Holographic multiple-input multiple-output (MIMO) method leverages spatial diversity to enhance the performance of wireless communications and is expected to be a key technology enabling for high-speed data services in the forthcoming sixth generation (6G) networks. However, the antenna array commonly used in the traditional massive MIMO cannot meet the requirements of low cost, low complexity and high spatial resolution simultaneously, especially in higher frequency bands. Hence it is important to achieve a feasible hardware platform to support theoretical study of the holographic MIMO communications. Here, we propose a near-field holographic MIMO communication architecture based on programmable digital coding metasurface (PDCM) and electromagnetic theory. The orthogonal holographic patterns on the transmitting and receiving apertures are firstly obtained using the Hilbert-Schmidt decomposition of the radiation operator. Then the information to be transmitted is pre-encoded on PDCM following the principle of direct digital modulations. A PDCM-based holographic MIMO prototype is designed and experimentally verified in microwave frequencies. The measured results of constellations show that the prototype can realize dual-channel signal transmissions under quadrature-phase shift keying scheme. The proposed paradigm features low complexity, low cost and low power consumption, and may become a valuable technique in beyond fifth generation and 6G wireless communications.

Digitally programmable metasurfaces are of potential use in next-generation mobile communications due to their ability to perform wireless data transmission without digital-to-analogue conversion or frequency mixing. However, communication networks based on programmable metasurfaces currently suffer from relatively low data transmission rates and low information mapping efficiencies (where the transmitted information per unit switching time is much lower than the information that encodes the programmable pattern). Here we report a programmable metasurface antenna that can approach the theoretical upper limit of the information mapping efficiency. Our approach combines non-recurrent encoding with spatial harmonic retrieval, and we show that the model maps most available programmable patterns to the first-harmonic direction in bijection. As a result, the approach can retrieve all of the encoding information through a single measurement. We also optimize the power efficiency of the communication architecture by using cascaded encoding to amplify the far-field radiation exclusively in the harmonic angles. By combining non-recurrent encoding with spatial harmonic retrieval, a programmable metasurface antenna can be created that can approach the theoretical upper limit of the information mapping efficiency.

Conventional wireless communication schemes indiscriminately transmit information into the whole space and pose inherent security risks. Recently, directional information modulation (DIM) has attracted enormous attention as a promising technology. DIM generates correct constellation symbols in the desired directions and distorts them in undesired directions, thus ensuring the security of the transmitted information. Although several DIM schemes have been reported, they suffer from defects of bulkiness, energy consumption, high cost, and inability to support two-dimensional (2D) and high-order modulations. Here, we propose a DIM scheme based on a 2-bit programmable metasurface (PM) that overcomes these defects. A fast and efficient discrete optimization algorithm is developed to optimize the digital coding sequences, and the correct constellation symbols can be generated and transmitted in multi-directional beams. As a proof-of-concept, three sets of constellation diagrams (8 phase shift keying (PSK), 16 quadrature amplitude modulation (QAM), and 64QAM) are realized in the multi-channel modes. This work provides an important route of employing DIM for ensuring physical-layer security and serves as a stepping stone toward endogenous secure communications.

To satisfy the increasing demands for transmission rates of wireless communications, it is necessary to use spatial resources of electromagnetic (EM) waves. In this context, EM information theory (EIT) has become a hot topic by integrating the theoretical framework of deterministic mathematics and stochastic statistics to explore the transmission mechanisms of continuous EM waves. However, the previous studies were primarily focused on frame analysis, with limited exploration of practical applications and a comprehensive understanding of its essential physical characteristics. In this paper, we present a three-dimensional (3-D) line-of-sight channel capacity formula that captures the vector EM physics and accommodates both near- and far-field scenes. Based on the rigorous mathematical equation and the physical mechanism of fast multipole expansion, a channel model is established, and the finite angular spectral bandwidth feature of scattered waves is revealed. To adapt to the feature of the channel, an optimization problem is formulated for determining the mode currents on the transmitter, aiming to obtain the optimal design of the precoder and combiner. We make comprehensive analyses to investigate the relationship among the spatial degree of freedom, noise, and transmitted power, thereby establishing a rigorous upper bound of channel capacity. A series of simulations are conducted to validate the theoretical model and numerical method. This work offers a novel perspective and methodology for understanding and leveraging EIT, and provides a theoretical foundation for the design and optimization of future wireless communications.

