Giant elastic-wave asymmetry in a linear passive circulator

Nonreciprocal transmission of waves is highly desirable for the transport and redistribution of energy. However, building an asymmetric system to break time-reversal symmetry is relatively difficult because it tends to work under stringent guidelines, narrow bandwidth, or external impetus, particularly in a three-port system. Without breaking reciprocity, realizing "one-way" transmission of elastic waves by a linear and passive structure in a higher-dimensional asymmetric system, such as a three-port circulator, poses quite a challenge. Here, based on the wave-vector modulation mechanism, we propose an elastic-wave circulator that achieves this without breaking reciprocity, enabling perfect mode transition and wave trapping simultaneously. Requiring neither activated media nor relying on the nonlinearity of nonreciprocal devices, the circulator routes elastic waves purely in a clockwise direction, offering superior performance in broad bandwidth, robust behavior, and simple configuration. Our study provides a feasible platform for asymmetric wave transport in a three-port system, which can be useful in the routing, isolation, and harvesting of energy and can also be extended to other fields, such as electromagnetic and acoustic waves.

Broadband localization of light at the termination of a topological photonic waveguide

Localized optical field enhancement enables strong light-matter interactions necessary for efficient manipulation and sensing of light. Specifically, tunable broadband energy localization in nanoscale hotspots offers many applications in nanophotonics and quantum optics. We experimentally demonstrate a mechanism for the local enhancement of electromagnetic fields based on strong suppression of backscattering. This is achieved at a designed termination of a topologically nontrivial waveguide that nearly preserves the valley degree of freedom. The symmetry origin of the valley degree of freedom prevents edge states to undergo intervalley scattering at waveguide discontinuities that obey the symmetry of the crystal. Using near-field microscopy, we reveal that this leads to strong confinement of light at the termination of a topological photonic waveguide, even without breaking reciprocity. We emphasize the importance of symmetry conservation by comparing different waveguide termination geometries, confirming that the origin of suppressed backscattering lies with the near conservation of the valley degree of freedom, and show the broad bandwidth of the effect.

Electromagnetic Multipole Theory for Two-Dimensional Photonics

We develop a full-wave electromagnetic (EM) theory for calculating the multipole decomposition in two-dimensional (2-D) structures consisting of isolated, arbitrarily shaped, inhomogeneous, anisotropic cylinders or a collection of such. To derive the multipole decomposition, we first solve the scattering problem by expanding the scattered electric field in divergenceless cylindrical vector wave functions (CVWFs) with unknown expansion coefficients that characterize the multipole response. These expansion coefficients are then expressed via contour integrals of the vectorial components of the scattered electric field evaluated via an electric field volume integral equation (EFVIE). The kernels of the EFVIE are the products of the tensorial 2-D Green's function (GF) expansion and the equivalent 2-D volumetric electric and magnetic current densities. We validate the theory using the commercial finite element solver COMSOL Multiphysics. In the validation, we compute the multipole decomposition of the fields scattered from various 2-D structures and compare the results with alternative formulations. Finally, we demonstrate the applicability of the theory to study an emerging photonics application on oligomer-based highly directional switching using active media. This analysis addresses a critical gap in the current literature, where multipole theories exist primarily for three-dimensional (3-D) particles of isotropic materials. Our work enhances the understanding and utilization of the optical properties of 2-D, inhomogeneous, and anisotropic cylindrical structures, contributing to advancements in photonic and meta-optics technologies.

Robust multimode interference and conversion in topological unidirectional surface magnetoplasmons

We have theoretically investigated surface magnetoplasmons (SMPs) in an yttrium-iron-garnet (YIG) sandwiched waveguide. The dispersion demonstrated that this waveguide can support topological unidirectional SMPs. Based on unidirectional SMPs, magnetically controllable multimode interference (MMI) is verified in both symmetric and asymmetric waveguides. Due to the coupling between the modes along two YIG-air interfaces, the asymmetric waveguide supports a unidirectional even mode within a single-mode frequency range. Moreover, these modes are topologically protected when a disorder is introduced. Utilizing robust unidirectional SMP MMI (USMMI), tunable splitters have been achieved. It has been demonstrated that mode conversion between different modes can be realized. These results provide many degrees of freedom to manipulate topological waves.

Wideband isolator based on one-way surface magnetoplasmons with ultra-high isolation

In this paper, we present a new type of isolator based on one-way surface magnetoplasmons (SMPs) at microwave frequencies, and it is the first time that an experimental prototype of isolator with wideband and ultra-high isolation is realized using SMP waveguide. The proposed model with gyromagnetic and dielectric layers is systematically analyzed to obtain the dispersion properties of all the possible modes, and a one-way SMP mode is found to have the unidirectional transmission property. In simulation and experiment with metallic waveguide loaded with yttrium-iron-garnet (YIG) ferrite, the scattering parameters and the field distributions agree well with the analysis and verify the one-way transmission property. The isolation is found to be as high as 80 dB and the typical value of insertion loss is 1 dB. Besides, the one-way transmission band can be controlled by changing the magnetic bias. From theoretical analysis and simulation, it is found that with a tiny value of 10 Oe of the magnetic bias, the relative bandwidth can be tuned to be greater than 50%. Compared with conventional isolators, this one-way SMP isolator has the advantages of ultra-high isolation, wide relative frequency band, and requires much smaller bias field, which has promising potential in non-reciprocal applications.

