Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces Xiao Peng Wang, Le Le[.]
Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces Xiao-Peng Wang, Le-Le Wan, Tian-Ning Chen, Ai-Ling Song, and Xiao-Wen Du Citation: AIP Advances 6, 065320 (2016); doi: 10.1063/1.4954750 View online: http://dx.doi.org/10.1063/1.4954750 View Table of Contents: http://aip.scitation.org/toc/adv/6/6 Published by the American Institute of Physics Articles you may be interested in Broadband unidirectional acoustic cloak based on phase gradient metasurfaces with two flat acoustic lenses AIP Advances 120, 014902014902 (2016); 10.1063/1.4954326 Subwavelength diffractive acoustics and wavefront manipulation with a reflective acoustic metasurface AIP Advances 120, 195103195103 (2016); 10.1063/1.4967738 Multi-frequency acoustic metasurface for extraordinary reflection and sound focusing AIP Advances 6, 121702121702 (2016); 10.1063/1.4968607 Broadband manipulation of acoustic wavefronts by pentamode metasurface AIP Advances 107, 221906221906 (2015); 10.1063/1.4936762 AIP ADVANCES 6, 065320 (2016) Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces Xiao-Peng Wang,a Le-Le Wan, Tian-Ning Chen, Ai-Ling Song, and Xiao-Wen Du School of Mechanical Engineering and State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’ an Jiaotong University, Xi’ an 710049, People’s Republic of China (Received 26 March 2016; accepted 13 June 2016; published online 20 June 2016) Acoustic metasurface (AMS) is a good candidate to manipulate acoustic waves due to special acoustic performs that cannot be realized by traditional materials In this paper, we design the AMS by using circular-holed cubic arrays The advantages of our AMS are easy assemble, subwavelength thickness, and low energy loss for manipulating acoustic waves According to the generalized Snell’s law, acoustic waves can be manipulated arbitrarily by using AMS with different phase gradients By selecting suitable hole diameter of circular-holed cube (CHC), some interesting phenomena are demonstrated by our simulations based on finite element method, such as the conversion of incoming waves into surface waves, anomalous reflections (including negative reflection), acoustic focusing lens, and acoustic carpet cloak Our results can provide a simple approach to design AMSes and use them in wavefront manipulation and manufacturing of acoustic devices C 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4954750] I INTRODUCTION The wavefronts manipulation of electromagnetic and acoustic waves has attracted more and more researchers’ attention in recent years Some previous studies have demonstrated that the bulk metamaterial can be used to manipulate electromagnetic and acoustic waves However, there are some disadvantages by using the bulk metamaterial, such as large size, high energy loss, and difficult assembly Recently, researchers have focused on designing metasurfaces1–5 to manipulate the electromagnetic waves at will By designing the structure of metasurface, we can obtain some novel phenomena, such as extraordinary refraction and reflection,2,4,5 the conversion of incoming waves into surface waves,3 and fabricate a flat lens and axicons.6 The acoustic waves are also investigated all the time Fang et al.7 experimentally demonstrated that 1D acoustic waveguide composed of Helmholtz resonators can realize an effective negative modulus In order to further research this similar system, Wang et al.8 numerically investigated the defect states in different parameters and demonstrated that point defect and line defect can play an important role in Bragg gap Lemoult et al.9,10 experimentally demonstrated that acoustic waves can be controlled and focused arbitrarily by using an array of soda cans as Helmholtz resonators, and found that both electromagnetic and acoustic waves can be manipulated by tailoring resonant unit cells The manipulation of acoustic waves has attracted increasing attentions with the emergence of AMS According to the generalized Snell’s law, the metasurfaces can easily manipulate the wavefront of electromagnetic waves Therefore, if the generalized Snell’s law and the theory of metasurfaces can be successfully applied in acoustics, it will improve the performance of existing acoustic devices We can use metallic antennas, e.g., ‘V’ antenna and ‘H’ antenna, as artificial resonant a The e-mail address of the corresponding author: xpwang@mail.xjtu.edu.cn 2158-3226/2016/6(6)/065320/11 6, 065320-1 © Author(s) 2016 065320-2 Wang et al AIP Advances 6, 065320 (2016) structure to design electromagnetic metasurface.1–5 But similar counterpart has not yet appeared to design AMS So it is very difficult to design AMS Ma et al.11 proposed a method to realize AMS to absorb acoustic waves totally based on the impedance-matching concept by using acoustic metamaterial to design membrane structure which can result in hybrid resonance in a certain frequency range Besides, some researchers have demonstrated that the structure of coiling-up space or subwavelength corrugated surface can be used to design AMS with the phase change covering 0∼2π range.12–22 And then some novel phenomena are demonstrated, such as the anomalous reflection and refraction,12–18 and the planar acoustic axicon and lens.19–22 Ding et al.23,24 have proposed that the split hollow sphere and double-split hollow sphere, as acoustic resonator, can be also used to construct AMS However, they may not be effective in a broad frequency range or at a given frequency In practice, they are also difficult to fabricate and assemble In this paper, we present a new method by using some CHCs to design AMS, which can manipulate the acoustic waves at a broadband frequency range near the designed center frequency Compared with Refs and 8, our AMS is comprised of a two-dimensional array of subwavelength Helmholtz resonators and our study is focused on the phase gradient What is more, compared with Refs and 10, our broadband reflected wavefronts manipulation is performed by controlling the phase change according to the generalized Snell’ law Besides, compared with Refs 23 and 24, our CHC is easy to fabricate and assemble due to its simple geometric profile (the surface is a plane and the inside is a cylinder) In the following sections, we first introduce one CHC unit cell and use ten cells to realize discrete phase shifts from to 2π with a step of π/5 in section II In section III, some interesting phenomena, such as the conversion of incoming waves into surface waves, anomalous reflections (including negative reflection), acoustic focusing lens, and acoustic carpet cloak, will be demonstrated by selecting suitable phase gradients Finally, a brief conclusion is given in section IV II MODELING AND SIMULATIONS In this section, we investigate one unit cell whose surface is a cube and inside is a cylinder, so we call the unit cell circular-holed cube A CHC is designed as shown in Fig 1, which can be used to construct AMS The hole diameter of CHC should be selected in terms of designed frequrency 1500 Hz If the designed frequency changes, these hole diameter will be calculated again to match designed frequrency If the frequency of incident waves is closed to the natural frequency of CHC, a FIG Three-dimensional structure of CHC The length of the cube is w = 20 mm It has a cylindrical cavity with diameter D = w-2t = 19 mm and height h = w-2t = 19 mm The diameter of the hole is d (d = mm in this example) The minimum thickness of the cube shell is t = 0.5 mm 065320-3 Wang et al AIP Advances 6, 065320 (2016) FIG (a) Cross-sectional diagram of one CHC (b) The reflected phase with different hole diameters of CHC at 1500 Hz The blue dots refer to selected d for ten cells with the phase step of π/5 (c) The designed AMS made of periodic reflected arrays with ten kinds of CHCs (d) The pressure field distributions of the reflected waves by the ten cells strong resonance will appear, which is similar with a single degree of freedom vibration system by mechanical equivalent principle as shown in Fig 2(a) The air in the cavity is equivalent to a spring, which has an acoustic capacitor with the capacitance of Ca = V/(ρ0c02) and the air in the hole acts as an acoustic mass Ma = ρ0ls When the acoustic waves are incident onto the hole, frictional damping will appear So the oscillatory system has a certain acoustic resistance Ra Where V is the volume of the cavity; t is the thickness of the cube shell; ρ0 is the density of air; c0 is the sound speed in air; s= πd 2/4 is the cross-sectional area of the opening hole; and l=t+0.85d is the effective length of the hole Therefore, we can get Helmholtz equation ∇2 P + (2π/λ 0)2 P = 0, (1) f = 1/(2π MaCa ), (2) and the resonant frequency where P is acoustic pressure in air and λ0 is the wavelength of incident waves in air It is necessary to point out that our simulations are done by commercial software COMSOL Multiphysics based on Finite Element Method The simulations