The modern theory of quantized polarization has recently extended from 1D dipole moment to multipole moment, leading to the development from conventional topological insulators (TIs) to higher-order TIs, i.e., from the bulk polarization as primary topological index, to the fractional corner charge as secondary topological index. The authors here extend this development by theoretically discovering a higher-order end TI (HOETI) in a real projective lattice and experimentally verifying the prediction using topolectric circuits. A HOETI realizes a dipole-symmetry-protected phase in a higher-dimensional space (conventionally in one dimension), which manifests as 0D topologically protected end states and a fractional end charge. The discovered bulk-end correspondence reveals that the fractional end charge, which is proportional to the bulk topological invariant, can serve as a generic bulk probe of higher-order topology. The authors identify the HOETI experimentally by the presence of localized end states and a fractional end charge. The results demonstrate the existence of fractional charges in non-Euclidean manifolds and open new avenues for understanding the interplay between topological obstructions in real and momentum space.

With the increasing demands for computing powers, wave-based computation has attracted researcher's attention due to its inherent high speed. Metasurfaces have flexible and powerful capabilities to manipulate electromagnetic waves and are good candidates for building a next-generation of wave-based computers. In this work, a computational-metasurface-based equation solver that yields real-time solutions to arbitrary complex matrix equations (CME) in the form of K center dot x + c = 0 is proposed. Full-wave simulations and experimental measurements are conducted to verify the functionality of the proposed solver. This work serves to provide a promising technique to overcome some shortcomings of the existing designs and lays the first stone of the bridge toward programmable wave-space computers. A computational-metasurface-based equation solver is proposed. It deals with complex matrix equations at quasi-light speed and yields the solution in real time. This work serves to provide a promising technique to overcome some shortcomings in existing designs and lays the first stone of the bridge toward programmable wave-space computers.image

A digital coding metasurface is a platform connecting the digital space and electromagnetic wave space, and has therefore gained much attention due to its intriguing value in reshaping wireless channels and realizing new communication architectures. Correspondingly, there is an urgent need for electromagnetic information theory that reveals the upper limit of communication capacity and supports the accurate design of metasurface-based communication systems. To this end, we propose a macroscopic model and a statistical model of the digital coding metasurface. The macroscopic model uniformly accommodates both digital and electromagnetic aspects of the meta-atoms and predicts all possible scattered fields of the digital coding metasurface based on a small number of simulations or measurements. Full-wave simulations and experimental results show that the macroscopic model is feasible and accurate. A statistical model is further proposed to correlate the mutual coupling between meta-atoms with covariance and to calculate the entropy of the equivalent currents of digital coding metasurface. These two models can help reconfigurable intelligent surfaces achieve more accurate beamforming and channel estimation, and thus improve signal power and coverage. Moreover, the models will encourage the creation of a precoding codebook in metasurface-based direct digital modulation systems, with the aim of approaching the upper limit of channel capacity. With these two models, the concepts of current space and current entropy, as well as the analysis of information loss from the coding space to wave space, is established for the first time, helping to bridge the gap between the digital world and the physical world, and advancing developments of electromagnetic information theory and new-architecture wireless systems.

Recent advances in digitally programmable metamaterials have accelerated the development of reconfigurable intelligent surfaces (RIS). However, the excessive use of active components (e.g., pin diodes and varactor diodes) leads to high costs, especially for those operating at millimeter-wave frequencies, impeding their large-scale deployments in RIS. Here, we introduce an entirely different approach—moiré metasurfaces—to implement dynamic beamforming through mutual twists of two closely stacked metasurfaces. The superposition of two high-spatial-frequency patterns produces a low-spatial-frequency moiré pattern through the moiré effect, which provides the surface impedance profiles to generate desired radiation patterns. We demonstrate experimentally that the direction of the radiated beams can continuously sweep over the entire reflection space along predesigned trajectories by simply adjusting the twist angle and the overall orientation. Our work opens previously unexplored directions for synthesizing far-field scattering through the direct contact of mutually twisted metallic patterns with different plane symmetry groups.

The effects of inhomogeneous environments on nearfield multi-input-multi-output (MIMO) communications are discussed by using full-polarization channel matrix that contains all necessary information. In particular, reflections from grounds are taken into account by full-wave simulations. It is found that the dielectric parameters of the grounds, the relative heights and distances between the transmitters and receivers can affect the electromagnetic effective degree of freedom, which represents the equivalent number of independent single-input-single-output systems. The simulated results also reveal that the extra propagation paths brought by the ground reflection have potential benefits and values in near-field MIMO communication when the number of the antennas of the MIMO system reaches a critical value.

