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Recent advances in the field of structured waves have resulted in sophisticated coherent wavefront shaping schemes that provide unprecedented control of waves in various complex settings. These techniques exploit multiple scattering events and the resulting interference of wave paths within these complex environments. Here, we introduce the concept of targeted mode transport (TMT), which enables energy transfer from specific input channels to designated output channels in multimode wave-chaotic cavities by effectively engaging numerous cavity modes. We develop a statistical theory that provides upper bounds on optimal TMT, incorporating operational realities such as losses, coupling strengths and the accessibility of specific interrogating channels. The theoretical predictions for the probability distribution of TMT eigenvalues are validated through experiments with microwave chaotic networks of coaxial cables as well as two-dimensional and three-dimensional complex cavities. These findings have broad implications for applications ranging from indoor wireless communications to imaging and beyond., Comment: 21 pages, 8 figures

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks, wavefront shaping protocols, active metasurface development, and more. At their core, these achievements rely on our ability to engineer the resonant spectrum of the underlying physical structures which is conventionally accomplished by carefully imposing geometrical and/or dynamical symmetries. In contrast, by taking active control over the boundary conditions in complex scattering environments which lack artificially-imposed geometric symmetries, we demonstrate via microwave experiments the ability to manipulate the spectrum of the scattering operator. This active control empowers the creation, destruction and repositioning of exceptional point degeneracies (EPD's) in a two-dimensional (2D) parameter space. The presence of EPD's signifies a coalescence of the scattering eigenmodes, which dramatically affects transport. The scattering EPD's are partitioned in domains characterized by a binary charge, as well as an integer winding number, are topologically stable in the two-dimensional parameter space, and obey winding number-conservation laws upon interactions with each other, even in cases where Lorentz reciprocity is violated; in this case the topological domains are destroyed. Ramifications of this understanding is the proposition for a unique input-magnitude and phase-insensitive 50:50 in-phase/quadrature (I/Q) power splitter. Our study establishes an important step towards complete control of scattering processes in complex non-Hermitian settings.

There has recently been a growing effort to understand in a comprehensive manner the physics and intricate dynamics of many-body and many-state (multimode) interacting bosonic systems. For instance, in photonics, nonlinear multimode fibers are nowadays intensely investigated due to their promise for ultra-high-bandwidth and high-power capabilities. Similar prospects are pursued in connection with magnon Bose-Einstein condensates, and ultra-cold atoms in periodic lattices for room-temperature quantum devices and quantum computation respectively. While it is practically impossible to monitor the phase space of such complex systems (classically or quantum mechanically), thermodynamics, has succeeded to predict their thermal state: the Rayleigh-Jeans (RJ) distribution for classical fields and the Bose-Einstein (BE) distribution for quantum systems. These distributions are monotonic and promote either the ground state or the most excited mode. Here, we demonstrate the possibility to advance the participation of other modes in the thermal state of bosonic oligomers. The resulting non-monotonic modal occupancies are described by a microcanonical treatment while they deviate drastically from the RJ/BE predictions of canonical and grand-canonical ensembles. Our results provide a paradigm of ensemble equivalence violation and can be used for designing the shape of thermal states., Comment: 17 pages, 11 figures

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation $\omega(k)$ of a periodic structure where the first and the second derivatives of $\omega$ with respect to $k$ vanish. An SIP is associated with a third order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Here, we propose a novel scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/ attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity., Comment: 4 pages, 3 figures

Damping typically results in attenuation of vibrations and elastic wave propagation in mechanical systems. Contrary to this conventional understanding, we demonstrate experimentally and explain theoretically the revival of an elastic wave transmitted through a periodic metastructure when a weak non-Hermitian defect (damping mechanism) induces violation of time-reversal symmetry. Damping alters the nature of the system's resonant modes, instigating interference in the scattering field. This leads to transmission revival, revealing the presence of hidden modes which are otherwise masked by the symmetry. Our findings offer an innovative approach for designing dissipation-driven switches and controllers and non-destructive structural health monitoring systems.

