diff --git "a/69E1T4oBgHgl3EQfBgJT/content/tmp_files/load_file.txt" "b/69E1T4oBgHgl3EQfBgJT/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/69E1T4oBgHgl3EQfBgJT/content/tmp_files/load_file.txt" @@ -0,0 +1,839 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf,len=838 +page_content='Coherent control of wave beams via unidirectional evanescent modes excitation Shuomin Zhong1*,∗ Xuchen Wang2*, and Sergei A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Tretyakov3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' School of Information Science and Engineering, Ningbo University, Ningbo 315211, China 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Institute of Nanotechnology, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Department of Electronics and Nanoengineering, Aalto University, Finland Conventional coherent absorption occurs only when two incident beams exhibit mirror symmetry with respect to the absorbing surface, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', the two beams have the same incident angles, phases, and amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In this work, we propose a more general metasurface paradigm for coherent perfect absorption, with impinging waves from arbitrary asymmetric directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' By exploiting excitation of unidirectional evanescent waves, the output can be fixed at one reflection direction for any amplitude and phase of the control wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We show theoretically and confirm experimentally that the relative amplitude of the reflected wave can be tuned continuously from zero to unity by changing the phase difference between the two beams, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' switching from coherent perfect absorption to full reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We hope that this work will open up promising possibilities for wave manipulation via evanescent waves engineering with applications in optical switches, one-side sensing, and radar cross section control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' INTRODUCTION Coherent control of propagation of a wave beam by tuning the amplitude and phase of another beam is a very promising approach to realize ultra fast optical devices for optical computing, sensing, and other applications [1– 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' One of the most important effects in coherent control of light is coherent perfect absorption [12–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In these devices, the level of absorption of one beam illuminating a thin sheet is controlled by another coherent beam that illuminates the same sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In earlier works, coherent perfect absorption (CPA) was achieved only when with illumination from different sides of a homogeneous lossy layer and for two incident waves at the same angle [12, 13, 15, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The mecha- nism of coherent perfect absorption is destructive cancel- lation of all scattered beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For homogeneous coher- ent perfect absorbers, there are only specular reflection and non-diffractive transmission, allowing coherent ab- sorption only with illumination of both sides and at the same incidence angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' From the theoretical point of view and for many applications, it is important to achieve co- herent control of output for illuminations from the same side of the metasurface sheet at two or more arbitrary incidence angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [17, 18, 23], coherent perfect absorption and scattering for two angularly asymmetric beams are realized by using surface plasmon-polariton (SPP) excitation at silver-based diffraction groove grat- ings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' However, such plasmonic grating designs have limi- tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In particular, the structures are non-planar and operate only for TM modes at optical frequencies, where SPP are supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Moreover, there are always two out- put beams for different values of the phase of the control waves, one of which may cause undesired noise to the useful output signal due to parasitic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This is- sue is critical in applications such as optical computing [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' ∗ Email: zhongshuomin@nbu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='cn, xuchen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='wang@kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='edu In this decade, the emergence of gradient metasurfaces [25–28] and metagratings [29–35] has opened a new av- enue for manipulation of light for arbitrary incidence an- gles and versatile functionalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For periodical metasur- faces or metagratings with the period larger than half of the wavelength, the incident plane wave from one direc- tion will be scattered into multiple directions, and the power carried by the incident wave can be redistributed among a number of diffraction modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Based on this concept, several metasurface devices with perfect anoma- lous reflection working at microwaves [36, 37] and optical bands [38] have been developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' However, in these previ- ous works, the functionality of metasurfaces is designed only for one incident angle and the response for other illu- minations is actually not considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To design metasur- faces with coherent control functions for multiple simul- taneously incident coherent beams from different direc- tions, the matching conditions of amplitude, phase, and wavevector(direction) of the scattering modes between all incidences are required [35, 39, 40], which is almost an impossible task using traditional gradient phase methods [25, 36] and brute-force numerical optimizations [37, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In this work, we perform inverse designs of CPA meta- surfaces by solving the surface impedance satisfying the boundary condition determined by two coherent incident waves from two arbitrary angles and the desired total scattered waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The engineering of evanescent waves in the scattered fields without altering the desired far- field outputs provides significant freedom in the CPA metasurface design, making another functionality of co- herent control of reflection with a single direction possi- ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It is demonstrated that excitation of unidirectional evanescent waves propagating along the surface in the direction of the incident-wave wavevector can be used to achieve single-direction output in coherently controlled optical devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Furthermore, a mathematical optimiza- tion method based on scattered harmonics analysis [42] is utilized to find the surface-impedance profile that si- multaneously ensures the CPA and coherent maximum reflection (CMR) in a single direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thereafter, the arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='02852v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='app-ph] 8 Jan 2023 2 substrate parameters are invoked as additional degrees of freedom in the optimization model, realizing reflection ef- ficiency of 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As an example, we experimentally vali- date the