were calculated by the module Pressure Acoustics, Frequency Domain When the strong resonance happen, the phase of the reflected waves will change 2π continuously It is clear that the natural frequency of CHC is related to the hole diameter d So we can adjust d to obtain the desired natural frequency at will, and then control the phase of the reflected waves In order to get the relationship between the phase of the reflected waves and d, we designed a simulation as shown in Fig 2(a) The background materials designed in the simulation are air and the CHC was fabricated by steel The left face is taken as plane wave radiation boundaries, the right face is set as sound hard boundaries, and the other four faces are set as periodic boundaries as shown in Fig 2(a) The blue arrow indicates the incident waves and the red indicates the reflected waves, respectively The values of w, h and D are fixed in the simulation When only changing the values of d from 0.01 to mm at a given frequency 1500 Hz, we will find that the reflected phases cover a range of 2π as shown in Fig 2(b) So it is easy to get ten cells that could realize discrete phase shifts covering the full 2π span with a step of 065320-4 Wang et al AIP Advances 6, 065320 (2016) π/5 The exact values of d for achieving these discrete phase shifts are also illustrated with blue dots in Fig 2(b) In the simulation, a reflected array composed of ten cells is regarded as one super unit cell, and then the reflected array is periodically arranged to realize the AMS as shown in Fig 2(c) In order to further explain the phase gradient, we show the reflected waves by ten cells in Fig 2(d) When the incident waves are cast onto AMS, the high maps of pressure field are applied to show the different phase shifts of each unit cells It is therefore reasonable to believe that the AMS can be fabricated by these CHCs The AMS has a thickness equal to λ/11.3, meaning that the AMS is a good candidate to design acoustic devices, such as small footprint sonar and medical ultrasonic scanners It is no doubt that the anomalous reflection will obey the generalized Snell’ law sin (θ r ) − sin (θ i ) = (λ/2πni )(dφ/dy), (3) where θ i is the incident angle; θ r is the reflected angle; λ is the wavelength; ni is the refractive index; and dφ/d y is the phase gradient in the y-axis III RESULTS AND DISCUSSIONS A Reflected waves modulation with different phase gradient In this section, we demonstrate that the AMS can turn the incident waves into surface waves by selecting suitable phase gradients If each CHC is arrayed with the spacing distance of 25 mm, we will obtain a phase gradient of π/125 rad/mm as shown in Fig 3(a) When ten cells are sufficiently close together with the spacing distance of 25 mm, we calculate the phases of ten cells, which agree well with those of individual cells as shown in Fig 3(a) Therefore, we can simply regard the abnormal reflected wave as a new acoustic radiation by a line of secondary sources with different phases modulated by the CHC with varying hole diameters According to the generalized Snell’s law, the reflected angle at 1360 Hz will be 90◦ The simulation result is shown in Fig 3(b), which is in a good agreement with theoretical result The white and black arrows represent the incident and reflected waves, respectively In order to investigate the influence of different phase gradients of the reflected waves, we simulate a normal material with the phase gradient of ξ = rad/mm as shown in Fig 4(a) From Fig 4(a), it can be seen that the acoustic waves are normally reflected, which obeys the traditional Snell’ law As a comparison, we calculate another three kinds of AMSes (labeled as sample A, B and C) with the phase gradients of π/125 rad/mm, π/250 rad/mm, and π/375 rad/mm, respectively The anomalous reflection phenomenon not only appears at a designed frequency, but at other frequencies as well When the acoustic waves are vertically incident onto three kinds of AMSes at 1600 Hz, the pressure field distributions of the reflected waves are shown in Fig 4(b)–4(d) From the simulation results, we can get that the reflected angles are 60◦, 27◦ and 17◦, which agree FIG (a) The AMS designed with the phase gradient of ξ = π/125 rad/mm in the y-axis (b) The pressure field distribution at 1360 Hz with the reflected angle of 90◦ The white and black arrows represent incident and reflected waves, respectively 065320-5 Wang et al AIP Advances 6, 065320 (2016) FIG (a) The reflected acoustic field