Network Of Resonators Research Articles

Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics in two coupled Kerr parametric oscillators.

Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of states manifest via a series of bifurcations, including bifurcations that proliferate purely unstable solutions. Here we demonstrate that the latter take a fundamental role in the stochastic dynamics of the system. Specifically, they determine the switching paths and the switching rates between stable solutions. We demonstrate experimentally the impact of the added unstable states on noise-activated switching dynamics in a network of two coupled parametric resonators.

Dynamical Gauge Fields with Bosonic Codes.

The quantum simulation of dynamical gauge field theories offers the opportunity to study complex high-energy physics with controllable low-energy devices. For quantum computation, bosonic codes promise robust error correction that exploits multiparticle redundancy in bosons. Here, we demonstrate how bosonic codes can be used to simulate dynamical gauge fields. We encode both matter and dynamical gauge fields in a network of resonators that are coupled via three-wave mixing. The mapping to a Z_{2} dynamical lattice gauge theory is established when the gauge resonators operate as Schrödinger cat states. We explore the optimal conditions under which the system preserves the required gauge symmetries. Our findings promote realizing high-energy models using bosonic codes.

An Ising machine based on networks of subharmonic electrical resonators

Combinatorial optimization problems are difficult to solve with conventional algorithms. Here we explore networks of nonlinear electronic oscillators evolving dynamically towards the solution to such problems. We show that when driven into subharmonic response, such oscillator networks can minimize the Ising Hamiltonian on non-trivial antiferromagnetically-coupled 3-regular graphs. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillators’ response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one exists, and probes frustration where appropriate. Theoretical modeling of the electronic oscillators and their couplings allows us to accurately reproduce the qualitative features of the experimental results and extends the results to larger graphs. This suggests the promise of this setup as a prototypical one for exploring the capabilities of such an unconventional computing platform.

High-Performance Pockels Effect Modulation and Switching in Silicon-Based GaP/Si, AlP/Si, ZnS/Si, AlN/3C-SiC, GaAs/Ge, ZnSe/GaAs, and ZnSe/Ge Superlattice-On-Insulator Integrated Circuits.

We propose new a Si-based waveguided Superlattice-on-Insulator (SLOI) platforms for high-performance electro-optical (EO) 2 × 2 and N × M switching and 1 × 1 modulation, including broad spectrum and resonant. We present a theoretical investigation based on the tight-binding Hamiltonian of the Pockels EO effect in the lattice-matched undoped , , , , , , and wafer-scale short-period superlattices that are etched into waveguided networks of small-footprint Mach-Zehnder interferometers and micro-ring resonators to yield opto-electronic chips. The spectra of the Pockels r33 coefficient have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces. The large obtained r33 values enable the SLOI circuit platforms to offer a very favorable combination of monolithic construction, cost-effective manufacturability, high modulation/switching speed, high information bandwidth, tiny footprint, low energy per bit, low switching voltage, near-IR-and-telecom wavelength coverage, and push-pull operation. By optimizing waveguide, clad, and electrode dimensions, we obtained very desirable values of the VπL performance metric, in the range of 0.062 to 0.275 V·cm, portending a bright future for a variety of applications, such as sensor networks or Internet of Things (IoT).

