Impurities usually play an important role in modifying the bulk properties of electronic or electromagnetic materials. In this work, we demonstrate a way to break this discipline and realize the extraordinary physical property of impurity-immunity, which leads to perfect transmission irrespective of embedded impurities of almost any material and shape. This extraordinary property comes from the exceptional points of a pair of parity-time ($PT$)-symmetric metasurfaces sandwiching a slab of epsilon-near-zero medium. By systematically investigating the $PT$-symmetric metasurfaces sandwiching a slab of dielectrics or metamaterials, we obtain the two complementary solutions of exceptional points corresponding to perfect transmission. Interestingly, when the permittivity of the slab approaches zero, the two solutions of exceptional points coalesce into one exceptional point. At such a critical point, we find that the original “doping” effect of impurities in epsilon-near-zero media, proposed by Nader Engheta’s group very recently [I. Liberal et al., Science 355, 1058 (2017)], is significantly suppressed. Our work shows that exceptional points can be used to eliminate scattering of impurities in a bulk medium.

Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations, which can involve loss and gain, require a different approach. In this work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks, it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Experimental Realization of Any Discrete Unitary Operator, Phys. Rev. Lett. 73, 58 (1994)] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.

The goal of this paper is to introduce a local form of Kirchhoff law to model light emission by nonequilibrium bodies. While absorption by a finite-size body is usually described using the absorption cross section, we introduce a local absorption rate per unit volume and also a local thermal emission rate per unit volume. Their equality is a local form of Kirchhoff law. We revisit the derivation of this equality and extend it to situations with subsystems in local thermodynamic equilibrium but not in equilibrium between them, such as hot electrons in a metal or electrons with different Fermi levels in the conduction band and in the valence band of a semiconductor. This form of Kirchhoff law can be used to model (i) thermal emission by nonisothermal finite-size bodies, (ii) thermal emission by bodies with carriers at different temperatures, and (iii) spontaneous emission by semiconductors under optical (photoluminescence) or electrical pumping (electroluminescence). Finally, we show that the reciprocity relation connecting light-emitting diodes and photovoltaic cells derived by Rau is a particular case of the local Kirchhoff law.

In this paper, we propose a new metasurface that is able to reflect a known incoming electromagnetic wave into an arbitrary direction, with perfect power efficiency. This seemingly simple task, which we hereafter call perfect anomalous reflection, is actually highly nontrivial because of the differing wave impedances and complex interference between the incident and reflected waves. Heretofore, proposed metasurfaces that achieve perfect anomalous reflection require complicated, deeply subwavelength and/or multilayer element structures, which allow them to couple to and from leaky and/or evanescent waves. In contrast, we demonstrate that using a bipartite Huygens’ metasurface (BHM)—a passive and lossless metasurface with only two cells per period—perfect anomalous reflection can be achieved over a wide angular and frequency range. Through simulations and experiments at 24 GHz, we show that a properly designed BHM can anomalously reflect an incident electromagnetic wave from ${\theta }_i=50°$ to ${\theta }_r=-22.5°$, with perfect power efficiency to within experimental precision.

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of “distractor” folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal’s paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of subpatterns that fold when cut out (“folding islands”). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.

The volume of ordinary materials decreases in response to a pressure increase exerted by a surrounding gas or liquid, i.e., the material volume compressibility is positive. Recently, poroelastic metamaterial architectures have been suggested theoretically that allow for an unusual negative effective static volume compressibility—which appears to be forbidden for reasons of energy conservation at first sight. The challenge in the three-dimensional (3D) fabrication of these blueprints lies in the necessary many hollow 3D crosses sealed by thin membranes, which we realize in this work by using 3D laser microlithography combined with a serendipitous mechanism. By using optical-microscopy cross-correlation analysis, we determine an extraordinarily large negative metamaterial effective volume compressibility of ${\kappa }_{\mathrm{eff}}=-0.8\%{\mathrm{bar}}^{-1}=-80{\mathrm{GPa}}^{-1}$ under pressure control.