distribution of normal material with the phase gradient of ξ = rad/mm (b)-(d) The reflected acoustic field distributions of AMS with the phase gradient of ξ = π/125 rad/mm, ξ = π/250 rad/mm, and ξ = π/375 rad/mm, respectively well with the theoretical results 58.2◦, 25.2◦ and 16.5◦ according to the generalized Snell’s law, respectively We have discussed that the incident angle is 0◦ and the phase gradient of AMS is a positive value In this part, we will discuss the situation that the acoustic waves are obliquely incident onto the AMS and the phase gradident is a negative value When the phase gradient dφ/dy is a negative value, different incident angles will lead to different reflected angles as shown in Fig 5(a)–5(c) In Ref 24, Ding et al demonstrated that negative reflection appears in the left side of the normal We disagree with this view, because negative reflection only appears in the right side of the normal as shown in Fig 5(b) According to traditional Snell’ law, the incident and reflected waves are on both sides of the normal and the reflected angle is equal to the incident angle However, our designed AMS will break this law The AMS was fabricated by using ten kinds of CHCs as shown in Fig 2(b), which can realize the phase change covering 0∼2π with a step of −π/5 The distance of adjacent CHCs is 22 mm, which means the phase gradient of AMS is ξ = −π/110 rad/mm In order to realize negative reflection, the incident angle should be less than 52◦ when we select incident frequency from 1450 Hz to 1950 Hz The bandwidth will be illustrated later Figure 6(a) shows that the theoretical reflected angle changes with the frequency of the incident waves from 1450 Hz to 1950 Hz and with the incident angle from 5◦ to 52◦ The simulation results are shown in Fig 6(b), which agrees well with theoretical analysis When the incident angle is 15◦ at 1500 Hz, the distribution of the reflected waves can be seen in Fig 6(c) with the reflected angle of −51◦ According to the generalized Snell’s law, the reflected angle θ r = arcsin (sin (θ i ) + (λ/2πni ) (dφ/dy)) = arcsin(sin(15◦) − 34/33) = −50.5◦ The simulation result is in a good agreement with the theoretical result The white and black arrows represent the incident and reflected waves, respectively 065320-6 Wang et al AIP Advances 6, 065320 (2016) FIG (a)-(c) The distributions of the reflected angles versus different incident angles when the phase gradient is a negative value along the y-axis B The broadband of anomalous reflection At first, we consider that the anomalous reflection only happens at a designed frequency 1500 Hz as shown in Fig 7(c) But this phenomenon also appears near 1500 Hz In order to study the AMS at a broad frequency range, the sample A is selected as a research object The distributions of the reflected waves are calculated at a broad frequency range from 1400 Hz to 2000 Hz as shown in Fig 7(a)–7(f) It is clear that the anomalous reflection exists at the frequencies of 1450 Hz, 1500 Hz, 1600 Hz, and 1950 Hz with different reflected angles of 70◦, 66◦, 60◦ and 45◦, which agrees well with the theoretical values 69.7◦, 65.0◦, 58.2◦ and 44.2◦ according to the generalized FIG (a) Theoretical reflection angles versus the frequency of the incident waves and incident angle (b) The reflected angle from the simulation versus the frequency of incident waves and incident angle (c) The left picture indicates the incident acoustic pressure field distribution with the incident angle of 15◦ and the right picture indicates the reflected acoustic pressure field distribution of AMS with the phase gradient of ξ = −π/110 rad/mm 065320-7 Wang et al AIP Advances 6, 065320 (2016) FIG Reflected pressure field distribution of AMS with the phase gradient of ξ = π/125 rad/mm (a) Acoustic pressure field distribution of normal reflection at 1400 Hz (b) Reflected acoustic pressure field distribution at 1450 Hz with 70◦ reflection, (c) 1500 Hz with 66◦ reflection, (d) 1600 Hz with 60◦ reflection and (e) 1950 Hz with 45◦ reflection (f) The field distribution of the acoustic scattering at 2000 Hz Snell’ law, respectively The acoustic waves will be vertically reflected at 1400 Hz as shown in Fig 7(a), which obeys the traditional Snell’ law In Fig 7(f), the reflected waves are irregular at 2000 Hz We can obtain that the AMS with the phase gradient of ξ = π/125 rad/mm can realize anomalous reflection at a broad frequency range from 1450 Hz to 1950 Hz with a bandwidth of 500 Hz, which will open a new