Convolutional neural networks with radio-frequency spintronic nano-devices

Convolutional neural networks (LeCun and Bengio 1998 The Handbook of Brain Theory and Neural Networks 255–58; LeCun, Bengio and Hinton 2015 Nature 521 436–44) are state-of-the-art and ubiquitous in modern signal processing and machine vision. Nowadays, hardware solutions based on emerging nanodevices are designed to reduce the power consumption of these networks. This is done either by using devices that implement convolutional filters and sequentially multiply consecutive subsets of the input, or by using different sets of devices to perform the different multiplications in parallel to avoid storing intermediate computational steps in memory. Spintronics devices are promising for information processing because of the various neural and synaptic functionalities they offer. However, due to their low OFF/ON ratio, performing all the multiplications required for convolutions in a single step with a crossbar array of spintronic memories would cause sneak-path currents. Here we present an architecture where synaptic communications are based on a resonance effect. These synaptic communications thus have a frequency selectivity that prevents crosstalk caused by sneak-path currents. We first demonstrate how a chain of spintronic resonators can function as synapses and make convolutions by sequentially rectifying radio-frequency signals encoding consecutive sets of inputs. We show that a parallel implementation is possible with multiple chains of spintronic resonators. We propose two different spatial arrangements for these chains. For each of them, we explain how to tune many artificial synapses simultaneously, exploiting the synaptic weight sharing specific to convolutions. We show how information can be transmitted between convolutional layers by using spintronic oscillators as artificial microwave neurons. Finally, we simulate a network of these radio-frequency resonators and spintronic oscillators to solve the MNIST handwritten digits dataset, and obtain results comparable to software convolutional neural networks. Since it can run convolutional neural networks fully in parallel in a single step with nano devices, the architecture proposed in this paper is promising for embedded applications requiring machine vision, such as autonomous driving.

Dispersive Delay Structures With Asymmetric Arbitrary Group-Delay Response Using Coupled-Resonator Networks With Frequency-Variant Couplings

This article reports the design of coupled-resonator-based microwave dispersive delay structures (DDSs) with arbitrary asymmetric-type group delay response. The design process exploits a coupling matrix representation of the DDS circuit as a network of resonators with frequency-variant couplings (FVCs). The group delay response is shaped using complex transmission zeros (TZs) created by dispersive cross-couplings. We also present an optimization-based synthesis procedure for characteristic polynomials with a prescribed group delay profile. Thus, when compared with prior-art DDS approaches, the proposed DDS solutions allow a general group delay profile to be patterned while incorporating optimization-based coupling matrix design techniques for their synthesis. The design method is validated by full-wave simulations and measurements of three built proof-of-concept prototypes of DDS devices with different shapes of group delay response in waveguide and microstrip technologies.

COMSOL modeling of time reversal focusing in a periodic network of Helmholtz resonators

This presentation will outline the physical and practical considerations for conducting a COMSOL simulation of time reversal focusing in air. Attempts to obtain sub-diffraction-limited time reversal focusing, along with physical and practical consideration, will be presented. Physical considerations include end-corrections, resonator shape and placement, computational domain and anechoic terminations. Practical considerations include mesh size and temporal length. While conducting a time domain study in COMSOL, mesh size is related to the highest frequency and the simulation length is related to the lowest frequency. To maximize computational resources, the simulation uses a restricted bandwidth. Extending the bandwidth is accomplished by combining multiple simulations. Comparison to previous super resolution studies as well as the authors’ equivalent circuit model will also be discussed.

Design of electromagnetic cloak with sequentially connected rectangular split ring resonators for S-band applications

<abstract> <p>An electromagnetic (EM) invisible cloak is designed and analyzed with serially interconnected split ring resonators (SRRs). The cloak consists of an array of a network of split ring resonators which operates at a 3 GHz resonating frequency. The split ring resonators are connected with transmission line and are wrapped around the cylindrical object. Cloak coupled with EM waves gets transferred around the cylindrical object and received to the other side of transmission. Scattering cross section (SCS) is analyzed for both cases, which results in the effect of resonance. The total scattering cross section of the cloaked object is reduced by using SRRs. The simulated and measured results are in great agreement with each other. The transmission-line-connected SRR cloak is useful for S-band applications specifically at 3 GHz resonance.</p> </abstract>

Multi-functional photonic processors using coherent network of micro-ring resonators

Silicon photonics have widespread applications in optical communications, photonic sensors, and quantum information processing systems. Different photonic integrated circuits often require similar basic functional elements such as tunable filters, optical switches, wavelength de-multiplexers, optical delay lines, and polarization crosstalk unscrambling. Other optical signal processing functional elements may be needed in specific applications, for example, the differentiation with respect to time of time-varying optical signals and the implementation of very high extinction interferometers in some integrated quantum photonic circuits. Just as reconfigurable electronic processors in microelectronics have advantages in terms of ready availability and low cost from large-volume generic manufacturing and are useful for configuration into different functionalities in the form of field-programmable gate arrays, here, we show how an integrated coherent network of micro-ring resonators can be used in reconfigurable photonic processors. We demonstrate the implementation of optical filters, optical delay lines, optical space switching fabric, high extinction ratio Mach–Zehnder interferometer, and photonic differentiation in a reconfigurable network where the control of the phase in the different arms of the coherent network can determine the implemented functionality.

