is delayed accordingly. The time delay is observed larger than that in free space because of the slow-wave nature of surface wave. One may also notice that the waveforms experience distortions to different degrees during the propagation process owing to the dispersion of TM-mode surface waves in the quartz substrate. As a comparison, we provide in Figure S8a the time-domain signals (amplitudes of Ez components) measured at the same positions as those in Figure 6c when the tensor coding metasurface is replaced by a perfectly reflecting mirror (used as reference, see Supporting Information Note S5). As expected, no signal was detected at all positions



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

except for some noises at lower frequencies.

The corresponding frequency spectrum at each position can be readily obtained by performing the fast Fourier transform (FFT) to the time-domain signal, as illustrated in Figure 6d. A significant peak is clearly observed on each curve from 0.71 to 0.75 THz, with the central frequency around 0.73 THz, which agrees very well with the simulation results in Figure S3c. The amplitudes of scattering peaks measured far from the convertor are lower than those at the nearer points due to the dielectric loss of the quartz substrate. The corresponding frequency spectra of the reference case are given in Figure S8b, where almost all curves exhibit flat frequency responses in the considered frequency range, proving that the detected signals in Figures 6c and d are indeed the TM-mode surface waves that are converted from the y-polarized normally incident THz waves by the tensor coding metasurface. Note that the detected intensity of electric field highly depends on the distance between the probe and the substrate surface. Therefore, the value of the vertical axis (with µV unit) in Figure 6c is directly obtained from the FFT operation for the comparison between each curve, and does not represent the conversion efficiency.

To further examine the performance of the surface wave at the designed frequency 0.73 THz (indicated by the vertical line), we plot the phases and amplitudes at all measured points in Figures 6e and f, respectively. The phase (Figure 6e) grades linearly along the scan line and experiences about 18.22×360 degrees across the distance from 2 to 8 mm. The corresponding wavelength of the surface wave can thus be calculated as 329 µm, having excellent agreement with the simulation result (328 µm). Both amplitudes (Figure 6f) and real parts (Figure S8c) of the surface waves show standing-wave-like distributions along the scan line, which are caused by the interference of


Page 16 of 37

Page 17 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


higher-order SW modes. We note that similar phenomena are found in numerical simulations, as shown in Figure S8d, where the amplitudes of surface waves also present obvious standing-wave-like distributions with almost the same number of wave nodes (3.5 wave nodes) in the considered distance. It can be also observed from these two plots that the measured amplitudes tend to decrease with the increasing of distance, which is resulted from the larger loss of the quartz substrate of the sample.

CONCLUSION

In summary, we have demonstrated a tensor coding metasurface at THz frequency that could take full-state controls of the EM wave in terms of polarization state, phase and amplitude profile, and wave vector mode. Owning to the off-diagonal elements that play the dominant role in the reflection matrix, we could convert the impinging wave to its cross-polarization with controllable wavefront. The planar geometry of the cross-polarized beam-bending lens allows them to be integrated with other THz devices using conventional microfabrication process. This design is suitable for the applications where polarization conversion and beam bending are both required, such as the background-free 90° linear polarizer that reflects the normal incidence to anomalous directions with cross polarization. Then it is possible to develop reflection-type meta-holograms supporting the normal-incidence and normal-reflection mode due to the low interference between cross-polarized reflection and the co-polarized incidence. One could also implement a programmable tensor coding metasurface by electrically controlling the carrier density of doped silicon,8 or illuminating the vanadium oxide (VO2) 13 with SLM, to realize real-time controls of THz wavefronts.

Most importantly, we have experimentally demonstrated, for the first time, the wave vector



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

mode conversion at terahertz frequencies, i.e. a PW-SW convertor. We should note that all previous PW-SW conversions implemented by the non-periodic nanoslits49 and metallic H-shaped structures48 only support TM-mode SWs, in which the polarization direction of the normal incidence must be the same as the propagation direction of SWs. The PW-SW convertor proposed in this work, however, is able to convert both the x- and y-polarized normal incidences to SWs with TE and TM modes, which has not been reported before. Owing to the lack of efficient excitations of SWs at terahertz frequencies, many previous investigations on metamaterial-based SW manipulation devices were limited at microwave frequency,27, 50, 53 The PW-SW convertor proposed in this work can be used as an efficient SW coupler and therefore may facilitate the design of spoof surface plasmon polariton52, 53

devices at THz frequencies. Interestingly, by combining the new PW-SW convertor with the

previously reported one,48 one can design a SW splitter which is able to separate the Ex and Ey polarizations included in the normal incidence to two TM-mode SWs travelling along opposite directions. We remark that the current design is not only limited to the terahertz frequency, but can be easily extended to microwave or visible spectra.

