Stability bounds on superluminal propagation in active structures.

Active materials have been explored in recent years to demonstrate superluminal group velocities over relatively broad bandwidths, implying a potential path towards bold claims such as information transport beyond the speed of light, as well as antennas and metamaterial cloaks operating over very broad bandwidths. However, causality requires that no portion of an impinging pulse can pass its precursor, implying a fundamental trade-off between bandwidth, velocity and propagation distance. Here, we clarify the general nature of superluminal propagation in active structures and derive a bound on these quantities fundamentally rooted into stability considerations. By applying filter theory, we show that this bound is generally applicable to causal structures of arbitrary complexity, as it applies to each zero-pole pair describing their response. As the system complexity grows, we find that only minor improvements in superluminal bandwidth can be practically achieved. Our results provide physical insights into the limitations of superluminal structures based on active media, implying severe constraints in several recently proposed applications.

High-Index Dielectric Metasurfaces Performing Mathematical Operations.

Image processing and edge detection are at the core of several newly emerging technologies, such as augmented reality, autonomous driving, and more generally object recognition. Image processing is typically performed digitally using integrated electronic circuits and algorithms, implying fundamental size and speed limitations, as well as significant power needs. On the other hand, it can also be performed in a low-power analog fashion using Fourier optics, requiring, however, bulky optical components. Here, we introduce dielectric metasurfaces that perform optical image edge detection in the analog domain using a subwavelength geometry that can be readily integrated with detectors. The metasurface is composed of a suitably engineered array of nanobeams designed to perform either first- or second-order spatial differentiation. We experimentally demonstrate the second-derivative operation on an input image, showing the potential of all-optical edge detection using a silicon metasurface geometry working at a numerical aperture as large as 0.35.

Nonreciprocal Willis Coupling in Zero-Index Moving Media.

Mechanical motion can break the symmetry in which sound travels in a medium, but significant nonreciprocity is typically achieved only for large motion speeds. We combine moving media with zero-index acoustic propagation, yielding extreme nonreciprocity and induced bianisotropy for modest applied speeds. The metamaterial is formed by an array of waveguides loaded by Helmholtz resonators, and it exhibits opposite signs of the refractive index sustained by asymmetric Willis coupling for propagation in opposite directions. We use this response to induce nonreciprocal positive-to-negative sound refraction, and we propose a nonreciprocal metamaterial lens focusing only with excitation from one side based on asymmetric Willis coupling.

Nonreciprocal acoustic propagation and leaky-wave radiation in a waveguide with flow.

Isolators, devices with unidirectional wave transmission, are integral components in computing networks, enabling a one-way division of a large system into independent subunits. Isolators are created by breaking the inversion symmetry between a source and a receiver, known as reciprocity. In acoustics, a steady flow of the background medium in which sound travels can break reciprocity, but significant isolation is typically achieved only for large, often impractical speeds. This article proposes acoustic isolator designs enabled by duct flow that do not require large flow velocities. A basic isolator design is simulated based on the acoustic analogue of a Mach-Zehnder interferometer, with monomodal entry and exit ports. The simulated device footprint is then reduced by using bimodal ports. Further, a nonuniform velocity profile combined with a grating to induce phononic transitions is considered, which, combined with filters, can provide significant isolation. By coupling a waveguide with flow to free space through an array of small apertures, largely nonreciprocal leaky-wave radiation is demonstrated, breaking the symmetry between reception and transmission patterns of an acoustic linear aperture array. These investigations open interesting pathways towards efficient acoustic isolation, which may be translated into integrated acoustic and surface acoustic waves, as well as phononic technology.

Radio Frequency Angular Momentum Biased Quasi-LTI Nonreciprocal Acoustic Filters.

We report on the design and operation of a novel class of nonreciprocal acoustic filters operating in the radio frequency (RF) range. These devices use the spectral characteristics of commercial acoustic filters placed in angular momentum biased networks to achieve large nonreciprocity, low insertion loss (I.L.), and wideband operation. Owing to the high rejection exhibited by acoustic filters, these novel devices can achieve an unprecedented suppression of undesired intermodulation products, thus approaching the spectral purity attained by conventional linear-time-invariant (LTI) filtering components. In addition, a new analytical model suitable to capture the behavior of any angular-momentum-biased nonreciprocal device is presented. This model allows us to identify the main characteristics of the transfer function (poles and zeroes) relative to this new class of nonreciprocal filters, thus enabling new synthesis capabilities through standard numerical methods. Ultimately, the performance of a built 1.1-GHz nonreciprocal acoustic filter prototype is reported. This device relies on a modulation implemented through switched capacitors and shows I.L., isolation, and half-power bandwidth values of 4.5 dB, 28 dB, and 20 MHz, respectively, achieved through the use of a 40-MHz modulation frequency. Moreover, by showing an intermodulation distortion lower than -34 dBc, it approaches the operation of LTI circuits.

Nonlocal Metasurfaces for Optical Signal Processing.