Unidirectional guided-wave-driven metasurfaces for arbitrary wavefront control

Metasurfaces are capable of fully reshaping the wavefronts of incident beams in desired manners. However, the requirement for external light excitation and the resonant nature of their meta-atoms, make challenging their on-chip integration. Here, we introduce the concept and design of a fresh class of metasurfaces, driven by unidirectional guided waves, capable of arbitrary wavefront control based on the unique dispersion properties of unidirectional guided waves rather than resonant meta-atoms. Upon experimentally demonstrating the feasibility of our designs in the microwave regime, we numerically validate the introduced principle through the design of several microwave meta-devices using metal-air-gyromagnetic unidirectional surface magneto-plasmons, agilely converting unidirectional guided modes into the wavefronts of 3D Bessel beams, focused waves, and controllable vortex beams. We, further, numerically demonstrate sub-diffraction focusing, which is beyond the capability of conventional metasurfaces. Our unfamiliar yet practical designs may enable full, broadband manipulation of electromagnetic waves on deep subwavelength scales.

Tunable triple plasmon-induced transparency in E-type graphene metamaterials

Enhancing light-matter interaction is crucial for boosting the performance of nanophotonic devices, which can be achieved via plasmon-induced transparency (PIT). This study introduces what we believe to be a novel E-type metamaterial structure crafted from a single graphene layer. The structure, comprising a longitudinal graphene ribbon and three horizontal graphene strips, leverages destructive interference at terahertz frequencies to manifest triple plasmon-induced transparency (triple-PIT). Through a comparison of simulations using the finite difference time domain (FDTD) method and theoretical coupled-mode calculations, we elucidate the physical mechanism behind triple-PIT. Our analysis shows that the PIT effect arises from the interplay between two single-PITs phenomena, further explored through field distribution studies. Additionally, we investigate the impact of varying Fermi levels and carrier mobility on the transmission spectrum, achieving amplitude modulation in photoelectric switches of 85.5%, 99.2%, and 93.8% at a carrier mobility of 2 m2/(V·s). Moreover, we explore the relationship between Fermi levels and carrier mobility concerning the slow light effect, discovering a potential group index of up to 1021 for the structure. These insights underscore the significant potential of this graphene-based metamaterial structure in enhancing optical switches, modulators, and slow light devices.

Dynamically tunable multi-band plasmon-induced absorption based on multi-layer borophene ribbon gratings

In this paper, we propose a borophene-based grating structure (BBGS) to realize multi-band plasmon-induced absorption. The coupling of two resonance modes excited by upper borophene grating (UBG) and lower borophene grating (LBG) leads to plasmon-induced absorption. The coupled-mode theory (CMT) is utilized to fit the absorption spectrum. The simulated spectrum fits well with the calculated result. We found the absorption peaks exhibit a blue shift with an increase in the carrier density of borophene grating. Further, as the coupling distance D increases, the first absorption peak shows a blue shift, while the second absorption peak exhibits a red shift, leading to a smaller reflection window. Moreover, the enhancement absorption effect caused by the bottom PEC layer is also analyzed. On this basis, using a three-layer borophene grating structure, we designed a three-band perfect absorber with intensities of 99.83%, 99.45%, and 99.96% in the near-infrared region. The effect of polarization angle and relaxation time on the absorption spectra is studied in detail. Although several plasmon-induced absorption based on two-dimensional (2D) materials, such as graphene, black phosphorus, and transition metal dichalcogenides (TMDs), have been previously reported, this paper proposes a borophene-based metamaterial to achieve plasmon-induced perfect absorption since borophene has some advantages such as high surface-to-volume ratios, mechanical compliance, high carrier mobility, excellent flexibility, and long-term stability. Therefore, the proposed borophene-based metamaterial will be beneficial in the fields of multi-band perfect absorber in the near future.

Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing

Nonlinear optical signal processing (NOSP) has the potential to significantly improve the throughput, flexibility, and cost-efficiency of optical communication networks by exploiting the intrinsically ultrafast optical nonlinear wave mixing. It can support digital signal processing speeds of up to terabits per second, far exceeding the line rate of the electronic counterpart. In NOSP, high-intensity light fields are used to generate nonlinear optical responses, which can be used to process optical signals. Great efforts have been devoted to developing new materials and structures for NOSP. However, one of the challenges in implementing NOSP is the requirement of high-intensity light fields, which is difficult to generate and maintain. This has been a major roadblock to realize practical NOSP systems for high-speed, high-capacity optical communications. Here, we propose using a parity-time (PT) symmetric microresonator system to significantly enhance the light intensity and support high-speed operation by relieving the bandwidth-efficiency limit imposed on conventional single resonator systems. The design concept is the co-existence of a PT symmetry broken regime for a narrow-linewidth pump wave and near-exceptional point operation for broadband signal and idler waves. This enables us to achieve a new NOSP system with two orders of magnitude improvement in efficiency compared to a single resonator. With a highly nonlinear AlGaAs-on-Insulator platform, we demonstrate an NOSP at a data rate approaching 40 gigabits per second with a record low pump power of one milliwatt. These findings pave the way for the development of fully chip-scale NOSP devices with pump light sources integrated together, potentially leading to a wide range of applications in optical communication networks and classical or quantum computation. The combination of PT symmetry and NOSP may also open up opportunities for amplification, detection, and sensing, where response speed and efficiency are equally important.

Supplementary Information

The online version contains supplementary material available at 10.1186/s43593-024-00062-w.

Slow light topological photonics with counter-propagating waves and its active control on a chip

Topological slow light exhibits potential to achieve stopped light by virtue of its widely known robust and non-reciprocal behaviours. Conventional approach for achieving topological slow light often involves flat-band engineering without disentangling the underlying physical mechanism. Here, we unveil the presence of counter-propagating waves within valley kink states as the distinctive hallmark of the slow light topological photonic waveguides. These counter-propagating waves, supported by topological vortices along glide-symmetric interface, provide significant flexibility for controlling the slowness of light. We tune the group velocity of light by changing the spatial separation between vortices adjacent to the glide-symmetric interface. We also dynamically control the group delay by introducing a non-Hermitian defect using photoexcitation to adjust the relative strength of the counter-propagating waves. This study introduces active slow light topological photonic device on a silicon chip, opening new horizons for topological photon transport through defects, topological light-matter interactions, nonlinear topological photonics, and topological quantum photonics.