Methods Simulation setup. For the simulation of anomalous reflection presented in Figure 2, a plane wave is set with the propagating vector along the –z direction. Far-field and near-field monitors are set at the corresponding frequencies to obtain far-field radiation patterns and near-field distributions. Figure S3a shows the simulation configuration for the PW-SW conversion in the commercial software, CST Microwave studio. The PW-SW convertor is the coding metasurface which consists of 24×24 coding particles. A waveguide port, with the inner aperture of 855×722µm2, is set at 600 µm above the


Page 18 of 37

Page 19 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


convertor to generate plane waves along the -z direction. To receive the surface waves converted by the PW-SW convertor, a quartz substrate (permittivity ε=4.4 and loss tangent δ=0.0004) with the size of 2050×1200×80µm3 (permittivity ε=4.4 and loss tangent δ=0.0004) is placed next to the PW-SW convertor. For easy comparison between the TM and TE modes, they share the same simulation setup, except for the direction of the waveguide port for generating the x and y polarizations.

Sample fabrication. The fabrication process mainly includes the preparation of two tensor coding metasurface samples and an 80µm-thick crystal-quartz substrate. The tensor coding metasurfaces are fabricated by first e-beam-evaporating a Ti/Au layer (10nm/180nm) on a 2-inch silicon wafer (400µm-thick, n-type, resistivity ρ=3-6 Ω·cm) to serve as the metallic ground sheet. Then the liquid polyimide (Yi Dun New Materials Co. Ltd, Suzhou) is coated with 1150 rpm spin rate onto the gold layer and solidified on a hot plate at 80, 120, 180 and 250 ºC for 5, 5, 5 and 20 minutes, respectively. The above spin-coating and curing processes are repeated twice to form the 20µm-thick polyimide layer. Next, another Ti/Au layer (10/180 nm) is deposited on top of a patterned photoresist made by the standard photolithography, after which a lift-off process helps enable the final metallic pattern. The 80µm-thick quartz substrate is fabricated by firstly cutting a 2 inch and 500µm-thick crystal quartz wafer (Crystal Orientation 0001, KJMT, Hefei, China) into small pieces with 16.6×12 mm2. We then reduce the thickness to 80 µm with grinding and polishing processes successively. A U-shaped gold layer is patterned at the edge of the substrate to help the levelling of the sample during the near-field scanning measurement.

Measurement systems. The rotary THz-TDS for far-field measurement. A pair of fiber-based terahertz photoconductive antennas (Model TR4100-RX1, API Advanced Photonix, Inc.), optically



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

excited by a commercial ultrafast erbium fiber laser system (T-Gauge, API Advanced Photonix, Inc.), is used to generate and detect the time-domain signals from 0.3 to 3.0 THz. Both the transmitter and sample holder are fixed on the optical stabilization platform. The receiver is mounted on the sample holder via a metal rod, allowing the receiver to rotate around the sample holder (see Figure 5d). During the measurement, the sample is illuminated by the vertically polarized (x-direction) THz wave generated from the transmitter, and the receiver scanned every 5º from 22.5º to 87.5º to record the horizontally polarized (y-polarization) electric fields scattered from the sample. The direct transmission when the transmitter and receiver are both vertically polarized is recorded as the reference for all incident angles.

The near-field measurement system. The y-polarized THz wave is firstly incident on the PW-SW convertor (the yellow board on the right) from underneath and is converted to SW (the right arrow), which is then guided to an 80µm-thick crystal quartz substrate (the light blue board on the left) placed next to the PW-SW convertor. To keep the exact position between the convertor and crystal quartz substrate, both the transmitter and receiver are fixed on a specially designed holder (See Figures S6a and b), which is placed on a metal platform. The height of the sample holder is designed to be 20 mm, which is large enough to avoid the signal reflected by the metal platform reaching the quartz substrate in the time window (80 ps). A photoconductive antenna-based probe (Protemics GmbH) is mounted on a 2D translation stage that could automatically move in the horizontal plane with high precision, and is used to measure the Ez components of the electric fields 100 µm above the surface of the quartz substrate. During the experiments, the probe is set to scan along the middle line of the substrate, starting from 2 mm and ending at 8 mm away from the PW-SW convertor with step of 0.04 mm (See Figure S6b). Please refer to Figure S7 for the details of


Page 20 of 37

Page 21 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the of the near-field scanning terahertz microscopy (NSTM) system.