Optical analog signal processing has been gaining significant attention as a way to overcome the speed and energy limitations of digital techniques. Metasurfaces offer a promising avenue towards this goal due to their efficient manipulation of optical signals over deeply subwavelength volumes. To date, metasurfaces have been proposed to transform signals in the spatial domain, e.g., for beam steering, focusing, or holography, for which angular-dependent responses, or nonlocality, are unwanted features that must be avoided or mitigated. Here, we show that the metasurface nonlocality can be engineered to enable signal manipulation in the momentum domain over an ultrathin platform. We explore nonlocal metasurfaces performing basic mathematical operations, paving the way towards fast and power-efficient ultrathin devices for edge detection and optical image processing.

Tunable Orbital Angular Momentum Radiation from Angular-Momentum-Biased Microcavities.

Lasers and light emitters do not typically radiate fields with orbital angular momentum (OAM). Here we show that a suitable scheme of spatiotemporal modulation of a microring cavity laser can impart a synthetic angular momentum, resulting in beams with well-defined OAM. The phenomenon relies on a traveling wave modulation of the refractive index of the microring, which breaks the degeneracy of oppositely oriented whispering gallery modes. In parallel, a static structural grating on the periphery of the microring enables efficient vertical radiation. The proposed structure is inherently tunable and can also emit fields with zero net OAM while retaining toroidal energy distributions similar to the effect of an axicon lens.

Maximum Willis Coupling in Acoustic Scatterers.

Willis coupling in acoustic materials defines the cross-coupling between strain and velocity, analogous to bianisotropic phenomena in electromagnetics. While these phenomena have been garnering significant attention in recent years, to date their effects have been considered mostly perturbative. Here, we derive general bounds on the Willis response of acoustic scatterers, show that these bounds can be reached in suitably designed scatterers, and outline a systematic venue for the realistic implementation of maximally bianisotropic acoustic inclusions. We then employ these inclusions to realize acoustic metasurfaces for bending and steering of sound with unitary efficiency.

Spectrum Control through Discrete Frequency Diffraction in the Presence of Photonic Gauge Potentials.

By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

Synchronized conductivity modulation to realize broadband lossless magnetic-free non-reciprocity.

Recent research has explored the spatiotemporal modulation of permittivity to break Lorentz reciprocity in a manner compatible with integrated-circuit fabrication. However, permittivity modulation is inherently weak and accompanied by loss due to carrier injection, particularly at higher frequencies, resulting in large insertion loss, size, and/or narrow operation bandwidths. Here, we show that the presence of absorption in an integrated electronic circuit may be counter-intuitively used to our advantage to realize a new generation of magnet-free non-reciprocal components. We exploit the fact that conductivity in semiconductors provides a modulation index several orders of magnitude larger than permittivity. While directly associated with loss in static systems, we show that properly synchronized conductivity modulation enables loss-free, compact and extremely broadband non-reciprocity. We apply these concepts to obtain a wide range of responses, from isolation to gyration and circulation, and verify our findings by realizing a millimeter-wave (25 GHz) circulator fully integrated in complementary metal-oxide-semiconductor technology.Optical non-reciprocity achieved through refractive index modulation can have its challenges and limitations. Here, Dinc et al. introduce the concept of non-reciprocity based on synchronized spatio-temporal modulation of conductivity to achieve different types of non-reciprocal functionality.

Metagratings: Beyond the Limits of Graded Metasurfaces for Wave Front Control.

Graded metasurfaces exploit the local momentum imparted by an impedance gradient to mold the impinging wave front. This approach suffers from fundamental limits on the overall conversion efficiency, and it is challenged by fabrication limitations on the spatial resolution. Here, we introduce the concept of metagratings, formed by periodic arrays of carefully tailored bianisotropic inclusions and show that they enable wave front engineering with unitary efficiency and significantly lower fabrication demands. We employ this concept to design reflective metasurfaces for wave front steering without limitations on efficiency. A similar approach can be extended to transmitted beams and arbitrary wave front transformation, opening opportunities for highly efficient metasurfaces for extreme wave manipulation.

Time-Reversal Symmetry Bounds on the Electromagnetic Response of Asymmetric Structures.

Asymmetric structures support different field distributions and electromagnetic responses when excited from different directions. Here we show that time-reversal symmetry imposes fundamental constraints on their overall response, beyond those dictated by reciprocity. For two-port devices, the asymmetry in field distribution for opposite excitations is shown to be fundamentally bounded by the reflection at the ports, and the fields are identical everywhere in space in the case of full transmission. In multiport and open scenarios, these bounds have implications on radiation and scattering at different ports and towards different directions. Beyond their theoretical significance, these results provide relevant insights into the operation of nonlinear isolators, metasurfaces, and other nanophotonic devices.

Static non-reciprocity in mechanical metamaterials.