We develop a Coherent Perfect Absorption (CPA) protocol for cases where scale invariance is violated due to the presence of nonlinear mechanisms. We demonstrate, using a microwave setting that lacks geometrical symmetries, that the nonlinearity offers new reconfigurable modalities: the destruction or formation of nonlinear CPAs (NL-CPAs), and their frequency positioning and bandwidth management using the incident power as a control knob. The latter occurs via the formation of exceptional point degeneracies of the zeroes of nonlinear scattering processes. Our results establish NL-CPA protocols as a versatile scheme for the creation of reconfigurable hot/cold-spots in complicated enclosures (e.g. buildings or vessels) with applications to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare., Comment: 16 pages, 9 figures

We show that a single nonlinear defect can thermalize an initial excitation towards a Rayleigh-Jeans (RJ) state in complex multimoded systems. The thermalization can be hindered by disorder-induced localization phenomena which drive the system into a metastable RJ state. It involves only a (quasi-)isolated set of prethermal modes and can differ dramatically from the thermal RJ. We develop a one-parameter scaling theory that predicts the density of prethermal modes and we derive the modal relaxation rate distribution, establishing analogies with the Thouless conductance. Our results are relevant to photonics, optomechanics, and cold atoms., Comment: 7 page, 4 figures

Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a non-equilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still {\it terra incognita}. Here, by combining Landauer and kinematics formalisms we develop a one-parameter scaling theory that describes the transport in one-dimensional MMNPCs from a ballistic to a diffusive regime. We also derive a photonic version of the Wiedemann -Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPC and may be useful for the design of all-optical cooling protocols., Comment: 6 pages, 3 figures && Supplementary Material (6 pages, no figures)

Bound states in the continuum (BICs) defy conventional wisdom that assumes a spectral separation between propagating waves, that carry energy away, and spatially localized waves corresponding to discrete frequencies. They can be described as resonance states with infinite lifetime, i.e., leaky modes with zero leakage. The advent of metamaterials and nanophotonics allowed the creation of BICs in a variety of systems. Mainly, BICs have been realized by destructive interference between outgoing resonant modes or exploiting engineered global symmetries that enforce the decoupling of a symmetry-incompatible bound mode from the surrounding radiation modes. Here, we introduce theoretically BICs relying on a different mechanism, namely local symmetries that enforce a field concentration on a part of a complex system without implying any global symmetry. We experimentally implement such BICs using microwaves in a compact one-dimensional photonic network and show that they emerge from the annihilation of two topological singularities, a zero and a pole, of the measured scattering matrix. Our alternative for achieving BICs in complex wave systems may be useful for applications like sensing, lasing, and enhancement of nonlinear interactions that require high-$Q$ modes., Comment: 11 pages, 6 figures

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing group velocity of its propagating component. We have developed a theoretical framework to study the time evolution of wavepackets centered at an SIP. Analysis of the evolution of statistical moments distribution of linear pulses shows a strong deviation from the conventional ballistic wavepacket dynamics in dispersive media. The presence of nonlinear interactions dramatically changes the situation, resulting in a mostly ballistic propagation of nonlinear wavepackets with the speed and even the direction of propagation essentially dependent on the wavepacket amplitude. Such a behavior is unique to nonlinear wavepackets centered at an SIP and can be used for the realization of a novel family of beam power routers for classical waves., Comment: 9 pages, 5 figures

Exceptional point degeneracies (EPD) of linear non-Hermitian systems have been recently utilized for hypersensitive sensing. This proposal exploits the sublinear response that the degenerate frequencies experience once the system is externally perturbed. The enhanced sensitivity, however, might be offset by excess (fundamental and/or technical) noise. Here, we developed a self-oscillating nonlinear platform that supports transitions between two distinct neuromorphic functionalities -- one having a spatially symmetric steady-state, and the other with an asymmetric steady-state -- and displays nonlinear EPDs (NLEPDs) that can be employed for noise-resilient sensing. The experimental setup incorporates a nonlinear electronic dimer with voltage-sensitive coupling and demonstrates two-orders signal-to-noise enhancement of voltage variation measurements near NLEPDs. Our results resolve a long-standing debate on the efficacy of EPD-sensing in active systems above self-oscillating threshold., Comment: 15 pages, 4 figures + Supplementary Information