CPA gradient metasurface design in microwaves for TE-polarized waves by engineering the Indium Tin Oxide (ITO) film mounted on a grounded dielectric sub- strate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It is showed that the normalized output power can be continuously controlled between 0 and 1 by tun- ing the phase of the control wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' DESIGN CONCEPT Dx x z Zs(x) θ1 θ2 I1 I2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' General scattering scenario for a periodically modu- lated impenetrable impedance surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Two coherent beams I1 and I2 are simultaneously incident from two angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Let us consider an impenetrable reciprocal metasur- face whose surface is periodically modulated along the x-direction, with the period Dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The surface is in the xy-plane of a Cartesian coordinate system (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The metasurface is simultaneously illuminated by two TE(s)-polarized plane waves I1 and I2 at the incidence angles θ1 and θ2 (θ1 > θ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The electric field amplitudes of the two beams I1 and I2 is E1 = E0 and E2 = αE0, respectively (α is the amplitude ratio).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The phase differ- ence between them is ∆φ=0, defined at the origin point (x = 0, z = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The electromagnetic properties of the metasurface can be characterized by the locally-defined surface impedance that stands for the ratio of the tangen- tial electric and magnetic field amplitudes at the surface plane Zs(x) = Et(x)/Ht(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The field reflected by a periodically modulated meta- surface can be interpreted as a sum of Floquet harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The tangential wavenumber of the n-th harmonic is re- lated to the period and the incident wavenumber k0 as krxn = k0 sin θi + 2πni/Dx, where i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The corre- sponding normal component of the reflected wavenumber equals krzn = � k2 0 − k2rxn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' If |krxn| is greater than the incident wave number, the wave is evanescent and it does not contribute to the far field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the harmonic wave sat- isfying |krxn| < k0, krzn is real, and this wave is propagat- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The evanescent harmonics will be dissipated by the lossy surface and the propagating harmonics will propa- gate into the far-zone at the angles θrn = arcsin(krxn/k0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In order to achieve coherent perfect absorption, it is nec- essary (but not sufficient) to ensure that all the diffracted propagating modes of two beams have the same set of angles θrn, that allows mutual cancellation, defining the period Dx = λ0/(sin θ1 −sin θ2) [43], where λ0 stands for the wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Our aim is to achieve coherent perfect absorption for two coherent in-phase waves simultaneously incident on the metasurface at two different angles θ1 and θ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' First, let us assume that no evanescent waves are excited for these two illuminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the CPA case, there should be no reflected field at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thus, the tangential components of the total electric field at the plane z = 0 can be written as Et(x) = E0(e−jk0 sin θ1x+αe−jk0 sin θ2x), where the time-harmonic dependency in the form ejωt is assumed and suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The corresponding total magnetic field reads Ht(x) = E0(cos θ1e−jk0 sin θ1x + α cos θ2e−jk0 sin θ2x)/Z0, with Z0 = � µ0/ϵ0 being the free-space wave impedance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The ratio of these electric and magnetic fields gives the required surface impedance ℜ(Zs) = Z0 cos θ1 + α2 cos θ2 + α cos Φ(cos θ1 + cos θ2) cos2 θ1 + α2 cos2 θ2 + 2α cos θ1 cos θ2 cos Φ , ℑ(Zs) = Z0 α(cos θ1 − cos θ2) sin Φ cos2 θ1 + α2 cos2 θ2 + 2α cos θ1 cos θ2 cos Φ, (1) where Φ = k0(sin θ1 − sin θ2)x is the linearly varying phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The real and imaginary parts of the surface impedance are even and odd functions of x, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As is seen from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (1), the periodicity of the surface impedance is D = λ0/(sin θ1 − sin θ2), in accord with the above analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For passive metasurfaces, the real part of the surface impedance must be non-negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Con- sequently, the amplitude ratio should satisfy α ≥ 1 or α ≤ cos θ1/ cos θ2 to ensure passive solution for CPA by the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As an example, we consider two incident waves with incidence angles of (θ1, θ2) = (45◦, 0◦) and the same am- plitude, assuming α = 1 for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (Other scenarios with (θ1, θ2) = (60◦, −30◦), (75◦, 15◦) are illustrated in the Supplemental Materials[43], corresponding to differ- ent surface impedance profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=') As is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(a), everywhere on the surface its resistance is non-negative, demonstrating that passive gradient periodic surfaces can realize CPA for two asymmetric incident beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To analyze the mechanism of CPA by the periodic impedance surface further, we can determine the ampli- tudes of all the Floquet scattered harmonics for general plane-wave illumination, using the method reported in [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The total reflected field can be represented as an infinite sum of Floquet harmonic modes: Er = ∞ � n=−∞ Ane−jkrznze−jkrxnx, (2) where An is the complex amplitude of the n-th Floquet harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Because the surface modulation is periodical, the surface admittance Ys(x) = 1/Zs(x) can be expanded 3 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8 1 200 0 200 400 (a) 8 6 4 2 0 2 4 6 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5 (b) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8 1 200 0 200 400 (c) 6 4 2 0 2 4 6 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5 (d) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (a) Analytical surface impedance over one period to realize CPA for two incidence beams with (θ1, θ2) = (45◦, 0◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (b) Magnitudes of the complex amplitudes of different Floquet scattered harmonics (normalized by the amlpitude of the incident electric field E0) when the gradient surface is illuminated by single-beam incidences at 45◦ and 0◦, and for two- beam incidences in phase and out of phase, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (c) Optimized surface impedance profile over one period to realize CPA for in-phase incidences and single-direction reflection for out-of-phase incidences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The optimized Fourier coefficients of Ys(x) read g0 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='654 × 10−3 + j1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='724 × 10−11, g1 = −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='770 × 10−4 − j1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='045 × 10−10, g2 = −(6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='565 + j4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='581) × 10−5, g3 = −9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='143×10−8 +j5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='720×10−6, g4 = (−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='644+j1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='992)×10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (d) Amplitudes of scattered harmonics when the optimized gradient surface in (c) is illuminated by single-beam incidences at 45◦ and 0◦, and for two-beam incidences in phase and out of phase, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' into Fourier series: Ys(x) = +∞ � n=−∞ gne−j2nπx/D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (3) A Toeplitz matrix Ys which we call the admittance ma- trix is determined only by the Fourier coefficients of the modulation function and filled with Ys(r, c) = gr−c at the r-th row and c-th column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The reflection matrix is found as [44] Γ = (Y0 + Ys)−1 (Y0 − Ys), (4) where Y0 = Z−1 0 is a diagonal matrix with its main entry representing the admittance of each space har- monic, which is Y0(n, n) =krzn/ω0µ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The amplitudes An of reflected harmonics for a given m-th order Flo- quet harmonic of the incident wave can be calculated as An = Γ(n, m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Note that Γ is a (2N + 1) × (2N + 1) square matrix and the columns and rows of Γ are indexed from −N to +N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' When the surface is illuminated by two waves simultaneously, the amplitudes of all the Floquet harmonics are linear superpositions of all harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As is seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(b), when the two incident waves are in phase, all the harmonics have zero amplitude, meaning that CPA with no reflected fields occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' How- ever, when the two incident waves are out of phase, the reflected harmonics come out, including both propagat- ing modes and evanescent ones, proving that the perfect absorption effect is phase-coherent, different from perfect absorption for two angles [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To understand the mech- anism of CPA in the metasurface better, the harmonics 4 of the reflected field when single beams illuminate the surface separately are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(b), the complex amplitudes of every scattered harmonic are equal and 180◦ out of phase (the phases are not shown here) for 45◦ and 0◦ incidences, resulting in destructive cancellation when the two beams illuminate simultane- ously in phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Here, the propagating harmonic of the order n = 0 is defined at the specular direction of θ1 for both incidences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' By properly designing the metasurface with the periodicity of D = λ0/(sin θ1 − sin θ2), three propagating modes corresponding to n = 0, −1, −2 are created, and all the diffracted modes for both incidences have the same wave vectors, ensuing coherent interfer- ence for all corresponding harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the out-of-phase incidence case, the amplitudes of all the scattered har- monics double as compared to the single-beam case, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The analytical method to solve the surface impedance boundaries used above is based on the objective to real- ize CPA with the amplitudes of both scattered propagat- ing and evanescent harmonics being zero when two co- herent beams illuminate the metasurface simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Indeed, the amplitudes of evanescent surface modes can be nonzero without breaking the CPA condition, because they do not radiate into the far zone and their power will be dissipated at the lossy surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thus, the so- lution of the surface impedance to achieve CPA is not unique if a certain set of evanescent waves with unknown complex amplitudes is excited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In addition to CPA, we invoke another functionality of coherent control of reflec- tion with single direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' eliminating the unwanted outgoing beams at n = −1, −2 orders and keeping the n = 0 order with the maximal amplitude, when the two coherent incident beams are out-of-phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In this case, finding the complex amplitudes of infinite numbers of evanescent modes for each incidence scenario is difficult or even impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thus, instead of using the analyti- cal method of calculating the surface impedance profile according to the total fields on the boundary, we ap- ply a mathematical optimization algorithm described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [42] and based on the scattering matrix calculation to find a surface impedance profile that simultaneously ensures the coherent control capability for absorption and reflection of the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' First, the metasurface is mod- elled as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To suppress propagating modes at the negative orders (n = −1, −2) and ensure that only the reflection channel at 45◦ is open, the Fourier series of the surface admittance Ys(x) are set to be unilateral as Ys(x) = �4 n=0 gne−j2nπx/D with non-negative-order se- ries coefficients being nonzero (only five coefficients from g0 to g4 are used for improving optimization efficiency).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This setting is reasonable because the unilateral surface admittance, making the admittance matrix Ys a lower triangular matrix, can lead to the reflection matrix Γ also being a lower triangular matrix, as is seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Consequently, the scattered modes contain only components of non-negative orders (n ≥ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This effect highlights the role of unidirectional evanescent fields as a mechanism of suppressing propagating modes at the negative orders (n = −1, −2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Moreover, to ensure that the grid is a passive metasurface, we need to impose con- straints ℜ(Ys) ≥ 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', ℜ(g0) ≥ |g1| + |g2| + |g3| + |g4|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Secondly, the optimization goal is formulated as 6 ob- jectives, including (|A0|, |A−1|, |A−2|) = (0, 0, 0) for the in-phase scenario, and (|A0|, |A−1|, |A−2|) = (A0max, 0, 0) for the out-of-phase scenario, where A0max is the maxi- mum magnitude of reflection in the out-of-phase case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In each trial of the optimization, an array of gn is as- sumed, and the value of all the objectives are calcu- lated using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The sum of errors calculated for all the objectives is defined as a cost function C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' By em- ploying MultiStart and fmincon optimization algorithms, the maximum magnitude of the out-of-phase reflection A0max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='34 is searched out, and the minimum value of C close to zero is achieved, meaning that the solu- tions of the impedance profile to realize the desired EM responses including CPA and single-direction-reflection are obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Figure 