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant Nos. 61631007, 61571117, 61302018 and 61401089, and 111 Project under the Grant No. 111-2-05.

Supporting Information Note S1. Simulation results for coding particle design and anomalous reflection; Note S2. Derivation of the anomalous scattering angle; Note S3. Simulation configurations and results for the PW-SW conversion; Note S4. Derivation for the analytical form of SW; Note S5. Experiments and measurements;

REFERENCES (1)

Veselago, V. G.; Electrodynamics of Substances with Simultaneously Negative Values of Sigma and Mu. Phys.-Usp., 1968, 10, 509.

(2)

Pendry, J. B.; Schurig, D.; Smith, D. R. Controlling Electromagnetic Fields. Science, 2006, 312, 1780-1782.

(3)

Liu, R.; Ji,C.; Mock, J. J.; Chin, J. Y.; Cui, T. J.; Smith, D. R. Broadband Ground-Plane Cloak. Science, 2009, 323, 366-369.

(4)

Kundtz, N.; Smith, D. R. Extreme-Angle Broadband Metamaterial Lens. Nat. Mater. 2010, 9, 129-132.

(5)

Schurig, D.; Mock, J. J.; Justice, B. J.; Cummer, S. A.; Pendry, J. B.; Starr, A. F.; Smith, D. R. Metamaterial Electromagnetic Cloak at Microwave Frequencies. Science, 2006, 314, 977-980.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(6)

Fan, K. B.; Strikwerda, A. C.; Tao, H.; Zhang, X.; Averitt, R. D. Stand-Up Magnetic Metamaterials at Terahertz Frequencies. Opt. Express, 2011, 19, 12619-12627.

(7)

Buckmann, T.; Stenger, N.; Kadic, M.; Kaschke, J.; Frolich, A.; Kennerknecht, T.; Eberl, C.; Thiel, M.; Wegener, M. Tailored 3D Mechanical Metamaterials Made by Dip-in Direct-Laser-Writing Optical Lithography. Adv. Mater. 2012, 24, 2710-2714.

(8)

Unlu, M.; Hasemi, M. R.; Berry, C. W.; Li, S.; Yang, S. -H.; Jarrahi, M. Switchable Scattering Meta-Surfaces for Broadband Terahertz Modulation. Sci. Rep. 2014, 4, 5708.

(9)

Burckel, D. B.; Wendt, J. R.; Eyck, G. A. T.; Ginn, J. C.; Ellis, A. R. Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers. Adv. Mater. 2010, 22, 5053.

(10)

Holloway, C. L.; Kueste, E. F.; Gordon, J. A.; Hara, J. O.; Booth, J.; Smith, D. R. An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials. IEEE Antennas Propag. Mag. 2012, 54, 10-35.

(11)

Yeh, T. T.; Genovesi, S.; Monorchio, A.; Prati, E.; Costa, F.; Huang, T.; Yen, T. Ultra-Broad and Sharp-Transition Bandpass Terahertz Filters by Hybridizing Multiple Resonances Mode in Monolithic Metamaterials. Opt. Express, 2012, 20, 7580-7589.

(12)

Lin, Y. S.; Qian, Y.; Ma, F. S.; Liu, Z.; Kropelnicki, P.; Lee, C. K.; Development of Stress-Induced Curved Actuators For a Tunable THz Filter Based on Double Split-Ring Resonators. Appl. Phys. Lett. 2013, 102, 111908.

(13)

Zhu, Y. H.; Vegesna, S.; Zhao, Y.; Kuryatkov, V.; Holtz, M.; Fan, Z. Y.; Saed, M.; Bernussi, A. A. Tunable Dual-Band Terahertz Metamaterial Bandpass Filters, Opt. Lett. 2013, 38, 2382-2384.