The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear wave transport, where nonlinear interactions are omitted, and are described using Random Matrix Theory (RMT). Here, using a nonlinear complex network of coaxial cables (graphs), we exploit both experimentally and theoretically the interplay of nonlinear interactions and wave chaos. We develop general theories that describe our asymmetric transport (AT) measurements, its universal bound, and its statistical description via RMT. These are controlled by the structural asymmetry factor (SAF) characterizing the structure of the graph. The SAF dictates the asymmetric intensity range (AIR) where AT is strongly present. Contrary to the conventional wisdom that expects losses to deteriorate the transmittance, we identify (necessary) conditions for which the AIR (AT) increases without deteriorating the AT (AIR). Our research initiates the quest for universalities in wave transport of nonlinear chaotic systems and has potential applications for the design of magnetic-free isolators., Comment: 21 pages, 9 figures

Archetypal motors produce work when two slowly varying degrees of freedom (DOF) move around a closed loop of finite area in the parameter space. Here, instead, we propose a simple autonomous {\it monoparametric} optomechanical engine that utilizes nonlinearities to turn a constant energy current into a nonconservative mechanical force. The latter self-sustains the periodic motion of a mechanical DOF whose frequency is orders of magnitude smaller than the photonic DOF. We have identified conditions under which the maximum extracted mechanical power is invariant and show a new type of self-induced robustness of the power production against imperfections and driving noise., Comment: Main text: 8 pages, 4 figures. Includes supplement: 8 pages, 5 figures

We study the elastodynamics of a periodic metastructure incorporating a defect pair that enforces a parity-time (PT) symmetry due to a judiciously engineered imaginary impedance elements - one having energy amplification (gain) and the other having an equivalent attenuation (loss) mechanism. We show that their presence affects the initial band structure of the periodic Hermitian metastructure and leads to the formation of numerous exceptional points (EPs) which are mainly located at the band edges where the local density of modes is higher. The spatial location of the PT-symmetric defect serves as an additional control over the number of emerging EPs in the corresponding spectra as well as the critical non-Hermitian (gain/loss) strength required to create the first EP - a specific defect location minimizes the critical non-Hermitian strength. We use both finite element and coupled-mode-theory-based models to investigate these metastructures, and use a time-independent second-order perturbation theory to further demonstrate the influence of the size of the metastructure and the PT-symmetric defect location on the minimum non-Hermitian strength required to create the first EP in a band. Our findings motivate feasible designs for the experimental realization of EPs in elastodynamic metastructures.

Exceptional points (EP) are non-Hermitian spectral degeneracies where both eigenvalues and their corresponding eigenvectors coalesce. Recently, EPs have attracted a lot of attention as a means to enhance the responsivity of sensors, via the abrupt resonant detuning occurring in their proximity. In many cases, however, the EP implementation is accompanied by noise enhancement leading to the degradation of the signal-to-noise performance of the sensor . The excess noise can be of fundamental nature (due to the eigenbasis collapse) or of technical nature associated with the use of amplification mechanisms utilized for the realization of EPs. Here we show, using an EP-based $\mathcal{PT}$-symmetric electromechanical accelerometer, that the enhanced technical noise can be surpassed by the enhanced responsivity to applied accelerations. The noise due to eigenbasis collapse is mitigated by exploiting the detuning from a transmission peak degeneracy (TPD), which forms when the sensor is weakly coupled to transmission lines, as a sensitivity measurant. These TPDs occur at a frequency and controlled parameters for which the bi-orthogonal eigen-basis is still complete and are distinct from the EPs of the $\mathcal{PT}$-sensor. They also show a slightly enhanced detuning rate compared to the typically utilized EPs. Our device demonstrates a three-fold signal-to-noise ratio enhancement compared to configurations for which the system operates away from the TPD.