Enhancing second harmonic generation by Q-boosting lossless cavities beyond the time bandwidth limit

Nanostructures proved to be versatile platforms to control the electromagnetic field at subwavelength scale. Indeed, high-quality-factors nanocavities have been used to boost and control nonlinear frequency generation by increasing the light-matter interaction. However, nonlinear processes are triggered by high-intensities, which are provided by ultrashort laser pulses with large bandwidth, which cannot be fully exploited in such devices. Time-varying optical systems allow one to overcome the time-bandwidth limit by modulating the cavity external coupling. Here we present a general treatment, based on coupled mode theory, to describe second harmonic generation in a doubly resonant cavity for which the quality-factor at the fundamental frequency is modulated in time. We identify the initial quality factor maximizing second harmonic efficiency when performing Q-boosting and we predict a theoretical energy conversion efficiency close to unity. Our results have direct impact on the design of next generation time-dependent metasurfaces to boost nonlinear frequency conversion of ultrashort laser pulses.

Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

The Lorentz reciprocal theorem-that is used to study various transport phenomena in hydrodynamics-is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here, we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque dipole can lead to directed motion.

Broadband unidirectional surface plasmon polaritons with low loss

Unidirectional surface plasmon polaritons (SPPs) have been proven to truly exist at an interface between a magnetized semiconductor and an opaque isotropic material, however, they suffer rather serious leakage loss (with propagation length shorter than two wavelengths) caused by nonlocality. In this work, we investigate an alternative category of unidirectional SPPs existing on a nonreciprocal plasmonic platform with a cladding composed of a dielectric heterostructure transversely terminated by metal. This unidirectional SPP mode exists for small wavenumbers within the entire upper bulk-mode bandgap of the magnetized semiconductor, hence it is robust against nonlocal effects over a broad band. In contrast to previous unidirectional SPPs, the leakage loss of the present unidirectional SPPs is significantly reduced by more than five times, since the portion of modal energy distributed in the cladding is substantially increased. A similar reduction in absorption losses associated with semiconductor dissipation is observed. Though the nonlocality induces a backward-propagating SPP with extremely large wavenumbers, it can be suppressed even at very small level of dissipation. Therefore, our proposed plasmonic waveguide actually exhibits exceptional unidirectional characteristics.

Topological Microlaser with a Non-Hermitian Topological Bulk

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.

Non-Hermitian topology in static mechanical metamaterials

The combination of broken Hermiticity and band topology in physical systems unveils a novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that breaks reciprocity is usually used to achieve NHSE, and gain and loss in energy are inevitably involved. Here, we demonstrate non-Hermitian topology in a mechanical metamaterial system by exploring its static deformation. Nonreciprocity is introduced via passive modulation of the lattice configuration without resorting to active control and energy gain/loss. Intriguing physics such as the reciprocal and higher-order skin effects can be tailored in the passive system. Our study provides an easy-to-implement platform for the exploration of non-Hermitian and nonreciprocal phenomena beyond conventional wave dynamics.

Geometrical Theory of Electromagnetic Nonreciprocity

Recent advances in electromagnetic nonreciprocity raise the question of how to engineer the nonreciprocal electromagnetic response with geometrical approaches. In this Letter, we examine this problem by introducing generalized electromagnetic continua consisting structured points, which carry extra degrees of freedom over coordinate transformation. We show that general nonreciprocal media have a unique time-varying Riemannian metric structure with local spinning components. It is demonstrated that the nonreciprocity can be alternatively identified as the torsion tensor of a Riemann-Cartan space, which could provide analytic expressions for the magneto-optical effect and the axionic magnetoelectric coupling. Our theory not only gives a deeper insight into the fundamental understanding of electromagnetic nonreciprocity but also provides a practical principle to geometrically design nonreciprocal devices through frame transformation.

Effect of symmetry breaking on multi-plasmon-induced transparency based on single-layer graphene metamaterials with strips and rings

A single-layer graphene metamaterial consisting of a horizontal graphene strip, four vertical graphene strips, and two graphene rings is proposed to realize tunable multi-plasma-induced transparency (MPIT) by the coupled mode theory and the finite-difference time-domain method. A switch with three modulation modes is realized by dynamically adjusting the Fermi level of graphene. Moreover, the effect of symmetry breaking on MPIT is investigated by controlling the geometric parameters of graphene metamaterials. Triple-PIT, dual-PIT, single-PIT can be transformed into each other. The proposed structure and results provide guidance for applications such as designing photoelectric switches and modulators.

Ill-Defined Topological Phases in Local Dispersive Photonic Crystals

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with few modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break down and the Chern topology becomes ill defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be noninteger notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.