(14)

Savo, S.; Shrekenhamer, D.; Padilla, W. J. Liquid Crystal Metamaterial Absorber Spatial Light


Page 22 of 37

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Modulator for Thz Applications. Adv. Opt. Mater. 2014, 2, 275-279. (15)

Liu, S.; Chen, H. B.; Cui, T. J. A Broadband Terahertz Absorber Using Multi-Layer Stacked Bars. Appl. Phys. Lett. 2015, 106, 163702.

(16)

Cong, L. Q.; Xu, N. N.; Han, J. G.; Zhang, W. L.; Singh, R. A Tunable Dispersion-Free Terahertz Metadevice With Pancharatnam-Berry-Phase-Enabled Modulation and Polarization Control. Adv. Mater. 27, 6630 (2015).

(17)

Fan, R. –H.; Zhou, Y.; Ren, X. -P.; Peng, R. -W.; Jiang, S.-C.; Xu, D. -H.; Xiong, X.; Huang, X. -R.; Wang,M. Freely Tunable Broadband Polarization Rotator for Terahertz Waves. Adv. Mater. 2015, 27, 1201-1206.

(18)

Karl, N.; Reichel, K.; Chen, H. -T.; Taylor, A. J.; Brener, I.; Benz, A.; Reno, J. L.; Mendis, R.; Mittleman, D. M. An Electrically Driven Terahertz Metamaterial Diffractive Modulator with More Than 20 dB of Dynamic Range, Appl. Phys. Lett. 2014, 104, 091115.

(19)

Wen, D. D.; Yue, F. Y.; Li, G. X.; Zheng, G. X.; Chan, K. L.; Chen, S. M.; Chen, M. K.; Li, F.; Wong, P. W. H.; Cheah, K. W. E.; Pun, Y. B.; Zhang, S.; Chen, X. Z. Helicity Multiplexed Broadband Metasurface Holograms. Nat. Comm. 2015, 6, 8241.

(20)

Chen, W. T.; Yang, K.-Y.; Wang, C.-M.; Huang, Y.-W.; Sun, G.; Chiang, I-D.; Liao, C. Y.; Hsu, W.-L.; Lin, H. T.; Sun, S.; Zhou, L.; Liu, A. Q.; Tsai, D. P. High-Efficiency Broadband Meta-Hologram with Polarization-Controlled Dual Images, Nano Lett. 2014, 14, 225-230.

(21)

Zheng, G. X.; Muhlenbernd, H.; Kenney, M.; Li, G. X.; Zentgraf, T.; Zhang, S. Metasurface Holograms Reaching 80% Efficiency, Nat. Nanotechnol., 2015, 10, 308-312.

(22)

Yu, N. F.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J. P.; Capasso, Gaburro, F. Z. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Science, 2011, 334, 333-337. (23)

Ni, X. J.; Emani, N. K.; Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Broadband Light Bending with Plasmonic Nanoantennas. Science, 2012, 335, 427-427.

(24)

Zhang, X. Q.; Tian, Z.; Yue, W. S.; Gu, J. Q. Zhang, S.; Han, J. G.; Zhang, W. L.; Broadband Terahertz Wave Deflection Based on C-Shape Complex Metamaterials with Phase Discontinuities. Adv. Mater. 2013, 25, 4567-4572.

(25)

Liu, L. X.; Zhang, X. Q.; Kenney, M.; Su, X. Q.; Xu, N. N.; Ouyang, C. M.; Shi, Y. L.; Han, J. G.; Zhang, W. L.; Zhang, S. Broadband Metasurfaces with Simultaneous Control of Phase and Amplitude. Adv. Mater. 2014, 26, 5031-5036.

(26)

Monnai, Y.; Jahn, D.; Withayachumnankul, W.; Koch, M.; Shinoda, H. Terahertz Plasmonic Bessel Beamformer. Appl. Phys. Lett. 2015, 106, 021101.

(27)

Wan, X.; Shen, X. P.; Luo, Y.; Cui, T. J. Planar Bifunctional Luneburg-Fisheye Lens Made of an Anisotropic Metasurface. Laser Photonics Rev. 2014, 8, 757-765.

(28)

Monticone, F.; Estakhri, N. M.; Alu, A. Full Control of Nanoscale Optical Transmission with a Composite Metascreen. Phys. Rev. Lett. 2013, 110, 203903.