2(c) shows a typical optimized solution of the surface impedance, which exhibits positive resistance ev- erywhere along the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The calculated ampli- tudes of scattered harmonics for single-beam incidences at 45◦ and 0◦, and for two-beam incidences in phase and out of phase, for the impedance profile in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(c), are given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(d), revealing the unilateral characteristic of scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We can see that the propagating compo- nents at n = −1, −2 orders are suppressed successfully by exciting the unidirectional evanescent wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The only remaining propagating reflected channel is n = 0 order at the outgoing angle of 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' When two incoming beams are in phase, the reflected propagating harmonic (n = 0) of each beam cancel each other because they have the same amplitude and π-reflection-phase difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Dis- tinct from the zero-amplitude of all the harmonics for the in-phase CPA scenario in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(b), the CPA in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(d) occurs with non-zero-amplitude evanescent modes in the n ≥ 1 orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The amplitude of reflected electric field at 45◦ (n = 0) is doubled into A0max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='34 when two incoming beams are out of phase (∆φ = π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We can conclude that the reflected power at 45◦ can be contin- uously controlled by phase tuning of the control beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' When the two beams are out of phase, the reflected power normalized by the incident beam power at 45◦ has the maximum reflection efficiency of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='56 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' OPTIMIZATION AND PRACTICAL DESIGN Low efficiency of the above design based on the im- penetrable impedance model calls for optimization with the help of additional degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' One possibility can be the use of one or more parameters of the actual implementation of the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In general, the impedance surface in the impenetra- ble model used above can be realized as a periodic metal 5 x z q1 D h I1 I2 n = 0 n = -1 n = -2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Schematics of reflection amplitude modulation for two coherent waves with the phase difference ∆φ incident on a periodic sheet over a grounded dielectric slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The amplitude of the output beam is modulated continuously by varying ∆φ, and switched between 0 (coherent perfect absorption) and 1 (coherent maximum reflection) when ∆φ is switched between even and odd multiples of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' pattern on a thin grounded dielectric slab, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The structure can be considered as a grid admit- tance of the top pattern with a shunt admittance of the grounded substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The characteristic admittance ma- trix Yd of the grounded substrate contains only diagonal terms Yd(n, n), where Yd(n, n) is the admittance of the n-th harmonic, and it is expressed as Yd(n, n) = kd rzn/[jµ0ω0 tan(kd rznh)], (5) where kd rzn = � ω2 0ϵ0ϵdµ0 − k2rxn is the normal compo- nent of the wavevector in the substrate (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='S23 of the Supplemental Material of [42]), ϵd and h are the permittivity and thickness of the substrate, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The reflection matrix is calculated as Γ = (Y0 + Yg + Yd)−1(Y0−Yg−Yd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' When the thickness h is ultra-thin compared with the wavelength, for low-order harmonics we have tan(kd rznh) ≈ kd rznh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As is seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (5), the admittance for low-order harmonics equals approxi- mately to 1/(jµ0ω0h), unrelated to the harmonic num- ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thus, we can approximately design the top surface with the grid admittance Yg(x) = 1/Zs(x) − Yd(0, 0) us- ing the optimized surface impedance Zs(x) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 2(c), similar to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Due to the lack of freedom in the sub- strate design, the evanescent fields engineering is quite limited in the impenetrable model, resulting in a low reflection efficiency (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='56 %) in the out-of-phase sce- nario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In order to implement CPA with a high reflec- tion efficiency, we need to use the substrate parameters as additional degrees of freedom in the design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Since the admittance of the grounded substrate with a moderate thickness strongly depends on the harmonic number, the need of complicated matrix operations makes it impos- sible to analytically solve the grid impedance and sub- strate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Thus, the optimization algorithm is extended by introducing the admittance matrix Yd of the grounded substrate, as described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [42], to search for an optimum solution for the grid impedance profile and substrate thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' According to the results of the impenetrable model, the period of the impedance sheet modulation is set to D = λ0/ sin 45◦, with three propagating channels at −45◦, 0◦, and 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The Fourier series of the grid admit- tance is set to be unilateral as Yg(x) = g0 + g1e−j2πx/D, ensuring that only the reflection channel at 45◦ is open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the optimization process, two Fourier terms g0 and g1 with four unknowns (the real and imaginary parts) are considered here to reduce complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The substrate thickness h is another unknown, and an available sub- strate with the permittivity ϵd = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8(1 − j0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='002) is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The optimization goal is formulated as 6 objectives, the same as the objectives in the impenetrable model above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The constraints ℜ(Yg) ≥ 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', ℜ(g0) ≥ |g1| are imposed to ensure the grid to be a passive metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Addi- tionally, to make the reactance easier to implement by patterning a thin conductive surface, another constraint ℑ(g0) ≥ |g1| is set to ensure that the surface reactance is always capacitive at all points of the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The maximum magnitude of reflection A0max in the out-of-phase scenario is searched out to be about 1 in the optimization, meaning that a reflection beam at 45◦ with amplitude equal to the incident beam I1 is obtained [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It reveals that the invocation of sub- strate design provides an important additional degree of freedom in engineering auxiliary evanescent modes to find a surface impedance that can realize