Equivalent circuit model to study super resolution in time reversal focusing in a periodic network of Helmholtz resonators

This presentation will introduce equivalent circuit modeling techniques that have been used to simulate the focusing of acoustic signals in a 1-D waveguide. The presence of resonators in the near field of the focus location decreases the effective wavelength of the focus and leads to super resolution. A circuit is created that represents the complete waveguide with the sources. Circuit elements are used to represent both resonators and the propagation of the wave. The spatial extent is simulated at individual frequencies using additional circuit junctions. The wideband response is determined by the superposition of the individual frequency results. Important parameters such as resonator density and the quality factor of the resonators are examined and their influence on the focus will be presented. Methods for solving the circuit models and improving computational efficiency will also be discussed.

Versatile silicon microwave photonic spectral shaper

Optical modulation plays arguably the utmost important role in microwave photonic (MWP) systems. Precise synthesis of modulated optical spectra dictates virtually all aspects of MWP system quality including loss, noise figure, linearity, and types of functionalities that can be executed. However, for such a critical function, the versatility to generate and transform analog optical modulation is severely lacking, blocking the pathways to truly unique MWP functions including ultra-linear links and low-loss high rejection filters. Here, we demonstrate a versatile radiofrequency (RF) photonic spectral shaper integrated in a silicon photonic circuit. The spectral shaper controls the two modulation bands generated from an electro-optic modulation process in their relative amplitude and phase, offering an enhanced versatility for microwave-photonic modulation applications. Using the spectral shaper, we show electrically tailorable modulation transformations. Furthermore, we show a series of unprecedented RF filtering experiments through monolithic integration of the spectral shaper with a network of reconfigurable ring resonators.

Networks of mutually coupled random lasers

Random lasers (RLs) rely on light amplification in a gain material with feedback from multiple scattering in disordered media. They are unconventional light sources characterized by multiple narrow peaks emission with high potential in imaging and sensing applications. At variance with ordinary lasers, optical interaction between single RLs arranged in networks of multiply interconnected resonators remains unexplored. The typical RL architecture where gain material and scatterers are spatially mixed, is unsuitable for the realization of singular devices on the same platform. Here, we use RLs in which gain is restricted to the line between two scattering regions to establish and probe mutual coupling between many RLs. We prove the interaction in the network by detecting the spectral rearrangement of the compound emission as compared to individual RLs. The engineering of coupled RLs sets the basis for building structures with potential to function as optical neural networks.

Heterogeneous Random Laser with Switching Activity Visualized by Replica Symmetry Breaking Maps

In the past decade, complex networks of light emitters are proposed as novel platforms for photonic circuits and lab-on-chip active devices. Lasing networks made by connected multiple gain components and graphs of nanoscale random lasers (RLs) obtained from complex meshes of polymeric nanofibers are successful prototypes. However, in the reported research, mainly collective emission from a whole network of resonators is investigated, and only in a few cases, the emission from single points showing, although homogeneous and broad, spatial emission. In all cases, simultaneous activation of the miniaturized lasers is observed. Here, differently, we realize heterogeneous random lasers made of ribbon-like and highly porous fibers with evident RL action from separated micrometric domains that alternatively switch on and off by tuning the pumping light intensity. We visualize this novel effect by building for the first time replica symmetry breaking (RSB) maps of the emitting fibers with 2 {\mu}m spatial resolution. In addition, we calculate the spatial correlations of the laser regions showing clearly an average extension of 50 {\mu}m. The observed blinking effect is due to mode interaction along light guiding fibers and opens new avenues in the fabrication of flexible photonic networks with specific and adaptable activity.