While boosting signals with amplification mechanisms is a well established approach, attenuation mechanisms are typically considered an anathema because they degrade the efficiency of the structures employed to perform useful operations on these signals. An emerging alternate viewpoint promotes losses as a novel design element by utilizing the notion of exceptional point degeneracies (EPDs) points in parameter space where the eigenvalues of the underlying system and the associated eigenvectors simultaneously coalesce. Here, we demonstrate a direct consequence of such eigenbasis collapse in elastodynamics, an unusual enhancement of actuation force by a judiciously designed non-Hermitian metamaterial supporting an EPD that is coupled to an actuation source. Intriguingly, the EPD enables this enhancement while maintaining a constant signal quality. Our work constitutes a proof-of-principle design which can promote a new class of reconfigurable nano-indenters and robotic-actuators. Importantly, it reveals the ramifications of non-Hermiticity in boosting the Purcell emissivity enhancement factor beyond its expected value, which can guide the design of metamaterials with enhanced emission that does not deteriorate signal quality for mechanical, acoustic, optical, and photonic applications., Comment: 16 Pages, 4 Figures

We establish dispersion engineering rules that allow us to control the thermalization process and the thermal state of an initial beam propagating in a multimode nonlinear photonic circuit. To this end, we have implemented a kinetic equation (KE) approach in systems whose Bloch dispersion relation exhibits bands and gaps. When the ratio between the gap-width to the band-width is larger than a critical value, the KE has stationary solutions which differ from the standard Rayleigh-Jeans (RJ) distribution. The theory also predicts the relaxation times above which such non-conventional thermal states occur. We have tested the validity of our results for the prototype SSH model whose connectivity between the composite elements allows to control the band-gap structure. These spectral engineering rules can be extended to more complex photonic networks that lack periodicity but their spectra consist of groups of modes that are separated by spectral gaps., Comment: 11 pages, 4 figures, 3 pages of supplementary material

Environmental perturbations and noise are source of mode mixing and interferences between the propagating modes of a complex multi-mode fiber. Typically, they are characterized by their correlation (paraxial) length, and their spectral content which describes the degree of coupling between various modes. We show that an appropriate control of these quantities allows to engineer Levy-type relaxation processes of an initial mode excitation. Our theory, based on Random Matrix Theory modeling, is tested against realistic simulations with multi-mode fibers., Comment: 5 pages, 5 figures

We numerically implement the concept of thermal radiation pumps in realistic photonic circuits and demonstrate their efficiency to control the radiation current, emitted between two reservoirs with equal temperature. The proposed pumping scheme involves a cyclic adiabatic modulation of two parameters that control the spectral characteristics of the photonic circuit. We show that the resulting pumping cycle exhibits maximum radiation current when a cyclic modulation of the system is properly engineered to be in the proximity of a resonance degeneracy in the parameter space of the photonic circuit. A developed Floquet scattering framework, which in the adiabatic limit boils down to the analysis of an instantaneous scattering matrix, is offering an engineering tool for designing and predicting the performance of such thermal pumps. Our predictions are confirmed by time-domain simulations invoking an adiabatically driven photonic cavity., Comment: Main text: 10 pages, 4 figures. Supplementary Material: 7 pages, 1 figure

We experimentally and theoretically challenge the concept of coherent perfect absorption (CPA) as a narrow frequency resonant mechanism associated with scattering processes that respect scale-invariance. Using a microwave platform, consisting of a lossy nonlinear resonator coupled to two interrogating antennas, we show that a coherent incident excitation can trigger a self-induced perfect absorption once its intensity exceeds a critical value. Importantly, a (near) perfect absorption persists for a broad band frequency range around the nonlinear CPA condition. Its origin is traced to a quartic behavior that the absorbance spectrum acquires in the proximity of a CPA associated with a new kind of exceptional point degeneracy related to the zeros of the nonlinear scattering operator., Comment: 11 pages (Manuscript: 7 pages, 3 figures, Supplemental: 4 pages, 4 figures)