the desired optimum scattering properties for all incidence scenar- ios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The optimized Fourier coefficients of the grid ad- mittance Yg(x) read g0 = (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='599 + 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='054j) × 10−3 and g1 = (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='807 + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='463j) × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The optimal substrate thickness is h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2525λ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The required grid impedance which is passive and capacitive along the metasurface is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Next, we analyse the scattered harmonics for the de- signed impedance sheet on the metal-backed dielectric substrate [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The reflection coefficient of the metasurface has the same magnitude of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5 at n = 0 order for 45◦ and 0◦ single-beam incidences, resulting from destructive interference when these two beams are in phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the out-of-phase scenario, the normalized magnitude of the reflected field at n = 0 order (45◦) is about unity, which means that the reflected power effi- ciency reaches 100% (normalized by the incoming power of the 45◦ beam).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Parasitic reflections into other direc- tions (n = −1, −2) are seen to be negligible, due to the unilateral property of the admittance of the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The evanescent harmonics are also unidirectional, but quite weak with the magnitude of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='008 at n = 1 order, and they are absorbed by the lossy structure, ensuring a CPA state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Figure 4(c) illustrates the phase-controlled modu- lation of reflections at three propagating orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The re- flection coefficient at 45◦ can be continuously controlled from 0 to 1 by phase tuning, with the other two par- asitic reflections maintained very close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This phase-sensitive modulation between CPA and coherent 6 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8 1 200 100 0 100 (a) 8 6 4 2 0 2 4 6 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5 1 (b) 0 1 2 ( ) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8 1 Amplitude (|An|/E0) n=0 n=-1 n=-2 (c) 𝐸𝑠𝑐/𝐸0 1 0 1 2 3 2 3 Df = 0 Df = p (d) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (a) The optimized and discretized grid impedance distribution over one period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (b) Amplitudes of the scattered harmonics when the optimized gradient metasurface is illuminated by a single beam at 45◦ and 0◦, and for two-beam in-phase and out-of-phase illuminations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (c) The normalized amplitudes of three propagating harmonics (n = 0, −1, −2) with a varying phase difference ∆φ between incidences at 45◦ and 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (d) The scattered electric fields and power density flow distributions for the metasurface modeled by the discretized grid impedance (step-wise approximation, 6 subcells per period) on top of a grounded dielectric substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Two plane-wave incidences are in phase (left) and out of phase (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' maximum reflection (CMR) without parasitic reflections is important in light switching applications where a low- return-loss characteristic is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' See the Supplemen- tal Animation [43] for the switch of reflected beam by an incident phase-controlled wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In implementations, the influence of discretization on the metasurface performance is an important factor (see detailed analysis of scattered harmonics versus the num- ber of subcells in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [43]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We use six subcells over a period and each discretized impedance value is set at the central point of each subcell, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The scattered fields from the ideal impedance sheet on the metal-backed dielectric slab for both in-phase and out-of-phase incidences are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4(d), using full-wave simulations in Comsol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The reflected field dis- tribution confirms that the metasurface with six subcells per period possesses the desired response: nearly per- fect absorption with reflection amplitude of only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='023 for two in-phase illuminations and nearly total reflection at 45◦ for two out-of-phase illuminations, relative to the intensity of the 45◦ incidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It is seen that the top lossy sheet and reflective ground separated by the slab act as a leaky-wave cavity with enhanced fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the in-phase scenario, the direct reflections of the top surface and leaky wave components of the cavity destructively cancel out, and all the power is absorbed by the lossy surface, causing CPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' By changing the initial phase dif- ference between the two coherent incidences into π, con- structive interference occurs among these components, which results in nearly total reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Note that in the out-of-phase case a half of the total incoming power (two incident beams) is still absorbed by the lossy surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' PHYSICAL IMPLEMENTATION AND EXPERIMENTAL VALIDATION The theory above is general and applies to any fre- quency, and we choose the microwave band for a proof of concept demonstration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The required impedance pro- file at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz is realized using an ITO film with the surface resistance of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5 Ω/sq supported by a grounded 7 f (GHz) 12 13 14 15 16 17 18 E/ciency 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content="8 1 90 9-1 9-2 9'0 9'-1 9'-2 Simulated (a) Transmitting antenna Receiving antenna Metasurface Scanning track (b) 3r (deg) 80 -60 -40 -20 0 20 40 60 80 S21;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='m (dB) 120 110 100 90 80 70 60 3i = 0o 3i = 45o (c) f (GHz) 12 13 14 15 16 17 18 E/ciency 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content="8 1 90 9-1 9'0 Measured (d) FIG." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (a) Simulated and (d) measured reflection efficiency spectrum for different diffracted modes of each single beam at 0◦ (solid lines) and 45◦ (dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (b) Schematic of the experimental setup (top) and photograph of the fabricated sample (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (c) Signals at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz measured by the receiving antenna at different orientation angles with the transmitting antenna at 0◦ and 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' dielectric slab with the thickness h = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='95 mm, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The detailed parameters and struc- tures of each unit cell are presented in the Supplementary Material[43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Due to the resolution limitation of picosec- ond laser micro-processing, the complex grid impedance is implemented as six subcells, and each subcell is divided into four equal sub-subcells in order to make the local design of the gradient impedance more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' By struc- turing the homogeneous resistive ITO film into I-shaped cells, the required grid resistance and reactance on a sur- face in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 4(a) can be created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For y-polarization inci- dent waves, such I-shaped resonators can be modeled as RLC series circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The required resistance is realized by tailoring the width and length of the ITO strips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Smaller width and longer length result in higher grid resistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The required reactance can be tailored by adjusting ca- pacitance of the gap, which can be increased by narrow- ing the gap or increasing the length or width of the bar, with a small influence on the resistive part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The 5th and 6th subcells degenerate into strips, to implement resistive parts as close to the theoretical value as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' How- ever, there are still deviations of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 Ω and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='1 Ω from the theoretical resistances of the 5th and 6th subcells, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The deviation can be eliminated if an ITO film with a lower surface resistance is utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To sim- plify the fabrication process, we neglect this deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The impact is analyzed theoretically, showing that the reflection amplitude in the in-phase scenario increases from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='023 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='065, which is tolerable in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Since the two beams with 0◦ and 45◦ incidence angles illuminate the surface simultaneously, all the elements should have angle-independent surface impedances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The OLMS EILMS SWAi CILAS S-iD SWAiN SWiM SWi8 I-shaped resonators have angle-insensitive impedance un- der TE incidences, satisfying this requirement [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the strips of the 5th and 6th subcells, narrow slits are cut out to reduce the angular sensitivity of the impedance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' All the subcells have been optimized with the geometrical dimensions specified in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Figure 5(a) shows the simulated frequency response of the metasurface for the normal and 45◦ incidences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the normal illumination, strong reflections occur at n = −1 and n = 0 harmonics (denoted as ξ−1 and ξ0), and the amplitude of the n = −2 scattered propagating mode is nearly zero in the whole frequency band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The reflection at the n = −1 mode (specular reflection at 0◦) also has a near-zero dip at the design frequency of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz, and the reflection efficiency at the n = 0 mode(anomalous re- flection at 0◦) is about 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='9% (the relative amplitude is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Note that for anomalous reflection, the efficiency is calculated as ξ = (Er/Ei)2cos θr/cos θi [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the 45◦ illumination, the reflections at both n = −1 and n = −2 modes (ξ′ −1 and ξ′ −2) are close to zero, and the efficiency at the n = 0 mode (ξ′ 0) is about 21% at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz (the relative amplitude is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='46).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Therefore, at the operating frequency 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz, the reflected modes for both incidences at the outgoing angle of 45◦ are al- most equal-amplitude, satisfying the condition of CPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The scattered electric field distributions of the designed metasurface illuminated by two beams in the in-phase and out-of-phase scenarios obtained from full-wave sim- ulations are presented in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It can be seen that when the two illuminations are in phase, the total scat- tered fields are quite small (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='02), indicating nearly per- fect coherent absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' However, when the two illumi- nations are switched into the out-of-phase state, the rel- ative amplitude of the scattered fields is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='91, and the coherent maximum reflection is mainly along the 45◦ direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We have fabricated a sample (see Methods) and car- ried out several experiments to validate the theoretical results (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' First, the transmitting antenna is fixed at 0◦, whereas the receiving antenna is moved along the scanning track with a step of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The signal reflected from the metasurface is measured by the receiv- ing antenna at different angles θr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Then, the transmitting antenna is fixed at 45◦ and the receiving antenna is scan- ning its position to measure the reflected signal in the other half space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(c), the main peaks of reflections for both two incidences occur at θr = 45◦, which is an expected result according to the theory and simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' There is another reflection peak at θr = 0◦ for the normal incidence case, which is about −10 dB lower than the main peak, corresponding to a low spec- ular reflection at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To estimate the amplitude efficiency of the metasurface at all three reflection channels, we replaced the metasur- face by a copper plate of the identical size and measured the specular reflection signal amplitudes from the refer- ence uniform metal mirror for θi = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5◦ (approximately normal incidence), 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5◦, and 45◦ incidence angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The specular reflection efficiency of the metasurface for 0◦ and 45◦ illuminations are calculated by normalizing the signal amplitude by the amplitude of the signal reflected from the reference plate, illuminated at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='5◦ and 45◦ angles, re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(d), at the design frequency of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz, the specular reflection efficiencies at 0◦ and 45◦ (ξ−1 and ξ′ 0) equal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8% and 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6% (the relative am- plitude is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='431), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For the anomalous reflec- tion at