Realization of tunable index-near-zero modes in nonreciprocal magneto-optical heterostructures

Epsilon-near-zero (ENZ) metamaterial with the relative permittivity approaching zero has been a hot research topic for decades. The wave in the ENZ region has infinite phase velocity (v=1/ε μ), but it cannot efficiently travel into the other devices or air due to the impedance mismatch or near-zero group velocity. In this paper, we demonstrate that the tunable index-near-zero (INZ) modes with vanishing wavenumbers (k = 0) and nonzero group velocities (v_g ≠ ~0) can be achieved in nonreciprocal magneto-optical systems. The INZ modes have been experimentally demonstrated in the photonic crystals at Dirac point frequencies, and that impedance-matching effect has been observed as well [Nat. Commun.8, 14871 (2017)10.1038/ncomms14871]. Our theoretical analysis reveals that the INZ modes exhibit tunability when changing the parameters of the one-way (nonreciprocal) waveguides. Moreover, owing to the zero-phase-shift characteristic and decreasing v_g of the INZ modes, several perfect optical buffers are proposed in the microwave and terahertz regimes. The theoretical results are further verified by the numerical simulations using the finite element method. Our findings may open new avenues for research in the areas of ultra-strong or -fast nonlinearity, perfect cloaking, high-resolution holographic imaging, and wireless communications.

Silicon-on-Insulator Optical Buffer Based on Magneto-Optical 1 × 3 Micro-Rings Array Coupled Sagnac Ring

Optical buffer is a key technology to control optical routing and solve channel competition, which directly determines the performance of information processing and storage. In this study, a switchable optical buffer using the nonreciprocal silicon-on-insulator (SOI) magneto-optical micro-ring (MOMR) array coupled with Sagnac ring was introduced, which can exceed the time-bandwidth limitation. The transmission equations and propagation characteristics of optical signal in 1 × 3 micro-rings and Sagnac ring coupled 1 × 3 micro-rings based on two kinds of phase-change materials were studied. The group time delay, effective buffer time and readout operation in the buffer were also investigated.

Optomagnonics in Dispersive Media: Magnon-Photon Coupling Enhancement at the Epsilon-near-Zero Frequency

Reaching strong light-matter coupling in solid-state systems has long been pursued for the implementation of scalable quantum devices. Here, we put forward a system based on a magnetized epsilon-near-zero (ENZ) medium, and we show that strong coupling between magnetic excitations (magnons) and light can be achieved close to the ENZ frequency due to a drastic enhancement of the magneto-optical response. We adopt a phenomenological approach to quantize the electromagnetic field inside a dispersive magnetic medium in order to obtain the frequency-dependent coupling between magnons and photons. We predict that, in the epsilon-near-zero regime, the single-magnon single-photon coupling can be comparable to the magnon frequency for a small magnetic volume and perfect mode overlap. For state-of-the-art illustrative values, this would correspond to achieving the single-magnon strong coupling regime, where the coupling rate is larger than all the decay rates. Finally, we show that the nonlinear energy spectrum intrinsic to this coupling regime can be probed via the characteristic multiple magnon sidebands in the photon power spectrum.

Triple plasmon-induced transparency and dynamically tunable electro-optics switch based on a multilayer patterned graphene metamaterial

A terahertz-band metamaterial composed of multilayer patterned graphene is proposed and triple plasmon-induced transparency is excited by coupling three bright modes with one dark mode. The Lorentz curve calculated by the coupled-mode theory agrees well with the finite-difference time-domain results. Dynamic tuning is investigated by changing the Fermi level. Multimode electro-optics switching can be designed and achieved, and the amplitude modulations of four resonance frequencies are 94.3%, 92.8%, 90.7%, and 93%, respectively, which can realize the design of synchronous and asynchronous electro-optics switches. It is hoped that these results can provide theoretical support and guidance for the future design and application of photonic and optoelectronic devices.

Photon coupling-induced spectrum envelope modulation in the coupled resonators from Vernier effect to harmonic Vernier effect

The Vernier effect and harmonic Vernier effect have attracted ever-increasing interest due to their freely tailored spectrum envelope in tunable laser, modulator, and precision sensing. Most explorations have mainly focused on configuring two isolated optical resonators, namely the reference and tunable resonator. However, this configuration requires a stable reference resonator to guarantee robust readout, posing a significant challenge in applications. Here, we discover the coupled-resonators configuration enabling a reference-free envelope modulation to address this problem. Specifically, all parameters of one resonator theoretically span a hypersurface. When the resonator couples to another one, photon coupling merit an escaped solution from the hypersurface, resulting in an envelope modulation independent of reference. We have first experimentally verified this mechanism in a coupled air resonator and polydimethylsiloxane resonator by inserting a semi-transparent 2-mercaptobenzimidazole-modified silver nanowire network. In addition, this novel mechanism provides a new degree of freedom in the reciprocal space, suggesting alternative multiplexing to combine more envelope modulations simultaneously. This study facilitates the fundamental research in envelope multiplexing. More importantly, the combination of silver nanowire network and flexible microcavity experimentally progress the spectral envelope modulation in optoelectronic integration inside resonators.

Realization of broadband truly rainbow trapping in gradient-index metamaterials

Unidirectionally propagating wave (UPW) such as surface magnetoplasmon (SMP) has been a research hotspot in the last decades. In the study of the UPW, metals are usually treated as perfect electric conductors (PECs). However, it was reported that the transverse resonance condition induced by the PEC wall(s) may significantly narrow up the complete one-way propagation (COWP) band. In this paper, ultra-broadband one-way waveguides are built by utilizing the epsilon-negative (ENG) metamaterial (MM) and/or the perfect magnetic conductor (PMC) boundary. In both cases, the total bandwidth of the COWP bands are efficiently enlarged by more than three times than the one in the original metal-dielectric-semiconductor-metal structure. Moreover, the one-way waveguides consisting of gradient-index metamaterial are proposed to achieve broadband truly rainbow trapping (TRT). In the full-wave simulations, clear broadband TRT without back reflection is observed in terahertz regime. Besides, giant electric field enhancement is achieved in a PMC-based one-way structure, and the amplitude of the electric field is enormously enhanced by five orders of magnitude. Our findings are beneficial for researches on broadband terahertz communication, energy harvesting and strong-field devices.