Millimeter wave (mm-wave) communications and radar receivers capable of processing small signals must be protected from high-power signals, which can damage sensitive receiver components. Many of these systems arguably can be protected by using photonic limiting techniques, in addition to electronic limiting circuits in receiver front-ends. Here we demonstrate, experimentally and numerically, a free-space, reflective mm-wave limiter based on a multilayer structure involving a nanolayer of vanadium dioxide (VO2), experiencing a thermal insulator-to-metal transition. The multilayer acts as a variable reflector, controlled by the input power. At low input power levels, VO2 remains dielectric, and the multilayer exhibits resonant transmittance. When the input power exceeds a threshold level, the emerging metallic phase renders the multilayer highly reflective while dissipating a small portion of the input power without damage to the limiter. In the case of a Gaussian beam, the limiter has a nearly constant output above the limiting threshold input., Comment: 18 pages, 6 figures, 3 supplementary figures and 1 supplementary table

A thermal current, generated by a temperature gradient between two reservoirs coupled to a carefully designed photonic or (micro-) electromechanical circuit, might induce non-conservative forces that impulse a mechanical degree of freedom to move along a closed trajectory. We show that in the limit of long - but finite - modulation periods, the extracted power and the efficiency of such autonomous motors can be maximized when an appropriately designed spatio-temporal symmetry violation is induced and when the motor operates in the vicinity of exceptional point (EP) degeneracies. These singularities appear in the spectrum of the effective non-Hermitian Hamiltonian that describes the combined circuit-reservoirs system when we judiciously tailor the coupling between them. In the photonic framework, these motors can be propelled by thermal radiation and can be utilized as autonomous self-powered microrobots, or as micro-pumps for microfluidics in biological environments. The same designs can be also implemented with electromechanical elements for harvesting ambient mechanical (or electrical) noise for powering a variety of auxiliary systems., Comment: 9 pages, 4 figures - Supp. Mat. 2 pages

We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits a frequency spectrum with unfolding (fractal) symmetries. Our study reveals a scale-free formation of exceptional points (EP) whose density is dictated by the fractal dimension of their Hermitian spectra. Demonstrated in a quasi-periodic Aubry-Harper, a geometric H-tree-fractal, and an aperiodic Fibonacci Ed-MetaMater, the universal route for EP-formation is established via a coupled mode theory model with controllable fractal spectrum. This universality will enable the rational design of novel Ed-MetaMater for hypersensitive sensing and elastic wave control.

By utilizing Floquet driving protocols and interlacing them with a judicious reservoir emission engineering we achieve extreme non-reciprocal thermal radiation. We show that the latter is rooted in an interplay between a direct radiation process occurring due to temperature bias between two thermal baths and the modulation process which is responsible for pumped radiation heat. Our theoretical results are confirmed via time-domain simulations with RF circuits., Comment: Main text (6 pages, 4 figures), and Supplemental Material ( 5 pages)

We investigate, using a microwave platform consisting of a non-Hermitian Su-Schrieffer-Heeger array of coupled dielectric resonators, the interplay of a lossy nonlinearity and CT-symmetry in the formation of defect modes. The measurements agree with the theory which predicts that, up to moderate pumping, the defect mode is an eigenstate of the CT-symmetric operator and retains its frequency at the center of the gap. At higher pumping values, the system undergoes a self-induced explicit \CT-symmetry violation which removes the spectral topological protection and alters the shape of the defect mode., Comment: 9 pages, 5 figures including supplement

We propose an optomechanical design, consisting of a parity-time symmetric multilayer structure tuned at exceptional-point degeneracy (EPD), with an adjustable layer that is coupled to micromechanical springs. The deflections of this layer in response to accelerations ${\alpha}$, lead to square-root resonance detuning ${\Delta}{\omega}\equiv{\omega}-{\omega}_{EPD}\propto \sqrt{\alpha}$ - thus dramatically enhancing the probe of ultra-small accelerations ${\alpha}\ll1$. Our design is scalable and can, in principle, support higher $N$ order EPDs with sensitivity ${\Delta}{\omega}\propto\sqrt[n]{\alpha}$. It also provides a pathway towards a new generation of on-chip hypersensitive accelerometers and vibrometers.