the n = 0 mode for the normal incidence, the re- flection angle is θr = arcsin(15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22/( √ 2f)), which equals 45◦ at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz and varies from 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='7◦ to 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='7◦ as the frequency changes from 12 GHz to 18 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Therefore, we choose the signal data of a different receiving angle θr calculated according to different frequency band and nor- malize its signal amplitude by the signal amplitude from the reference mirror for different θr/2 incidence angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Additionally, we divide the obtained value by an esti- mated correction factor [37] � cos(θr)/ cos(θr/2), which gives the ratio between the theoretically calculated sig- nal amplitudes from an ideal metasurface (of the same size and made of lossless materials) and a perfectly con- ducting plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' At the design frequency of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz, the correction factor is equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='91, thus the reflection efficiency is calculated as 12%(the relative amplitude is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='412), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The measured efficiency is in good agreement with the results obtained using numer- ical simulations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(a)), except for some ripples in the ξ0 curve caused by the discrete angular scanning step in the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The relative amplitudes of reflec- tions for both incidences at the n = 0 mode are almost equal in the measurements, verifying the capability for CPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To experimentally verify the phase-controlled reflec- tion by the metasurface, in the last measurement shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 6(a), two transmitting antennas fed via a power divider illuminate the metasurface normally and at 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' A receiving antenna is placed at the 45◦ angle to mea- sure the total power reflected by the metasurface under two simultaneous illuminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To avoid severe insertion loss caused by the use of a phase shifter in one branch, which may increase the amplitude inequality between two beams, we mimic the phase-difference-tuning process by moving the metasurface along the x direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 6(b), the phase difference between the two beams is linearly varying when we change the horizontal position of the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Therefore, this shift is equivalent to a phase change between the two beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To ensure the effectively-illuminated area of the metasurface to remain stable during the moving process, we put two pieces of ab- sorbing foam on top of both sides of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The to- tal received power, normalized by the maximum power of reflected wave is changing with varying the distance ∆x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' As is seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 6(c), the modulation depths reach 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='04 at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz and 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='47 GHz, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This result indicates that coherent enhancement and cancella- tion near the design frequency can be achieved by tuning the phase difference of the two incident beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The pe- riod of the modulation is about 29 mm, almost equal to 9 Receiving antenna Transmitting antenna 1 Transmitting antenna 2 Moving direction Absorbing foam Absorbing foam (a) ∆∅ = 2𝜋∆𝑥/𝐷 𝜃 ∆∅ O’ O (b) "x (mm) 0 10 20 30 40 Normalized Recieved Power 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8 1 13GHz 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22GHz 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='47GHz 17GHz (c) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (a) Experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Two transmitting antennas fed via a power divider illuminate the metasurface normally and at 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' A receiving antenna is placed at 45◦ to measure the total reflected power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Due to the periodicity of the metasurface, continuously-changing phase difference between the two beams can be emulated by moving the metasurface horizontally along the impedance variation direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Two pieces of absorbing foam are put on both sides, ensuring that the effective exposure area of the metasurface remains fixed when the surface is shifted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (b) The reference point O is the intersection point of the 0◦ and 45◦ beams on the metasurface when the phase difference is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The phase difference at a distance ∆x from the reference point O is ∆φ = 2π∆x/D, which is linearly varying as a function of the horizontal distance ∆x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' (c) The normalized received power for different metasurface positions at 13, 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22, 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='47, and 17 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' the period of the metasurface, which validates the theo- retical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' However, at the frequency far from the designed one, for instance at 13 GHz and 17 GHz, the coherent phenomenon becomes much weaker, as is seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 6(c), due to a mismatch of the main reflection angles and the reflection amplitudes of the normally and obliquely incident waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' DISCUSSION We have demonstrated coherent perfect absorption of two beams incident at arbitrary angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' It has been found that this effect is possible for relative beam amplitudes within a certain range using a gradient passive planar structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' When these two incidences change into out- of-phase state, reflections at all three propagating chan- nels come out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To realize coherent control of reflection with single direction, the other parasitic reflections can be suppressed by introducing unidirectional evanescent modes excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' To realize a larger reflection for out- of-phase scenario, we use an optimization algorithm to search for an optimum solution of grid impedance profile and substrate thickness, which is powerful when many degrees of freedom are required in multi-channel meta- surface design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the other design methodologies such as non-local metasurface [37] and plasmonic grating [23, 48], where the interference between all the elements of a unit cell are important for the device performance, a brute- force optimization process in full-wave simulations is re- quired, which is time consuming and even cannot work when multiple input beams and multi-functionalities for multiple channels are involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Compared