Large-area unidirectional surface magnetoplasmons using uniaxial μ-near-zero material

We have theoretically investigated surface magnetoplasmons (SMPs) in a waveguide consisting of a uniaxial μ-near-zero (UMNZ) material slab sandwiched between two ferrite materials with opposite remanences. It is shown that this waveguide can support robust unidirectional SMP (USMP), whose electric field extends almost uniformly in the UMNZ layer, hence USMP can acquire modal sizes far larger than the wavelength. We have demonstrated that such large-area USMP (LUSMP) provides many degrees of freedom to manipulate waves. Using LUSMP, waves can be completely trapped with hot spots of wavelength size.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

Time scale disparity yielding acoustic nonreciprocity in a two-dimensional granular-elastic solid interface with asymmetry

We study nonreciprocal wave transmission across the interface of two dissimilar granular media separated by an elastic solid medium. Specifically, a left, larger-scale and a right smaller-scale granular media composed of two-dimensional, initially uncompressed hexagonally packed granules are interfacing with an intermediate linearly elastic solid, modeled either as a thin elastic plate or a linear Euler-Bernoulli beam. The granular media are modeled by discrete elements and the elastic solid by finite elements assuming a plane stress approximation for the thin plate. Accounting for the combined effects of Hertzian, frictional and rotational interactions in the granular media, as well as the highly discontinuous interfacial effects between the (discrete) granular media and the (continuous) intermediate elastic solid, the nonlinear acoustics of the integrated system is computationally studied subject to a half-sine shock excitation applied to a boundary granule of either the left or right granular medium. The highly discontinuous and nonlinear interaction forces coupling the granular media to the elastic solid are accurately computed through an algorithm with interrelated iteration and interpolation at successive adaptive time steps. Numerical convergence is ensured by monitoring the (linearized) eigenvalues of a nonlinear map of interface forces at each (variable) time step. Due to the strong nonlinearity and hierarchical asymmetry of the left and right granular media, time scale disparity occurs in the response of the interface which breaks acoustic reciprocity. Specifically, depending on the location and intensity of the applied shock, propagating wavefronts are excited in the granular media, which, in turn, excite either (slow) low-frequency vibrations or (fast) high-frequency acoustics in the intermediate elastic medium. This scale disparity is due to the size disparity of the left and right granular media, which yields drastically different wave speeds in the resulting propagating wavefronts. As a result, the continuum part of the interface responds with either low-frequency vibrations-when the shock is applied to the larger-scale granular medium, or high-frequency waves-when the shock is applied to the smaller-scale granular medium. This provides the fundamental mechanism for breaking reciprocity in the interface. The nonreciprocal interfacial acoustics studied here apply to a broad class of asymmetric hybrid (discrete-continuum) nonlinear systems and can inform predictive designs of highly effective granular shock protectors or granular acoustic diodes.

Magnon-mediated nonreciprocal microwave transmission based on quantum interference

Nonreciprocity has always been a subject of interest and plays a key role in a variety of applications like signal processing and noise isolation. In this work, we propose a simple and feasible scheme to implement nonreciprocal microwave transmission in a high-quality-factor superconducting cavity with ferrimagnetic materials. We derive necessary requirements to create nonreciprocity in our system where a magnon mode and two microwave modes are coupled to each other, highlighting the adjustability of a static magnetic field controlled nonreciprocal transmission based on quantum interference between different transmission paths, which breaks time-reversal symmetry of the three-mode cavity magnonics system. The high light isolation adjusted within a range of different magnetic fields can be obtained by modulating the photon-magnon coupling strength. Due to the simplicity of the device and the system tunability, our results may facilitate potential applications for light magnetic sensing and coherent information processing.

Broadband plasmon-induced transparency modulator in the terahertz band based on multilayer graphene metamaterials

In this study, multilayer graphene metamaterials comprising graphene blocks and graphene ribbon are proposed to realize dynamic plasmon-induced transparence (PIT). By changing the position between the graphene blocks, PIT phenomenon will occur in different terahertz bands. Furthermore, PIT with a transparent window width of 1 THz has been realized. In addition, the PIT shows redshifts or blueshifts or disappears altogether upon changing the Fermi level of graphene, and hence a frequency selector from 3.91 to 7.84 THz and an electro-optical switch can be realized. Surprisingly, the group index of this structure can be increased to 469. Compared with the complex and fixed structure of previous studies, our proposed structure is simple and can be dynamically adjusted according to demands, which makes it a valuable platform for ideas to inspire the design of novel electro-optic devices.

Triple plasmon-induced transparency and optical switch desensitized to polarized light based on a mono-layer metamaterial

A mono-layer metamaterial comprising four graphene-strips and one graphene-square-ring is proposed herein to realize triple plasmon-induced transparency (PIT). Theoretical results based on the coupled mode theory (CMT) are in agreement with the simulation results obtained using the finite-difference time-domain (FDTD). An optical switch is investigated based on the characteristics of graphene dynamic modulation, with modulation degrees of the amplitude of 90.1%, 80.1%, 94.5%, and 84.7% corresponding to 1.905 THz, 2.455 THz, 3.131 THz, and 4.923 THz, respectively. Moreover, the proposed metamaterial is insensitive to the change in the angle of polarized light, for which the triple-PIT is equivalent in the cases of both x- and y-polarized light. The optical switch based on the proposed structure is effective not only for the linearly polarized light in different directions but also for left circularly polarized and right circularly polarized light. As such, this work provides insight into the design of optoelectronic devices based on the polarization characteristics of the incident light field on the optical switch and PIT.