The angular response of thin diffractive optical elements is highly correlated. For example, the angles of incidence and diffraction of a grating are locked through the grating momentum determined by the grating period. Other diffractive devices, including conventional metasurfaces, have a similar angular behavior due to the fixed locations of the Fresnel zone boundaries and the weak angular sensitivity of the meta-atoms. To alter this fundamental property, we introduce angle-multiplexed metasurfaces, composed of reflective high-contrast dielectric U-shaped meta-atoms, whose response under illumination from different angles can be controlled independently. This enables flat optical devices that impose different and independent optical transformations when illuminated from different directions, a capability not previously available in diffractive optics.

Weyl semimetals are recently discovered materials supporting emergent relativistic fermions in the vicinity of band-crossing points known as Weyl nodes. The positions of the nodes and the low-energy spectrum depend sensitively on the time-reversal and inversion symmetry breaking in the system. We introduce the concept of Weyl metamaterials where the particles experience a 3D curved geometry and gauge fields emerging from smooth spatially varying time-reversal- and inversion-breaking fields. The Weyl metamaterials can be fabricated from semimetal or insulator parent states where the geometry can be tuned, for example, through inhomogeneous magnetization. We derive an explicit connection between the effective geometry and the local symmetry-breaking configuration. This result opens the door for a systematic study of 3D designer geometries and gauge fields for relativistic carriers. The Weyl metamaterials provide a route to novel electronic devices as highlighted by a remarkable 3D electron lens effect.

Recent advances in engineered gradient metasurfaces have enabled unprecedented opportunities for light manipulation using optically thin sheets, such as anomalous refraction, reflection, or focusing of an incident beam. Here, we introduce a concept of multichannel functional metasurfaces, which are able to control incoming and outgoing waves in a number of propagation directions simultaneously. In particular, we reveal a possibility to engineer multichannel reflectors. Under the assumption of reciprocity and energy conservation, we find that there exist three basic functionalities of such reflectors: specular, anomalous, and retroreflections. Multichannel response of a general flat reflector can be described by a combination of these functionalities. To demonstrate the potential of the introduced concept, we design and experimentally test three different multichannel reflectors: three- and five-channel retroreflectors and a three-channel power splitter. Furthermore, by extending the concept to reflectors supporting higher-order Floquet harmonics, we forecast the emergence of other multichannel flat devices, such as isolating mirrors, complex splitters, and multi-functional gratings.

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature, orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state because of the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow, the system additionally supports long-wavelength propagating sound modes that get gapped by the curvature of the underlying substrate. We analytically compute the steady-state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry-protected topological modes that get localized to special geodesics on the surface (the equator or the neck, respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal “Fermi arc surface states” in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.

“Schroeder diffuser” is a classical design, proposed over 40 years ago, for artificially creating optimal and predictable sound diffuse reflection. It has been widely adopted in architectural acoustics, and it has also shown substantial potential in noise control, ultrasound imaging, microparticle manipulation et al. The conventional Schroeder diffuser, however, has a considerable thickness on the order of one wavelength, severely impeding its applications for low-frequency sound. In this paper, a new class of ultrathin and planar Schroeder diffusers are proposed based on the concept of an acoustic metasurface. Both numerical and experimental results demonstrate satisfactory sound diffuse reflection produced from the metasurface-based Schroeder diffuser despite it being approximately 1 order of magnitude thinner than the conventional one. The proposed design not only offers promising building blocks with great potential to profoundly impact architectural acoustics and related fields, but it also constitutes a major step towards real-world applications of acoustic metasurfaces.

Invisibility cloaking based on transformation optics has brought about unlimited space for reverie. However, the design and fabrication of transformation-optics-based cloaks still remain fairly challenging because of the complicated, even extreme, material prescriptions, including its meticulously engineered anisotropy, inhomogeneity and singularity. And almost all the state-of-the-art cloaking devices work within a narrow and invariable frequency band. Here, we propose a novel mechanism for all-dielectric temperature-controllable cloaks. A prototype device was designed and fabricated with ${\mathrm{SrTiO}}_3$ ferroelectric cuboids as building blocks, and its cloaking effects were successfully demonstrated, including its frequency-agile invisibility by varying temperature. It revealed that the predesignated cloaking device based on our proposed strategy could be directly scaled in dimensions to operate at different frequency regions, without the necessity for further efforts of redesign. Our work opens the door towards the realization of tunable cloaking devices for various practical applications and provides a simple strategy to readily extend the cloaking band from microwave to terahertz regimes without the need for reconfiguration.