(29)

Pfeiffer, C.; Grbic, A. Metamaterial Huygens' Surfaces: Tailoring Wave Fronts with Reflectionless Sheets. Phys. Rev. Lett. 2013, 110, 197401.

(30)

Yu, N.; Aieta, F.; Genevet, P.; Kats, M. A.; Gaburro, Z.; Capasso, F. Background-Free Quarter-Wave Plate Based on Plasmonic Metasurfaces. Nano Lett. 2012, 12, 6328-6333.

(31)

Giovampaola, C. D.; Engheta, N. Digital Metamaterials. Nat. Mater. 2014, 14, 1115-1121.

(32)

Cui, T. J.; Qi, M. Q.; Wan, X.; Zhao, J. Cheng, Q. Coding Metamaterials, Digital Metamaterials and Programmable Metamaterials. Light-Sci. Appl. 2014, 3, e218.


Page 24 of 37

Page 25 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33)

Gao, L. H.; Cheng, Q.; Yang, J.; Ma, S. J.; Zhao, J.; Liu, S.; Chen, H. B.; He, Q.; Jiang, W. X.; Ma, H. F.; Wen, Q. Y.; Liang, L. J.; Jin, B. B.; Liu, W. W.; Zhou, L.; Yao, J. Q.; Wu, P. H.; Cui, T. J. Broadband Diffusion of Terahertz Waves by Multi-Bit Coding Metasurfaces. Light-Sci. Appl. 2015, 4, e324.

(34)

Dong, D. S.; Jing, Y.; Cheng, Q.; Zhao, J.; Gao, L. H.; Ma, S. J.; Liu, S.; Chen, H. B.; He, Q.; Liu, W. W.; Fang, Z. Y.; Zhou, L.; Cui, T. J. Terahertz Broadband Low-Reflection Metasurface by Controlling Phase Distributions. Adv. Opt. Mater. 2015, 3, 1405-1410.

(35)

Liang, L. J.; Qi, M. Q.; Yang, J.; Shen, X. P.; Zhai, J. Q.; Xu, W. Z.; Xu, B. B.; Liu, W. W.; Feng, Y. J.; Zhang, C. H.; Lu, H.; Chen, H. T.; Kang, L.; Xu, W. W.; Chen, J.; Cui, T. J.; Wu, P. H. Liu, S. G. Anomalous Terahertz Reflection and Scattering by Flexible and Conformal Coding Metamaterials. Adv. Opt. Mater. 2015, 3, 1374-1380.

(36)

Liu, S.; Cui, T. J.; Xu, Q.; Bao, D.; Du, L. L.; Wan, X.; Tang, W. X.; Ouyang, C. M.; Zhou, X. Y.; Yuan, H.; Ma, H. F.; Jiang, W. X.; Han, J. G.; Zhang, W. L.; Cheng, Q. Anisotropic Coding Metamaterials and Their Powerful Manipulation to Differently Polarized Terahertz Waves. Light-Sci. Appl. 2015, 5, e16076.

(37)

Aieta, F.; Genevet, P.; Yu, N. F.; Kats, M. A.; Gaburro, Z.; Capasso, F. Out-of-Plane Reflection and Refraction of Light by Anisotropic Optical Antenna Metasurfaces with Phase Discontinuities. Nano Lett. 2012, 12, 1702.

(38)

Liu, S.; Zhang, L.; Yang, Q. L.; Xu, Q.; Yang, Y.; Noor, A.; Zhang, Q., Iqbal, S.; Wan, X.; Tian, Z.; Tang, W. X.; Cheng, Q.; Han, J. G.; Zhang, W. L.; Cui, T. J. Frequency-Dependent Dual-Functional Coding Metasurfaces at Terahertz Frequencies. Adv. Opt. Mater. 2016, 4, 1965.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(39)

Nayeri, P.; Yang, F.; Elsherbeni, A. Z. Bifocal Design and Aperture Phase Optimizations of Reflectarray Antennas for Wide-Angle Beam Scanning Performance. IEEE Trans. Antennas Propag. 2013, 61, 4588-4597.

(40)

Cheng, Y. Z.; Withayachumnankul, W.; Upadhyay, A.; Headland, D.; Nie, Y.; Gong, R. Z.; Bhaskaran, M.; Sriram, S.; Abbott, D. Ultrabroadband Reflective Polarization Convertor for Terahertz Waves. Appl. Phys. Lett. 2014, 105, 181111.