with them, our approach is much more robust and efficient due to a rigorous theoretical analysis, particularly by introduc- ing unidirectional evanescent mode in the scattered field to eliminate parasitic reflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Moreover, the angle- dependence of the impedance of substrate is also con- sidered in our algorithm, which is vital in metasurface design for multiple-angle incidence scenarios [49, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' We have realized a gradient metasurface with angular- asymmetric coherent perfect absorption and reflection functionalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The concept of wave control via evanes- cent harmonics engineering and independent control of the electromagnetic response for multiple illuminations can be applied for engineering multi-functional wave pro- cesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Metasurface-based designs are attractive in prac- tical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' For example, by placing a planar structure on a metal-grounded dielectric layer, the veloc- ity or position of the object can be detected by monitor- 10 ing the total reflection of such a object under two coher- ent illuminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Additionally, we hope that this work can find promising applications in phased-array anten- nas, one-side detection and sensing, and optical switches with low insertion loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' METHODS Design and modeling of the metasurface The prototype presented in this work was designed for operation at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The grid impedance is dis- cretized into 6 sub-cells, and each sub-cell is divided into 4 equal sub-sub-cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The effective grid impedance of each sub-sub-cell is retrieved from simulated reflection coefficient (S11) through the transmission-line method approach (see the Supplementary Material[43]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Numeri- cal simulations are carried out using a frequency-domain solver, implemented by CST MWS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Excitations propa- gating along the z-direction from port 1 with the electric field along the y-direction and the magnetic field along the x-direction are used in the simulations to obtain the S11 parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The dimensions of all the elements in the unit cells are designed and optimized one by one to fit the theoretically found required surface impedance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Once the dimensions of all the elements in the unit cells are found, we perform numerical simulations of the unit cell in CST MWS for the normal and 45◦ incidences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The simulation domain of the complete unit cell was D× Dy × D (along the x, y, and z directions), the unit cell boundary condition and the Floquet port were set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The scattered fields for the normal and 45◦ incidences were calculated by subtracting the incident waves from the total fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Finally, the total scattered fields when the metasurface is illuminated by two waves silmutaneously were obtained by adding the scattered field of each single beam with different phase differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Realization and measurement The ITO pattern of the metasurface was manufactured using the picosecond laser micromachining technology on a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='175-mm-thick ITO/PET film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The sample comprises 10 unit cells along the x axis and 66 unit cells along the y axis [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(b)] and has the size of 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='15λ × 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='04λ = 278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='9 mm × 198 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The ITO/PET film was adhered to a 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='95-mm-thick F4BTM substrate with ϵ = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='8(1 − j0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='01) backed by a copper ground plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The operation of the designed metasurface was tested using a NRL-arc setup [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 5(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' In the experiment, two double-ridged horn antennas with 17 dBi gain at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='22 GHz are connected to a vector network analyzer as the transmitter and receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The metasurface was lo- cated at a distance of 2 m (about 101λ) from both the transmitting and receiving antennas where the radiation from the antenna can be approximated as a plane wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' The antennas are moved along the scanning track to mea- sure the reflection towards different angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Time gating is employed to filter out all the multiple scattering noise signals received by the antenna [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors upon reason- able request.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' [50] Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', Fan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' & Chang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Con- trol of angular dispersion in dielectric gratings for mul- tifunctional wavefront shaping and dynamic polarization conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Photonics Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' 9, 2190–2195 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' ACKNOWLEDGEMENTS The authors are grateful to Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Viktar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Asadchy for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' acknowledges support from China Scholarship Council.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' This research was also sup- ported by the Natural Science Foundation of Zhejiang Province(LY22F010001), the Natural Science Founda- tion of China (61701268), and the Fundamental Research Funds for the Provincial Universities of Zhejiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' AUTHOR CONTRIBUTIONS S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' conceived the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' per- formed the numerical calculations, and designed the sam- 12 ples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' conducted the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=', and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' wrote the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' supervised the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' All authors contributed to scientific discussions and editing the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' COMPETING INTERESTS The authors declare no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' ADDITIONAL INFORMATION Supplementary information The online version contains supplementary material available at https:xxxx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'} +page_content=' Correspondence and requests for materials should be addressed to Shuomin Zhong or Xuchen Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/69E1T4oBgHgl3EQfBgJT/content/2301.02852v1.pdf'}