door to for our AMS to acoustic applications When the frequency is near the designed frequency 1500 Hz, a strong resonance of CHCs appears, which means that the reflected amplitude of CHCs is equal to and the reflected phases of CHCs are the designed values by the generalized Snell’ law Therefore, the anomalous manipulation of the reflected waves can be realized near 1500 Hz The similation results indicate that our designed AMS is effective in a broadband frequency range with the bandwidth of 500 Hz 065320-8 Wang et al AIP Advances 6, 065320 (2016) C Acoustic focusing lens constructed by AMS We have proved that the CHC can be used to design an AMS with an ultrathin structure which can manipulate the reflected waves at will In this section, we will show that an acoustic focusing lens can be designed successfully by our AMS In order to achieve acoustic focusing at a given position (0, f ), the hyperboloidal phase gradient is applied along the y-axis, as shown in Fig 8(a) FIG (a) Schematic diagram of acoustic focusing lens (b) The theoretical continuous phase shifts (red line) and the discrete phase gradient provided by AMS (blue dots) along the y-axis (c) The distribution of the acoustic pressure field for the designed lens (d) Transverse cross-section of intensity distribution at y = mm along the z-axis (e) Spatial intensity distribution |p|2 (f) Transverse cross-section of intensity distribution at z = 634 mm along the y-axis The blue dash line refers to the intensity of the incident waves 065320-9 Wang et al AIP Advances 6, 065320 (2016) The phase shift φ( y) is required as follows: φ ( y) = k · ( ) y2 + f − f , (4) where k is the wave vector and f is the focal length According to the generalized Snell’ law, the desirable continuous phase gradient (red line) and the discrete phase gradient (blue dots) provided by the AMS are plotted in Fig 8(b) The acoustic focusing lens can be designed by 29 CHCs according to the phase gradient The acoustic pressure field distribution with f = 3λ (λ = 21.25 cm) is shown in Fig 8(c) The transverse cross-section intensity distribution at y = mm along the z-axis is shown in Fig 8(d) Spatial intensity distribution |p|2 of acoustic focusing is shown in Fig 8(e) In order to further quantify the focusing effect of the acoustic focusing lens, the transverse cross-section intensity distribution at z = 634 mm along the y-axis is shown in Fig 8(f) The intensity of pressure at the focal spot is nearly 15.1 times larger than that of the incident waves as shown in Fig 8(f) with blue dash line, which shows a excellent focusing effect D Acoustic carpet cloak designed by AMS Yang et al.25 have demonstrated that a metasurface carpet cloak constructed by AMS can be used to hide large objects In this section, we demonstrate that acoustic carpet cloak can also be FIG (a)-(c) Reflected pressure field distribution when the acoustic waves are incident onto a flat wall, onto the object without cloak, and onto the object with cloak vertically, respectively (d)-(f) Total pressure field distribution when the acoustic waves are incident onto a flat wall, onto the object without cloak, and onto the object with cloak vertically, respectively (g) Local reflected phase of each unit cell 065320-10 Wang et al AIP Advances 6, 065320 (2016) designed by our AMS We simulate a triangle acoustic carpet cloak with the incident angle of 0◦ The outline of the triangle object is expressed as: z = −0.577 | y | + 11w (−19w < y < 19w), (5) where w is the length of CHC When the acoustic waves are incident onto the triangle object vertically without cloak, the phase of the reflected waves is distorted by the object as shown in Fig 9(b) In order to reconstruct the reflection field and compensate the phase difference, we use acoustic carpet cloak to cover this object by recovering the reflected phase at each point The reflected phase should be expressed as φ = −2k z, (6) where k0 is the wave vector in air; z is the height of each unit cells from the ground The reflected phase of each unit cells is shown in Fig 9(g) The distance of adjacent unit cells is mm The non-detectability effect of acoustic carpet cloak is given in Fig 9, where (a)-(c) and (d)-(f) are reflected pressure field distributions and total pressure field distributions, respectively When the acoustic waves are incident onto a flat wall, the distributions of the reflected pressure field and total pressure field are shown in Fig 9(a) and 9(d), respectively As expected, with