Slow wave and truly rainbow trapping in a one-way terahertz waveguide

Slowing down or even trapping electromagnetic (EM) waves attract researchers' attention for its potential applications in energy storage, optical signal processing and nonlinearity enhancement. However, conventional trapping, in fact, is not truly trapping because of the existence of strong coupling effects and reflections. In this paper, a novel metal-semiconductor-semiconductor-metal (MSSM) heterostructure is presented, and novel truly rainbow trapping of terahertz waves is demonstrated based on a tapered MSSM structure. More importantly, functional devices such as optical buffer, optical switch and optical filter are achieved in one single structure based on the truly rainbow trapping theory. Owing to the property of one-way propagation, these new types of optical devices can be high performance and are expected to be used in integrated optical circuits.

Quasi-distributed acoustic sensing with interleaved identical chirped pulses for multiplying the measurement slew-rate

Quasi-distributed acoustic sensing (Q-DAS) based on ultra-weak fiber Bragg grating (UWFBG) is currently attracting great attention, due to its high sensitivity and excellent multiplexing capability. Phase-sensitive optical time-domain reflectometry (Φ-OTDR) based on phase demodulation is one of the most promising interrogation schemes for Q-DAS. In this article, a novel interleaved identical chirped pulse (IICP) approach is proposed on the basis of pulse compression Φ-OTDR with coherent detection. Different from the frequency-division-multiplexing (FDM) method, the identical pulses are used for multiplexing in the IICP scheme, and the mixed reflection signals can be demodulated directly, so the inconsistent phase offsets in FDM can be avoided. As a result, this scheme can enlarge the measurement slew-rate (SR) of Q-DAS by times compared with traditional single pulse scheme. In the proof-of-principle experiment, the SR of 28.9 mɛ/s has been achieved with an 860 m sensing range, which is 5 times as that of the traditional single pulse scheme; meanwhile, the response bandwidth has been enlarged by 5 times. The 277 kHz response bandwidth has been achieved, with 5 m spatial resolution and 2.8 pε/Hz strain sensitivity.

Polarization-sensitive triple plasmon-induced transparency with synchronous and asynchronous switching based on monolayer graphene metamaterials

A monolayer graphene metamaterial comprising four graphene strips and four graphene blocks is proposed to produce triple plasmon-induced transparency (PIT) by the interaction of three bright modes and one dark mode. The response of the proposed structure is analyzed by using couple mode theory and finite-difference time-domain simulations, with the results of each method showing close agreement. A quadruple-mode on-to-off modulation based on synchronous or asynchronous switching is realized by tuning the Fermi levels in the graphene, its modulation degrees of amplitude are 77.7%, 58.9%, 75.4%, and 77.6% corresponding to 2.059 THz, 2.865 THz, 3.381 THz, and 3.878 THz, respectively. Moreover, the influence of the polarized light angle on triple-PIT is investigated in detail, demonstrating that the polarization angle affects PIT significantly. As a result, a multi-frequency polarizer is realized, its polarization extinction ratios are 4.2 dB, 7.8 dB, and 12.5 dB. Combined, the insights gained into the synchronous or asynchronous switching and the polarization sensitivity of triple-PIT provide a valuable platform and ideas to inspire the design of novel optoelectronic devices.

Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom

We demonstrate a novel path to localizing topologically nontrivial photonic edge modes along their propagation direction. Our approach is based on the near-conservation of the photonic valley degree of freedom associated with valley-polarized edge states. When the edge state is reflected from a judiciously oriented mirror, its optical energy is localized at the mirror surface because of an extended time delay required for valley index flipping. The degree of energy localization at the resulting topology-controlled photonic cavity is determined by the valley-flipping time, which is in turn controlled by the geometry of the mirror. Intuitive analytic descriptions of the "leaky" and closed topology-controlled photonic cavities are presented, and two specific designs-one for the microwave and the other for the optical spectral ranges-are proposed.

Free-space optical delay line using space-time wave packets

An optical buffer featuring a large delay-bandwidth-product-a critical component for future all-optical communications networks-remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity is continuously tunable in free space provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of  ~100 for pulses of width  ~1 ps are observed, with no fundamental limit on the system bandwidth.

Asymmetric optical camouflage: tuneable reflective colour accompanied by the optical Janus effect

Going beyond an improved colour gamut, an asymmetric colour contrast, which depends on the viewing direction, and its ability to readily deliver information could create opportunities for a wide range of applications, such as next-generation optical switches, colour displays, and security features in anti-counterfeiting devices. Here, we propose a simple Fabry-Perot etalon architecture capable of generating viewing-direction-sensitive colour contrasts and encrypting pre-inscribed information upon immersion in particular solvents (optical camouflage). Based on the experimental verification of the theoretical modelling, we have discovered a completely new and exotic optical phenomenon involving a tuneable colour switch for viewing-direction-dependent information delivery, which we define as asymmetric optical camouflage.

Bioinspired metagel with broadband tunable impedance matching

To maximize energy transmission from a source through a media, the concept of impedance matching has been established in electrical, acoustic, and optical engineering. However, existing design of acoustic impedance matching, which extends exactly by a quarter wavelength, sets a fundamental limit of narrowband transmission. Here, we report a previously unknown class of bioinspired metagel impedance transformers to overcome this limit. The transformer embeds a two-dimensional metamaterial matrix of steel cylinders into hydrogel. Using experimental data of the biosonar from the Indo-Pacific humpback dolphin, we demonstrate through theoretical analysis that broadband transmission is achieved when the bioinspired acoustic impedance function is introduced. Furthermore, we experimentally show that the metagel device offers efficient implementation in broadband underwater ultrasound detection with the benefit of being soft and tunable. The bioinspired two-dimensional metagel breaks the length-wavelength dependence, which paves a previously unexplored way for designing next-generation broadband impedance matching devices in diverse wave engineering.