Wavefront shaping (WFS) schemes for efficient energy deposition in weakly lossy targets is an ongoing challenge for many classical wave technologies relevant to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare. In many circumstances these targets are embedded inside complicated enclosures which lack any type of (geometric or hidden) symmetry, such as complex networks, buildings, or vessels, where the hypersensitive nature of multiple interference paths challenges the viability of WFS protocols. We demonstrate the success of a new and general WFS scheme, based on coherent perfect absorption (CPA) electromagnetic protocols, by utilizing a network of coupled transmission lines with complex connectivity that enforces the absence of geometric symmetries. Our platform allows for control of the local losses inside the network and of the violation of time-reversal symmetry via a magnetic field; thus establishing CPA beyond its initial concept as the time-reversal of a laser cavity, while offering an opportunity for better insight into CPA formation via the implementation of semiclassical tools., Comment: Figures have been updated with new simulation data that utilized a more detailed modeling of the experimental set-up. New result of a double CPA event captured in a 2D quarter bow-tie billiard is added

We investigate the collective dynamics of nonlinearly interacting modes in multimode photonic settings with long-range couplings. To this end, we have established a connection with the theory of spin networks. The emerging "photonic spins" are complex, soft (their size is not fixed) and their dynamics has two constants of motion. Our analysis shed light on the nature of the thermal equilibrium states and reveals the existence of optical phase-transitions which resemble a paramagnetic to a ferromagnetic and to a spin-glass phase transitions occurring in spin networks. We show that, for fixed average optical power, these transitions are driven by the type (constant or random couplings) of the network connectivity and by the total energy of the optical signal.

We present a microwave realization of a reflective topological limiter based on an explicit self-induced violation of a charge-conjugation (CT) symmetry. The starting point is a bipartite structure created by coupled dielectric resonators with a topological defect placed at the center and two lossy resonators placed on the neighboring sites of the defect. This defect supports a resonant mode if the CT-symmetry is present, while it is suppressed once the symmetry is violated due to permittivity changes of the defect resonator associated with high irradiances of the incident radiation. This destruction leads to a suppression of transmittance and a subsequent increase of the reflectance while the absorption is also suppressed., Comment: 7 pages, 13 figures, 1 table

Receiver protectors (RPs) shield sensitive electronics from high-power incoming signals that might damage them. Typical RP schemes range from simple fusing and PIN diodes, to superconducting circuits and plasma cells - each having a variety of drawbacks ranging from unacceptable system downtime and self-destruction to significant insertion losses and power consumption. Here, we theoretically propose and experimentally demonstrate a unique self-shielding RP based on a coupled-resonator-microwave-waveguide (CRMW) with a topological defect being inductively coupled to a diode. This RP utilizes a charge-conjugation (C) symmetric resonant defect mode that is robust against disorder and demonstrates high transmittance at low incident powers. When incident power exceeds a critical value, a self-induced resonant trapping effect occurs leading to a dramatic suppression of transmittance and a simultaneous increase of the reflectance close to unity. The proposed RP device is self-protected from overheating and electrical breakdown and can be utilized in radars, reflection altimeters, and a broad range of communication systems., Comment: 9 pages, 4 figures

We control the direction and magnitude of thermal radiation, between two bodies at equal temperature (in thermal equilibrium), by invoking the concept of adiabatic pumping. Specifically, within a resonant near-field electromagnetic heat transfer framework, we utilize an {\it instantaneous} scattering matrix approach to unveil the critical role of wave interference in radiative heat transfer. We find that appropriately designed adiabatic pumping cycling near diabolic singularities can dramatically enhance the efficiency of the directional energy transfer. We confirm our results using a realistic electronic circuit set-up.