We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry-breaking (nonreciprocal) flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the $\alpha =1/4$ Hofstadter model. To induce photon-photon interactions, the cavities are coupled to superconducting qubits; we find these interactions are sufficient to stabilize a $\nu =1/2$ bosonic Laughlin puddle. Exact diagonalization studies demonstrate that this architecture is robust to experimentally achievable levels of disorder. These advances provide an exciting opportunity to employ the quantum circuit toolkit for the exploration of strongly interacting topological materials.

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micromachines.

Lens design for focusing and imaging has been optimized through centuries of developments; however, conventional lenses, even in their most ideal realizations, still suffer from fundamental limitations, such as limits in resolution and the presence of optical aberrations, which are inherent to the laws of refraction. In addition, volume-to-volume imaging of three-dimensional regions of space is not possible with systems based on conventional refractive optics, which are inherently limited to plane-to-plane imaging. Although some of these limitations have been at least theoretically relaxed with the advent of metamaterials, several challenges still stand in the way of ideal imaging of three-dimensional regions of space. Here, we show that the concept of parity-time symmetry, combined with tailored nonlocal responses, enables overcoming some of these challenges, and we propose the design of a loss-immune, linear, transversely invariant, planarized metamaterial lens, with reduced aberrations and the potential to realize volume-to-volume imaging.

Relying on abrupt phase discontinuities, metasurfaces characterized by a transversely inhomogeneous surface impedance profile have been recently explored as an ultrathin platform to generate arbitrary wave fronts over subwavelength thicknesses. Here, we outline fundamental limitations of passive gradient metasurfaces in molding the impinging wave and show that local phase compensation is essentially insufficient to realize arbitrary wave manipulation, but full-wave designs should be considered. These findings represent a critical step towards realistic and highly efficient conformal wave manipulation beyond the scope of ray optics, enabling unprecedented nanoscale light molding.

Narrow-band invisibility in an otherwise opaque medium has been achieved by electromagnetically induced transparency (EIT) in atomic systems. The quantum EIT behavior can be classically mimicked by specially engineered metamaterials via carefully controlled interference with a “dark mode.” However, the narrow transparency window limits the potential applications that require a tunable wideband transparent performance. Here, we present a macroscopic quantum superconducting metamaterial with manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional EIT or its classical analogs. A near-complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bistability of the meta-atoms and can be tuned on and off easily by altering rf and dc magnetic fields, temperature, and history. Hysteretic in situ 100% tunability of transparency paves the way for autocloaking metamaterials, intensity-dependent filters, and fast-tunable power limiters.

As the basis of a diverse set of photonic applications, such as hologram imaging, polarization, and wave front manipulation, the local phase control of electromagnetic waves is fundamental in photonic research. However, currently available bulky, passive, range-limited phase modulators pose an obstacle in photonic applications. Here, we propose a new mechanism to achieve a wide phase modulation range, with graphene used as a tunable loss to drive an underdamped to overdamped resonator transition. Based on this mechanism, we present widely tunable phase modulation in the terahertz regime, realized in gate-tuned ultrathin reflective graphene metasurfaces. A one-port resonator model, supported by full-wave simulations, explains the underlying physics of the discovered extreme phase modulation and indicates general strategies for designing tunable photonic devices. As an example, we demonstrate a gate-tunable terahertz (THz) polarization modulator with a graphene metasurface. Our findings establish the possibility for photonic applications based on active phase manipulation.

Simple chiroptically active metamaterials are difficult to realize in practice but could pave the way for a range of important applications, such as sensitive optical biosensors, asymmetric catalysis, and novel polarization manipulation devices. We show that a metasurface based on a random arrangement of anisotropic but aligned gold nanoparticles can exhibit an almost perfect selectivity towards incident photon spin for evanescent excitation with visible to near-infrared light. The experimentally attained reflection contrast between left- and right-handed circularly polarized light peaks at $\sim 90\%$, in excellent agreement with analytical theory. These results are important for the development of future photonic and plasmonic polarization-based technologies.