Arbitrarily high time bandwidth performance in a nonreciprocal optical resonator with broken time invariance

Most present-day resonant systems, throughout physics and engineering, are characterized by a strict time-reversal symmetry between the rates of energy coupled in and out of the system, which leads to a trade-off between how long a wave can be stored in the system and the system's bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, or of any other nature) wave for more time, will inevitably also reduce the bandwidth of the system. Until recently, this time-bandwidth limit has been considered fundamental, arising from basic Fourier reciprocity. In this work, using a simple macroscopic, fiber-optic resonator where the nonreciprocity is induced by breaking its time-invariance, we report, in full agreement with accompanying numerical simulations, a time-bandwidth product (TBP) exceeding the 'fundamental' limit of ordinary resonant systems by a factor of 30. We show that, although in practice experimental constraints limit our scheme, the TBP can be arbitrarily large, simply dictated by the finesse of the cavity. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband and possessing long storage times, thereby offering a potential for new functionalities in wave-matter interactions.

Photoelectric switch and triple-mode frequency modulator based on dual-PIT in the multilayer patterned graphene metamaterial

A multilayer patterned graphene metamaterial composed of rectangular graphene, square graphene, and X-shaped graphene is proposed to achieve dual plasmon-induced transparency (PIT) at terahertz frequency. The coupled mode theory calculations are highly consistent with the finite-difference time-domain numerical results. Interestingly, a photoelectric switch has been realized, whose extinction ratio and modulation degree of amplitude can be 7.77 dB and 83.3% with the insertion loss of 7.2%. In addition, any dips can be modulated by tuning the Fermi levels of three graphene layers with minor or ignorable changes of the other two dips. The modulation degrees of frequency are 8.0%, 7.4% and 11.7%, respectively, which can be used to design a triple-mode frequency modulator. Moreover, the group index of the multilayer structure can be as high as 150. Therefore, it is reasonable to believe that a multifunctional device can be realized by the proposed structure.

Optical isolation enabled by two time-modulated point perturbations in a ring resonator

In this paper we achieve non-reciprocity in a silicon optical ring resonator, by introducing two small time-modulated perturbations into the ring. Isolators are designed using this time-perturbed ring, side-coupled to waveguides. The underlying operation of the time-modulated ring and isolator is analyzed using Temporal Coupled Mode Theory (TCMT). The TCMT is used to find the angular distance, phase difference and thickness of the two time-modulated points on the ring resonator and also to find and justify the optimum values for the modulation frequency and amplitude, which yields maximum isolation in the isolator arrangements. Insight into the major players that determine isolation are also presented, with the aid of TCMT. Our proposed structure is much simpler to implement compared to other ring-based optical isolators, as it does not require spatio-temporal modulation, or large regions with modulation, but only two point perturbations on the ring. All results are obtained using realistic values of modulation and validated using an in-house full-wave solver. We achieve 21 dB isolation and -0.25 dB insertion loss at the telecommunication wavelengths.

Coherently controllable terahertz plasmon-induced transparency using a coupled Fano-Lorentzian metasurface

Metamaterials have been engineered to achieve electromagnetically induced transparency (EIT)-like behavior, analogous to those in quantum optical systems. These meta-devices are opening new paradigms in terahertz communication, ultra-sensitive sensing and EIT-like anti-reflection. The controlled coupling between a sub-radiant and a super-radiant particle in the unit cells of these metamaterial can enable multiple narrow plasmon induced transparency (PIT) windows over a broad band, with considerable group delay of electromagnetic field (slow light effect). Phase coherence between these PIT windows is highly desired for next-generation multichannel communication network. Herein, we numerically and experimentally validate a controllable frequency hopping mechanism between "slow light" windows in the terahertz (THz) regime. The effective media are composed of plasmonic "molecules" in which an asymmetric split-ring resonator (ASRR) or Fano resonator is displaced on the side of a cut-wire (Lorentz oscillator). Two metasurfaces where ASRR is on opposite side of the cut-wire are investigated. In these two cases, the proximity of the cut-wire to the gap on the ASRR having asymmetry is different. On one side, when the gap is nearer to the cut wire, displacing the ASRR along the cut-wire, produces only one narrow transparency window at 0.8 THz, corresponding to 20 ps group delay. When the ASRR is positioned on the opposite side, such that the gap is further, two transparency windows are observed when the ASRR is displaced along the cut-wire. That is, the transparency window hops from 0.8 THz to 1.2 THz. This corresponds to an increase from 20 to 30 ps in slow light effect. Numerical simulations suggest these single or multiple PIT windows occur if the couplings between the plasmonic modes in the different arrangements are either in-phase or out-of-phase, respectively.

Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics

In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for continuous topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging wave numbers. Considering a nonreciprocal plasma as a model system, we show that the inclusion of spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wave numbers. Most importantly, however, our findings show that, for the considered cases, the correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Our work helps clarifying the subtle and rich topological wave physics of continuous media.

Absence of unidirectionally propagating surface plasmon-polaritons at nonreciprocal metal-dielectric interfaces

In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical using both a general thermodynamic argument and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton at metal-dielectric interfaces remains bidirectional for all frequencies.

The local Drude model predicts that, under certain conditions, surface plasmon polaritons at a metal-dielectric surface have a frequency range where only unidirectional propagation is supported. Here, the authors show that in more realistic non-local models surface plasmon polaritons exhibit bidirectional propagation for all frequencies.