Imperfections in multimode systems lead to mode-mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution). We show that the long-scale dynamics of an initial excitation that spread in mode space can be tailored by the coherent dynamics on short-scale. In particular we unveil a universal crossover from exponential to power-law ballistic-like decay of the initial mode. Our results have applications to various wave physics frameworks, ranging from multimode fiber optics to quantum dots and quantum biology.

The ability to control and direct acoustic energy is essential for many engineering applications such as vibration and noise control, invisibility cloaking, acoustic sensing, energy harvesting, and phononic switching and rectification. The realization of acoustic regulators requires overcoming fundamental challenges inherent to the time-reversal nature of wave equations. Typically, this is achieved by utilizing either a parameter that is odd-symmetric under time-reversal or by introducing passive nonlinearities. The former approach is power consuming while the latter has two major deficiencies: it has high insertion losses and the outgoing signal is harvested in a different frequency than that of the incident wave due to harmonic generation. Here, we adopt a unique approach that exploits spatially distributed linear and nonlinear losses in a fork-shaped resonant metamaterial. Our compact design demonstrates asymmetric acoustic reflectance and transmittance, and acoustic switching. In contrast to previous studies, our non-Hermitian metamaterial exhibits asymmetric transport with high frequency purity of the outgoing signal.

We utilize an effective Hamiltonian formalism, within the Floquet scattering framework, to design a class of driving-induced non-reciprocal components with {\it minimal} complexity. In the high driving-frequency limit, where our scheme is formally applicable, these designs demonstrate a leading order non-reciprocal performance which is inverse proportional to the driving frequency. Surprisingly, the optimal non-reciprocal behavior persists also in the slow driving regime. Our approach highlights the importance of physical loops in the design of these driven non-reciprocal components.

The design of time-independent effective Hamiltonians that describe periodically modulated systems, provides a promising approach to realize new forms of matter. This, so-called, Floquet engineering approach is currently limited to the description of wavepacket dynamics. Here, we utilize the notion of effective Hamiltonians and develop a Floquet engineering scattering formalism that relies on a systematic high-frequency expansion of the scattering matrix. The method unveils the critical role of micromotion. An application to the case of non-reciprocal transport is presented., Comment: 5 pages, 2 figures

We demonstrate that the integration of a phase-change material (PCM) in one of the two microresonators of a photonic metamolecule, coupled to a bus waveguide, can lead to unidirectional Fano resonances and to the emergence of a unidirectional transmission window. The phase change is caused by light-induced heating and is accompanied by an abrupt increase in the extinction coefficient of the PCM resonator. Due to the photonic circuit asymmetry, the critical value of the input light intensity triggering the phase change is strongly dependent on the input light direction. The latter determines the unidirectional nature of the emerging transmission window. This effect can be utilized in on-chip magnetic-free isolators and Q-switches.

We introduce the concept of multichannel Floquet Perfect Absorbers (FPAs) which are periodically modulated lossy interferometric traps that completely absorb incident monochromatic waves. The proposed FPA protocols utilize a Floquet engineering approach which inflicts a variety of emerging phenomena and features: reconfigurability of perfect absorption (PA) for a broad range of frequencies of the incident wave; PA for infinitesimal local losses, and PA via critical coupling with high-Q modes by inducing back-reflection dynamical mirrors., Comment: 7 pages, 1 page of supplementary material, 3 figures

We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic scattering -- thus minimizing the use of information related to the exact characteristics of the chaotic enclosure. The proposed theory applies equally well to systems with and without time-reversal symmetry., Comment: 8 pages, 3 figures, version 2 with more details in the supplement

We introduce the notion of adiabatic state-flip of a Floquet Hamiltonian associated with a non-Hermitian system that it is subjected to two driving schemes with clear separation of time scales. The fast (Floquet) modulation scheme is utilized to re-allocate the exceptional points in the parameter space of the system and re-define the topological features of an adiabatic cyclic modulation associated with the slow driving scheme. Such topological re-organization can be used in order to control the adiabatic transport between two eigenmodes of the Floquet Hamiltonian. The proposed scheme provides a degree of reconfigurability of adiabatic state transfer which can find applications in system control in photonics and microwave domains., Comment: 5 pages, 2 figures