Reciprocity is a general, fundamental principle governing various physical systems, which ensures that the transfer function-the transmission of a physical quantity, say light intensity-between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity (and therefore show non-reciprocity) have been mostly considered in dynamic systems involving electromagnetic, acoustic and mechanical wave propagation associated with fields varying in space and time. Here we show that it is possible to break reciprocity in static systems, realizing mechanical metamaterials that exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. This is achieved by combining large nonlinearities with suitable geometrical asymmetries and/or topological features. In addition to extending non-reciprocity and isolation to statics, our work sheds light on energy propagation in nonlinear materials with asymmetric crystalline structures and topological properties. We anticipate that breaking reciprocity will open avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.

An invisible acoustic sensor based on parity-time symmetry.

Sensing an incoming signal is typically associated with absorbing a portion of its energy, inherently perturbing the measurement and creating reflections and shadows. Here, in contrast, we demonstrate a non-invasive, shadow-free, invisible sensor for airborne sound waves at audible frequencies, which fully absorbs the impinging signal, without at the same time perturbing its own measurement or creating a shadow. This unique sensing device is based on the unusual scattering properties of a parity-time (PT) symmetric metamaterial device formed by a pair of electro-acoustic resonators loaded with suitably tailored non-Foster electrical circuits, constituting the acoustic equivalent of a coherent perfect absorber coupled to a coherent laser. Beyond the specific application to non-invasive sensing, our work broadly demonstrates the unique relevance of PT-symmetric metamaterials for acoustics, loss compensation and extraordinary wave manipulation.

Negative refraction and planar focusing based on parity-time symmetric metasurfaces.

We introduce a new mechanism to realize negative refraction and planar focusing using a pair of parity-time symmetric metasurfaces. In contrast to existing solutions that achieve these effects with negative-index metamaterials or phase conjugating surfaces, the proposed parity-time symmetric lens enables loss-free, all-angle negative refraction and planar focusing in free space, without relying on bulk metamaterials or nonlinear effects. This concept may represent a pivotal step towards loss-free negative refraction and highly efficient planar focusing by exploiting the largely uncharted scattering properties of parity-time symmetric systems.

Extinction symmetry for reciprocal objects and its implications on cloaking and scattering manipulation.

Using Lorentz reciprocity and power conservation, we prove that the extinction cross section of an arbitrarily shaped scatterer is always the same when illuminated from opposite directions and with the same polarization. For lossless and passive objects, this finding implies identical scattering cross sections for opposite excitations, with relevant implications on cloaking designs and scattering suppression schemes. This scattering symmetry can be broken by introducing absorption into the system, providing a path toward large scattering asymmetries when combined with Fano interference.

Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.

Acoustic isolation and nonreciprocal sound transmission are highly desirable in many practical scenarios. They may be realized with nonlinear or magneto-acoustic effects, but only at the price of high power levels and impractically large volumes. In contrast, nonreciprocal electromagnetic propagation is commonly achieved based on the Zeeman effect, or modal splitting in ferromagnetic atoms induced by a magnetic bias. Here, we introduce the acoustic analog of this phenomenon in a subwavelength meta-atom consisting of a resonant ring cavity biased by a circulating fluid. The resulting angular momentum bias splits the ring's azimuthal resonant modes, producing giant acoustic nonreciprocity in a compact device. We applied this concept to build a linear, magnetic-free circulator for airborne sound waves, observing up to 40-decibel nonreciprocal isolation at audible frequencies.

Terahertz magnetoplasmon energy concentration and splitting in Graphene PN Junctions.

Terahertz plasmons and magnetoplasmons propagating along electrically and chemically doped graphene p-n junctions are investigated. It is shown that such junctions support non-reciprocal magnetoplasmonic modes which get concentrated at the middle of the junction in one direction and split away from the middle of the junction in the other direction under the application of an external static magnetic field. This phenomenon follows from the combined effects of circular birefringence and carrier density non-uniformity. It can be exploited for the realization of plasmonic isolators.

Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials.

Breaking time-reversal symmetry enables the realization of non-reciprocal devices, such as isolators and circulators, of fundamental importance in microwave and photonic communication systems. This effect is almost exclusively achieved today through magneto-optical phenomena, which are incompatible with integrated technology because of the required large magnetic bias. However, this is not the only option to break reciprocity. The Onsager-Casimir principle states that any odd vector under time reversal, such as electric current and linear momentum, can also produce a non-reciprocal response. These recently analysed alternatives typically work over a limited portion of the electromagnetic spectrum and/or are often characterized by weak effects, requiring large volumes of operation. Here we show that these limitations may be overcome by angular momentum-biased metamaterials, in which a properly tailored spatiotemporal modulation is azimuthally applied to subwavelength Fano-resonant inclusions, producing largely enhanced non-reciprocal response at the subwavelength scale, in principle applicable from radio to optical frequencies.

Non-reciprocal magnetoplasmon graphene coupler.

The non-reciprocity of the edge magnetoplasmon modes of a graphene strip is leveraged to design a non-reciprocal magnetoplasmon graphene coupler, coupling only in one direction. The proposed coupler consists of two coplanar parallel magnetically biased graphene strips. In the forward direction, the modes along the adjacent strip edges of the strips have the same wavenumber and therefore couple to each other. In the backward direction, the modes along the adjacent strip edges have different wavenumbers and therefore no coupling occurs.