(41)

Chen, H. Y.; Wang, J. F.; Ma, H.; Qu, S. B.; Xu, Z.; Zhang, A. X.; Yan, M. B.; Li, Y. F. Ultra-Wideband Polarization Conversion Metasurfaces Based on Multiple Plasmon Resonances. J. Appl. Phys. 2014, 115, 154504.

(42)

Grady, N. K.; Heyes, J. E.; Chowdhury, D. R.; Zeng, Y.; Reiten, M. T.; Azad, A. K.; Taylor, A. J.; Dalvit, D. A. R.; Chen, H. T. Terahertz Metamaterials for Linear Polarization Conversion and Anomalous Refraction. Science, 2013, 340, 1304-1307.

(43)

Encinar, J. A. Design of Two-Layer Printed Reflectarrays Using Patches of Variable Size. IEEE Trans. Antennas Propag. 2001, 49, 1403-1410.

(44)

Encinar, J. A.; J.A. Zornaza. Broadband Design of Three-Layer Printed Reflectarrays. IEEE Trans. Antennas Propag. 2003, 51, 1662-1664.

(45)

Encinar, J. A.; Datashvili, L. S.; Zornaza, A.; Arrebola, M.; Sierra-Castaner, M.; Besada-Sanmartin, J. L.; Legay, H. Dual-Polarization Dual-Coverage Reflectarray for Space Applications. IEEE Trans. Antennas Propag. 2006, 54, 2827-2837.

(46)

Cui, T. J.; Liu, S.; Li, L. L. Information Entropy of Coding Metasurface. Light-Sci. Appl. 2016, 5, e16172.

(47)

Liu, S.; Cui, T. J.; Zhang, L.; Xu, Q.; Wang, Q.; Wan, X.; Gu, J. Q.; Tang, W. X.; Qi, M. Q.;


Page 26 of 37

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Han, J. G.; Zhang, W. L.; Zhou, X. Y.; Cheng, Q. Convolution Operations on Coding Metasurface to Reach Flexible and Continuous Controls of Terahertz Beams. Adv. Sci. 2016, 3, 1600156. (48)

Sun, S. L.; He, Q.; Xiao, S. Y.; Xu, Q.; Li, X.; Zhou, L. Gradient-Index Meta-Surfaces as a B Bridge Linking Propagating Waves and Surface Waves. Nat. Mater. 2012, 11, 426-431.

(49)

Tanemura, T.; Balram, K. C.; Ly-Gagnon, D. S.; Wahl, P.; White, J. S.; Brongersma, M. L.; Miller, D. A. B. Multiple-Wavelength Focusing of Surface Plasmons with a Nonperiodic Nanoslit Coupler. Nano Lett. 2011, 11, 2693-2698.

(50)

Li, Y. B.; Cai, B. G.; Cheng, Q.; Cui, T. J. Isotropic Holographic Metasurfaces for Dual-Functional Radiations without Mutual Interferences. Adv. Funct. Mater. 2016, 26, 29-35.

(51)

Li, Y. B.; Wan, X.; Cai, B. G.; Cheng, Q.; Cui, T. J. Frequency-Controls of Electromagnetic Multi-Beam Scanning by Metasurfaces. Sci. Rep. 2014, 4, 6921.

(52)

Shen, X. P.; Cui, T. J.; Martin-Cano, D.; Garcia-Vidal, F. J. Conformal Surface Plasmons Propagating on Ultrathin and Flexible Films. Proc. Natl. Acad. Sci. USA 2013, 110, 40-45.

(53)

Zhang, H. C.; Liu, S.; Shen, X. P.; Chen, L. H.; Li, L. M.; Cui, T. J. Broadband Amplification of Spoof Surface Plasmon Polaritonsat Microwave Frequencies. Laser Photon. Rev. 2015, 9, 83-90.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1 The illustration of tensor coding metasurface and structure design. (a) The structure of the coding particle, which consists of a metallic RSRR and metallic ground sheet, separated by a polyimide layer. (b) An example to demonstrate the anomalous reflection with cross-polarization, in which the y-polarized normal incidence (red arrow) is bent away from the surface normal to the