We present a low-cost and high-performance 5-bit programmable phased array antenna at Ku-band, which consists of 1-bit reconfigurable radiation structures, digital phase shifters, and a coplanar waveguide feeding network. The 1-bit reconfigurable radiation structure utilizes symmetric geometries and PIN diodes to form stable 180 degrees phase difference. The digital phase shifter provides 168.75 degrees phase difference and together with the radiation structure form a 348.75 degrees phase coverage. The antenna operates between 14.4 and 15.4 GHz, and the overall array contains 24 x 2 elements with each of them being individually addressable. By changing the states of the diodes and thus adjusting the phase coding sequences of the array, the antenna achieves 0 degrees-60 degrees precise beam scanning at 14.8 GHz, with the sidelobe level, cross-polarization, and gain fluctuation being less than -16 dB, -26 dB, and 2.4 dB, respectively. A prototype was fabricated to verify the design, and the measurement results agree well with simulations. Compared with traditional phased arrays composed of numerous phase shifters and T/R components, the proposed antenna features high performance, high flexibility, low profile, and low cost. The antenna provides a new and feasible solution of wavefront steering and will benefit the various application scenarios.

Abstract Topological phases of matter are conventionally characterized by the bulk‐boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d − 1)‐dimensional boundary states. By extension, higher‐order topological insulators reveal a bulk‐edge‐corner correspondence, such that nth order topological phases feature (d − n)‐dimensional boundary states. The advent of non‐Hermitian topological systems sheds new light on the emergence of the non‐Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher‐order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach—physics‐graph‐informed machine learning (PGIML)—to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second‐order NHSE in a 2D non‐Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk‐boundary correspondence in the second‐order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non‐Hermitian systems.

Inspired by the design philosophy of information metasurfaces based on the digital coding concept,a planar 4-bit reconfigurable antenna array with low profile of 0.15λ 0 （where λ 0 is the free-space wavelength）is presented.The array is based on a digital coding radiation element consisting of a 1-bit magnetoelectric（ME） dipole and a miniaturized reflection-type phase shifter（RTPS）.The proposed 1-bit ME dipole can provide two digital states of "0" and "1"（with 0° and 180° phase responses） over a wide frequency band by individually exciting its two symmetrical feeding ports.The designed RTPS is able to realize a relative phase shift of 173°.By digitally quantizing its phase in the range of 157.5°,additional eight digital states at intervals of 22.5° are obtained.To achieve low sidelobe levels,a 1:16 power divider based on the Taylor line source method is employed to feed the array,A prototype of the proposed 4-bit antenna array has been fabricated and tested,and the experimental results are in good agreement with the simulations.Scanning beams within a ±45° range were measured with a maximum realized gain of 13.4 dBi at12 GHz.The sidelobe and cross-polarization levels are below-14.3 and-23.0 dB,respectively.Furthermore,the beam pointing error is within 0.8°,and the 3 dB gain bandwidth of the broadside beam is 25%.Due to its outstanding performance,the array holds potential for significant applications in radar and wireless communication systems.

Ce Shang,1, ∗ Shuo Liu,2, ∗ Ruiwen Shao,2, ∗ Peng Han,3 Xiaoning Zang,1 Xiangliang Zhang,4, 3 Khaled Nabil Salama,3 Wenlong Gao,5 Ching Hua Lee,6 Ronny Thomale,7 Aurélien Manchon,8, † Shuang Zhang,9, ‡ Tie Jun Cui,2, § and Udo Schwingenschlögl1, ¶ King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal 23955-6900, Saudi Arabia. State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China. King Abdullah University of Science and Technology (KAUST), Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE), Thuwal 23955-6900, Saudi Arabia. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Paderborn University, Department of Physics, Warburger Str. 100, 33098 Paderborn, Germany Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany. CINaM, Aix-Marseille University, CNRS, Marseille, France. Department of Physics, The University of Hong Kong, Hong Kong, China

The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

For one-dimensional (1D) topological insulators, the edge states always reside in the bulk bandgaps as isolated modes. The emergence and vanishing of these topological edge states are always associated with the closing/reopening of the bulk bandgap and changes in topological invariants. In this work, we discover a special kind of edge state in a 1D electrical circuit, which can appear not only inside the bandgap but also outside the bulk bands with the changing of bulk circuit parameters, resembling Tamm states or Shockley states. We prove analytically that the emergence/vanishing of this edge state and its position relative to the bulk bands depends on the intersections of certain critical frequencies. Specifically, the edge mode in the proposed circuit can be mathematically described by polynomials with roots equal to some critical frequencies in the bulk circuit. From this point of view, the transition of the edge state is uniquely determined by the order of the critical frequencies in the bulk circuit. Such topological behaviors shown by the edge state in the proposed electrical circuit may indicate, in a broader sense, the presence of certain type of topology.