We develop a theoretical framework that lays out the fundamental rules under which a periodic (Floquet) driving scheme can induce non-reciprocal transport. Our approach utilizes an extended Hilbert space where a Floquet network with an extra (frequency) dimension naturally arises. The properties of this network (its on-site potential and the intersite couplings) are in one-to-one correspondence with the initial driving scheme. Its proper design allows for a control of the multipath scattering processes and the associated interferences. We harness this degree of freedom to realize driving schemes with narrow or broad-band non-reciprocal transport., Comment: Extension discussing Floquet designs for broad band versus narrow band control of Non-Reciprocal Transport

Periodic structures with Bloch dispersion relation supporting a stationary inflection point (SIP) can display a unique scattering feature, the frozen mode regime (FMR). The FMR is much more robust than common cavity resonances; it is much less sensitive to the boundary conditions, structural imperfections, and losses. Using perturbation theory, we analyze the FMR in the realistic case of a finite fragment of a periodic structure. We show that in close proximity of SIP frequency, the character of the FMR is qualitatively different from the known case of a semi-infinite structure., Comment: 7 pages, 2 figures with the supplement included

We propose a new driving scheme, when different parts of a system are driven with different, generally incommensurate, frequencies. Such driving provides a flexible handle to control various properties of the system and to obtain new types of effective (static) Hamiltonians with arbitrary static on-site potential, be it deterministic or random. This allows us to obtain reconfigurable changes in transport, from ballistic to localized (including sub- and super-diffusion), depending on the driving protocol. The versatile reconfigurability extends also to scattering from (locally) driven extended targets. We demonstrate our scheme using, an analytically solvable example, of an one-dimensional tight-binding chain with appropriately driven couplings between nearby sites., Comment: accepted version

We provide an experimental framework where periodically driven PT-symmetric systems can be investigated. The set-up, consisting of two UHF oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT-symmetric broken domains bounded by exceptional point degeneracies. These domains are analyzed and understood using an equivalent Floquet frequency lattice with local PT-symmetry. Management of these PT-phase transition domains is achieved through the amplitude and frequency of the drive., Comment: 6 pages, 3 figures

Phase changing materials (PCM) are widely used for optical data recording, sensing, all-optical switching, and optical limiting. Our focus here is on the case when the change in the transmission characteristics of the optical material is caused by the input light itself. Specifically, the light-induced heating triggers the phase transition in the PCM. In this paper, using a numerical example, we demonstrate that incorporating the PCM in a photonic structure can lead to a dramatic modification of the effects of light-induced phase transition, as compared to a stand-alone sample of the same PCM. Our focus is on short pulses. We discuss some possible applications of such phase-changing photonic structures for optical sensing and limiting., Comment: 8 pages, 5 figures

We show that gyrotropic structures with balanced gain and loss that respect anti-linear symmetries exhibit a giant non-reciprocity at the so-called exact phase where the eigenfrequencies of the isolated non-Hermitian set-up are real. The effect occurs in a parameter domain near an exceptional point (EP) degeneracy, where mode-orthogonality collapses. The theoretical predictions are confirmed numerically in the microwave domain, where a non-reciprocal transport above 90dB is demonstrated, and are further verified using lump-circuitry modeling. The analysis allows us to speculate the universal nature of the phenomenon for any wave system where EP and gyrotropy can co-exist., Comment: 7 pages, 5 figures

We employ the Random Matrix Theory framework to calculate the density of zeroes of an $M$-channel scattering matrix describing a chaotic cavity with a single localized absorber embedded in it. Our approach extends beyond the weak-coupling limit of the cavity with the channels and applies for any absorption strength. Importantly it provides an insight for the optimal amount of loss needed to realize a chaotic coherent perfect absorbing (CPA) trap. Our predictions are tested against simulations for two types of traps: a complex network of resonators and quantum graphs., Comment: published version