only an object, the distributions of reflected pressure field and total pressure field will be distorted as shown in Fig 9(b) and 9(e), respectively After covering the object with acoustic carpet cloak constructed by our AMS, we find that the distributions of reflected pressure field and total pressure field are recovered as shown in Fig 9(c) and 9(f), respectively By comparison, the simulation results verify the non-detectability effect of acoustic carpet cloak, which can be used to hide large objects IV CONCLUSIONS In summary, we have proved that the AMS can be designed by periodic reflected array with ten CHCs, which can control the reflected waves at will It has been demonstrated that the conversion of incoming waves into surface waves and the anomalous reflections including negative reflection can be realized by employing linear phase gradient, which follows the generalized Snell’ law The simulation results also showed that the anomalous reflection of our designed AMS not only exists at a designed center frequency, but also can be obtained in a broadband frequency range with the bandwidth of 500 Hz Furthermore, acoustic focusing lens can be constructed by using the hyperbolic phase gradient Finally, acoustic carpet cloak can aslo be designed by our AMS to hide large objects It is meaningful that the AMS composed of ten CHCs can be easily realized in experiment Our results have potential applications in acoustic imaging, medical ultrasound and the non-detectable cloak of warship ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the National Basic Research Program of China (No.2011CB610306), the Project of National Natural Science Foundation of China (No.51275377), and Collaborative Innovation Center of Suzhou Nano Science and Technology N.F Yu, P Genevet, M.A Kats, F Aieta, J.-P Tetienne, F Capasso, and Z Gaburro, Science 334, 333–7 (2011) X.J Ni, N.K Emani, A.V Kildishev, A Boltasseva, and V.M Shalaev, Science 335, 427 (2012) S.L Sun, Q He, S.Y Xiao, Q Xu, X Li, and L Zhou, Nat Mater 11, 426 (2012) S.L Sun, K.Y Yang, C.M Wang, T.K Juan, W.T Chen, C.Y Liao, Q He, S.Y Xiao, W.T Kung, G.Y Guo, L Zhou, and D.P Tsai, Nano Lett 12, 6223 (2012) C Pfeiffer and A Grbic, Phys Rev Lett 110, 197401 (2013) F Aieta, P Genevet, M A Kats, N.F Yu, R Blanchard, Z Gaburro, and F Capasso, Nano Lett 12, 4932–4936 (2012) N Fang, D Xi, J Xu, M Ambati, W Srituravanich, C Sun, and X Zhang, Nat Mater 5, 452-456 (2006) Z.G Wang, S.H Lee, C.K Kim, C.M Park, K Nahm, and S.A Nikitov, J Appl Phys 103, 064907 (2008) F Lemoult, M Fink, and G Lerosey, Phys Rev Lett 107, 064301 (2011) 10 F Lemoult, N Kaina, M Fink, and G Lerosey, Nat Phys 9, 55-60 (2013) 11 G.C Ma, M Yang, S.W Xiao, Z.Y Yang, and P Sheng, Nat Mater 13, 873 (2014) 12 K Tang, C.Y Qiu, M.Z Ke, J.Y Lu, Y.T Ye, and Z.Y Liu, Sci Rep 4, 06517 (2014) 065320-11 13 Wang et al AIP Advances 6, 065320 (2016) Z.M Gu, B Liang, X.Y Zou, and J.C Cheng, EPL 111, 64003 (2015) B.G Yuan, Y Cheng, and X.J Liu, Appl Phys Express 8, 027301 (2015) 15 S.L Zhai, H.J Chen, C.L Ding, F.L Shen, C.R Luo, and X.P Zhao, Appl Phys A 120, 1283–1289 (2015) 16 H.T Sun, Y Cheng, J.S Wang, and X.J Liu, Chinese Phys B 24, 104302 (2015) 17 Y.F Zhu, X.Y Zou, B Liang, and J.C Cheng, Appl Phys Lett 107, 113501 (2015) 18 Y.F Zhu, X.Y Zou, B Liang, and J.C Cheng, Appl Phys Lett 106, 173508 (2015) 19 Y Li, B Liang, Z.M Gu, X.Y Zou, and J.C Cheng, Sci Rep 3, 02546 (2013) 20 Y Li, X Jiang, R.Q Li, B Liang, X.Y Zou, L.L Yin, and J.C Cheng, Phys Rev Appl 2, 064002 (2014) 21 Y.F Zhu, X.Y Zou, R.Q Li, X Jiang, J Tu, B Liang, and J.C Cheng, Sci Rep 5, 10966 (2015) 22 Y.B Xie, W.Q Wang, H.Y Chen, A Konneker, B.-I Popa, and S.A Cummer, Nat Commun 5, 5553 (2014) 23 C.L Ding, H.J Chen, S.L Zhai, S Liu, and X.P Zhao, J Phys D Appl Phys 48, 045303 (2015) 24 C.L Ding, X.P Zhao, H.J Chen, S.L Zhai, and F.L Shen, Appl Phys A 120, 487–493 (2015) 25 Y.H Yang, H.P Wang, F.X Yu, Z.W Xu, and H.S Chen, Sci Rep (2016) 14 ...AIP ADVANCES 6, 065320 (2016) Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces Xiao-Peng Wang,a Le-Le Wan, Tian-Ning Chen, Ai-Ling... our study is focused on the phase gradient What is more, compared with Refs and 10, our broadband reflected wavefronts manipulation is performed by controlling the phase change according to the... continuous phase gradient (red line) and the discrete phase gradient (blue dots) provided by the AMS are plotted in Fig 8(b) The acoustic focusing lens can be designed by 29 CHCs according to the phase