We present a novel X-band 1-bit reconfigurable transmitarray with excellent polarization conversion. The basic element consists of two layers of metal patterns connected by a metal through-hole and feed structures. The top layer is used to realize a 1-bit phase response by controlling the states of two PIN diodes; the bottom layer is composed of a rectangular patch with a U-slot to realize conversion from linear polarization to cross polarization. The agreement between simulation and measurement results indicates that when the diode states are switched in turn, this unit achieves the phase difference of cross-polarized transmitted waves within 180° ± 15° and high transmittance in a broad band. The scattering patterns demonstrate that beam splitting or multi-beam generation can be achieved by controlling the different coding sequences of each column unit. The element offers low transmission loss, wide bandwidth of 1-bit phase control, and small thickness for easy integration. Thereby, it has numerous potential applications in radar and wireless communications.

Recently, digital coding metasurfaces have attracted significant attention due to their capability to dynamically control electromagnetic waves in programmable ways. When the digital bit of a metasurface is higher, its controlling capability will be stronger. However, it is extremely difficult to realize 3-bit and higher digital coding metasurfaces since an bit digital element will require many active devices (e.g., p-i-n diodes) to achieve 2n digital states. Here, we propose to realize arbitrary multi-bit programmable phases using 2-bit time-domain digital coding metasurface at the central frequency or harmonic frequencies. We introduce the method of vector synthesis to design the phase coverages, from which 4-bit and arbitrarily higher-bit coding phases are synthesized by a physical coding metasurface with only 2-bit phases, simply by manipulating the time-coding sequences. A prototype controlled by a field-programmable gate array is used to validate this methodology. The experimental results are in good agreement with the theoretical analysis, which demonstrate good performance of the proposed method in dynamically realizing arbitrary multi-bit programmable phases. This time-varying coding strategy provides a new way to design higher bit programmable metasurface and simplify the structural design and control system, which will find many potential applications such as high-resolution imaging and high-capacity wireless communications.

Digital coding metasurfaces make it possible to control EM waves in real time, and allow to implement many different functionalities in a programmable way. Here, we propose a method of harmonic beam scanning based on space-time-modulated coding metasurface by using the time shift theorem of the Fourier transform and the generalized Snell's laws. Numerical results demonstrate good performance of the digital beam scanning, which has potential applications to wireless communications and direction finding.

Metasurfaces are artificially engineered ultrathin structures that can finely tailor and control electromagnetic wavefronts. There is currently a strong interest in exploring their capability to lift some fundamental limitations dictated by Lorentz reciprocity, which have strong implications in communication, heat management, and energy harvesting. Time-varying approaches have emerged as attractive alternatives to conventional schemes relying on magnetic or nonlinear materials, but experimental evidence is currently limited to devices such as circulators and antennas. Here, the recently proposed concept of space-time-coding digital metasurfaces is leveraged to break reciprocity. Moreover, it is shown that such nonreciprocal effects can be controlled dynamically. This approach relies on inducing suitable spatiotemporal phase gradients in a programmable way via digital modulation of the metasurface-elements' phase repsonse, which enable anomalous reflections accompanied by frequency conversions. A prototype operating at microwave frequencies is designed and fabricated for proof-of-concept validation. Measured results are in good agreement with theory, hence providing the first experimental evidence of nonreciprocal reflection effects enabled by space-time-modulated digital metasurfaces. The proposed concept and platform set the stage for “on-demand” realization of nonreciprocal effects, in programmable or reconfigurable fashions, which may find several promising applications, including frequency conversion, Doppler frequency illusion, optical isolation, and unidirectional transmission.

In article number 1904069, Vincenzo Galdi, Tie Jun Cui, and co-workers report the design and fabrication of electromagnetic metasurfaces that can break Lorentz reciprocity. The mechanism is based on anomalous reflections accompanied by frequency conversions, which can be programmed and reconfigured via a spatio-temporal digital code stored in a field-gate-programmable array.