Page 28 of 37

Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


anomalous direction with the cross polarization (green arrow). (c,d) The illustrations for the PW-SW conversion. The PW-SW convertor on the right side is illuminated by a normally incident plane wave with (c) y-polarization (red arrow) and (d) x-polarization (blue arrow), which are converted to TM and TE mode SWs (purple arrows) propagating on the quartz substrate, respectively. (e) The phases and amplitudes of the cross-polarized reflections for the eight coding particles (shown at the bottom) at 0.93 THz. The phase difference between adjacent coding particles maintains around 45º and the amplitudes (S11) of all coding particles are larger than 0.8.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2 Coding patterns, scattering patterns and near-field distributions of the anomalous reflections with cross polarizations. (a) Coding pattern for the gradient coding sequence ‘001 011 101 111 001 011 101 111 …’ with super unit cell size 3×3. (b,d) Scattering patterns for anomalous reflections under the y- and x-polarizations at 1THz and 0.87THz, respectively. The remaining lobes at the backscattering direction (-z-direction) indicate the co-polarized scattering due to the non-ideal


Page 30 of 37

Page 31 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


polarization conversion of each coding particle. (c,e) Near electric-field distributions for the anomalous reflections under the y- and x-polarizations at 1THz and 0.87 THz, respectively.

Figure 3 Simulated electric-field distributions for the PW-SW conversion. (a,b) Electric-field distributions (Ex and Ey components) for the TM-mode SWs at 0.75 THz, respectively. The obvious difference between the Ex and Ey components of electric fields indicates that the y-polarized normal incidence is converted to TM-mode SW. (c,d) Electric-field distributions (Ey and Ex components) for the TE- mode SWs at 1.05 THz, respectively. The lower intensity of the electric field compared with the TM case is attributed to the size of the super unit cell 1×1.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4 Theoretical and simulated results of the converted SWs. (a,b) The theoretically calculated 2D (x-z plane) electric-field distributions on the quartz substrate for the TM- and TE-mode SWs, respectively. (c,d) Electric-field distributions extracted on a line normal to the substrate surface in cases Figures 3(a) and (c), respectively. Unlike the case of TM-mode SWs, most of the electric fields of the TE-mode SWs are confined inside the quartz substrate. (e,f) The theoretically calculated electric-field distributions on the line normal to the substrate surface for the TM- and TE-mode SWs, respectively.


Page 32 of 37

Page 33 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5 Fabricated sample, experimental setup and measurement results for the spatial wave mode manipulation. (a,b) Photograph and microscopy image of the fabricated sample, respectively, which covers an area of 35×35 mm2. (c,d) Schematic and photo of the experimental configuration based on rotary TDS. In the schematic illustration, the sample is illuminated by the vertically polarized THz wave (x-direction, blue arrow), which is redirected to anomalous directions with horizontal polarization (red arrow), detected by the receiving antenna that rotates around the sample from 22.5º



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

to 87.5º with a step of 5º. (e) The measured anomalous reflections as a function of the receiving angle and frequency. The scattering peak shifts to larger angles with the decrease of frequency. (f) The measured anomalous reflections versus the receiving angle at 0.7, 0.8, 0.9 and 1.0 THz, which are extracted from the four blue lines in (e). The amplitude reaches the maximum value of 0.64 at the 30º receiving angle for the curve of 1 THz.


Page 34 of 37

Page 35 of 37


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6 Experimental configuration and measured results of the PW-SW conversions. (a,b) Schematic and photo of the experimental configuration for near-field measurement system. In the schematic illustration, the THz probe could scan in the x-y plane with high precision to measure SW (red arrow) converted from the normally incident propagating wave (blue arrow) by the PW-SW convertor. (c) The time-domain signal of the TM-mode SW (Ez component) measured on the middle line of the quartz substrate from 2 to 8 mm with a step of 0.4 mm from 0 to 80 ps. The wave packet is delayed in time and broadened in shape with the increase of distance. (d) The corresponding frequency spectra from 0.4 to 1.2 THz of the time-domain signals in (c). The obvious peak in each curve from 0.71 to 0.75 represents the frequency spectrum of the measured surface wave, which gradually decreases in amplitude due to the loss of the quartz substrate. (e,f) The variations of (e) phases and (f) amplitudes of the surface waves, as the distance increases from 2 to 8 mm at 0.73 THz, which is indicated by the vertical line.


Page 36 of 37

Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Contents (TOC)


Full-State Controls of Terahertz Waves Using Tensor Coding

Recommend Documents