Current vortices in aromatic carbon molecules

The local current flow through three small aromatic carbon molecules, namely benzene, naphthalene and anthracene, is studied. Applying density functional theory and the non-equilibrium Green's function method for transport, we demonstrate that pronounced current vortices exist at certain electron energies for these molecules. The intensity of these circular currents, which appear not only at the anti-resonances of the transmission but also in vicinity of its maxima, can exceed the total current flowing through the molecular junction and generate considerable magnetic fields. The $\pi$ electron system of the molecular junctions is emulated experimentally by a network of macroscopic microwave resonators. The local current flows in these experiments confirm the existence of current vortices as a robust property of ring structures. The circular currents can be understood in terms of a simple nearest-neighbor tight-binding H\"uckel model. Current vortices are caused by the interplay of the complex eigenstates of the open system which have energies close-by the considered electron energy. Degeneracies, as observed in benzene and anthracene, can thus generate strong circular currents, but also non-degenerate systems like naphthalene exhibit current vortices. Small imperfections and perturbations can couple otherwise uncoupled states and induce circular currents.

Compact low‐pass/band‐pass filters based on quarter‐mode substrate integrated waveguide and a connected network of CSRRs

In this study, a compact low-pass filter (LPF) and two compact dual-wideband band-pass filters (BPFs) are proposed based on a connected network of complementary split-ring resonators (CSRRs) and open CSRRs (OCSRRs). The LPF is designed based on microstrip structure, and then the structure is changed to quarter-mode substrate integrated waveguide for designing the dual-band BPFs. The 3 dB cutoff frequency of the LPF is 1.84 GHz and its size is 0.094λ g × 0.094λ g , where λ is the guide wavelength at 3 dB cutoff frequency. The LPF has a wide stop-band, up to 16 GHz. The first proposed dual-wideband BPF has the centre frequencies of 3.85 and 8.03 GHz, with 3 dB fractional bandwidths of 31.69 and 13.7%, respectively. Finally, a sharper dual-band BPF is obtained by cascading two proposed dual-wideband BPFs and optimising them for the desirable response. The measured centre frequencies of the second dual-band BPF are 3.65 and 7.15 GHz with 3 dB fractional bandwidths of 28.21 and 12.52%, respectively. The measurement results of the fabricated filters are in good agreement with the simulation ones. The filters are compared with similar reported filters in the literature, which confirm the compactness of the proposed filters..

Hyperbolic lattices in circuit quantum electrodynamics.

After two decades of development, cavityquantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space.

Observation of the Crossover from Photon Ordering to Delocalization in Tunably Coupled Resonators.

Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.

Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals

We demonstrate that photonic and phononic crystals consisting of closely spaced inclusions constitute a versatile class of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystal form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous photonic (phononic) crystals are in fact asymptotically equivalent, at low frequencies, to discrete capacitor-inductor (mass-spring) networks whose lumped parameters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch, or branches when the discrete analogue is polyatomic, is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power ; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals. The insight gained from the network approach is used to show that, surprisingly, the continuum created by a closely packed hexagonal lattice of cylinders is represented by a discrete honeycomb lattice. The analogy is utilised to show that the hexagonal continuum lattice has a Dirac-point degeneracy that is lifted in a controlled manner by specifying the area of a symmetry-breaking defect.

Distribution of zeros of the S-matrix of chaotic cavities with localized losses and coherent perfect absorption: non-perturbative results

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 trap. Our predictions are tested against simulations for two types of traps: a complex network of resonators and quantum graphs.

Low frequency bandgaps in lightweight metamaterial panels using rotation inertia multiplication

Of all possible features of structural metamaterials, the formation of bandgaps is the most studied one due to its direct application for sound and vibration isolation. While achieving low frequency values for the position of the first bandgap is, in general terms, not an unsurmountable challenge, the combination of material properties such as high stiffness, low density, and reduced size of the unit cell, with low (in absolute terms) frequency bandgaps, may well require some careful consideration. In previous work, we designed panels with a 3D network of resonators, clearly improving the vibration isolation compared to a homogeneous panel with the same weight. Recently, we have devised a novel implementation of inertia amplification, based on coupling the energy of longitudinal waves into the rotational oscillation of inertia elements within the unit cell. In this contribution, we present examples of phononic crystals based on this approach, and we discuss the interaction of acoustic waves with the discussed lattices.