Magnetic field assisted beam-scanning leaky-wave antenna utilizing one-way waveguide

We propose a Leaky-Wave Antenna (LWA) based on one-way yttrium-iron-garnet (YIG)-air-metal waveguide. We first analyze the dispersion of the LWA, showing the one-way feature and the radiation loss. Owing to the unique one-way dispersive property, the beam radiated from the LWA can have very narrow beam width, at the same time having large scanning angle. The main beam angle obtained by full-wave simulation is consistent with our theoretical prediction with the aid of the dispersion. For a given frequency, we can realize continuous beam scanning by varying the magnetic field, where the 3 dB beam width is much narrower than previously demonstrated. Our results pave a new way to realize continuous angle scanning at a fix frequency for modern communications.

Demonstration of group delay above 40 ps at terahertz plasmon-induced transparency windows

Herein, we demonstrate one of the highest terahertz group delay of 42.4 ps achieved experimentally at 0.23 THz, on a flexible planar metamaterial. The unit cell of metasurface is made up of a textured closed cavity and another experimentally concentric metallic arc. By tuning the central angle of the metallic arc, its intrinsic dipolar mode is in destructive interference with the spoof localized surface plasmon (SLSP) on textured closed cavity, which results in a plasmon-induced transparency phenomenon. The measured transmittances of as-fabricated samples using terahertz-time domain spectroscopy validate numerical results using extended coupled Lorentz oscillator model. It is found that the coupling coefficient and damping ratio of SLSP relies on the radius of the ring structure of textured closed cavity. As a consequence, the slow light maximum values become manoeuverable in strength at certain frequencies of induced transparency windows. To the best of our knowledge, our experimental result is currently the highest value demonstrated so far within metasurface at terahertz band.

Dual dynamically tunable plasmon-induced transparency in H-type-graphene-based slow-light metamaterial

An H-type-graphene-based slow-light metamaterial is proposed to produce a dual plasmon-induced transparency phenomenon, which can be effectively modulated by Fermi level, carrier mobility of graphene, and the medium environment. The data calculated by coupled mode theory and results of numerical simulation show prominent agreement. In addition, both the simplicity and continuity of the units of graphene-based metamaterial are extraordinary advantages. Furthermore, the slow-light characteristics of the proposed structure show that the group refractive index is as high as 237, which is more competitive than some other slow-light devices.

Nanoscale nonreciprocity via photon-spin-polarized stimulated Raman scattering

Time reversal symmetry stands as a fundamental restriction on the vast majority of optical systems and devices. The reciprocal nature of Maxwell's equations in linear, time-invariant media adds complexity and scale to photonic diodes, isolators, circulators and also sets fundamental efficiency limits on optical energy conversion. Though many theoretical proposals and low frequency demonstrations of nonreciprocity exist, Faraday rotation remains the only known nonreciprocal mechanism that persists down to the atomic scale. Here, we present photon-spin-polarized stimulated Raman scattering as a new nonreciprocal optical phenomenon which has, in principle, no lower size limit. Exploiting this process, we numerically demonstrate nanoscale nonreciprocal transmission of free-space beams at near-infrared frequencies with a 250 nm thick silicon metasurface as well as a fully-subwavelength plasmonic gap nanoantenna. In revealing all-optical spin-splitting, our results provide a foundation for compact nonreciprocal communication and computing technologies, from nanoscale optical isolators and full-duplex nanoantennas to topologically-protected networks.

Proof of concept of a frequency-preserving and time-invariant metamaterial-based nonlinear acoustic diode

Acoustic filters and metamaterials have become essential components for elastic wave control in applications ranging from ultrasonics to noise abatement. Other devices have been designed in this field, emulating their electromagnetic counterparts. One such case is an acoustic diode or rectifier, which enables one-way wave transmission by breaking the wave equation-related reciprocity. Its achievement, however, has proved to be rather problematic, and current realizations display a number of shortcomings in terms of simplicity and versatility. Here, we present the design, fabrication and characterization of a device able to work as an acoustic diode, a switch and a transistor-like apparatus, exploiting symmetry-breaking nonlinear effects like harmonic generation and wave mixing, and the filtering capabilities of metamaterials. This device presents several advantages compared with previous acoustic diode realizations, including versatility, time invariance, frequency preserving characteristics and switchability. We numerically evaluate its efficiency and demonstrate its feasibility in a preliminary experimental realization. This work may provide new opportunities for the practical realization of structural components with one-way wave propagation properties.

Breather arrest, localization, and acoustic non-reciprocity in dissipative nonlinear lattices

The effect of on-site damping on breather arrest, localization, and non-reciprocity in strongly nonlinear lattices is analytically and numerically studied. Breathers are localized oscillatory wavepackets formed by nonlinearity and dispersion. Breather arrest refers to breather disintegration over a finite "penetration depth" in a dissipative lattice. First, a simplified system of two nonlinearly coupled oscillators under impulsive excitation is considered. The exact relation between the number of beats (energy exchanges between oscillators), the excitation magnitude, and the on-site damping is derived. Then, these analytical results are correlated to those of the semi-infinite extension of the simplified system, where breather penetration depth is governed by a similar law to that of the finite beats in the simplified system. Finally, motivated by the experimental results of Bunyan, Moore, Mojahed, Fronk, Leamy, Tawfick, and Vakakis [Phys. Rev. E 97, 052211 (2018)], breather arrest, localization, and acoustic non-reciprocity in a non-symmetric, dissipative, strongly nonlinear lattice are studied. The lattice consists of repetitive cells of linearly grounded large-scale particles nonlinearly coupled to small-scale ones, and linear intra-cell coupling. Non-reciprocity in this lattice yields either energy localization or breather arrest depending on the position of excitation. The nonlinear acoustics governing non-reciprocity, and the surprising effects of existence of linear components in the coupling nonlinear stiffnesses, in the acoustics, are investigated.