Chaotic Cavities Research Articles

Optimal Blind Focusing on Perturbation‐Inducing Targets in Sub‐Unitary Complex Media

AbstractThe scattering of waves in a complex medium is perturbed by polarizability changes or displacements of embedded targets. These perturbations can serve as perfectly non‐invasive guidestars for focusing on the targets. Here, a fundamental but to‐date overlooked difference between these two perturbation types is theoretically derived: the change of the scattering matrix is of rank one [two] for a polarizability change [displacement] of a point‐like target; optimal strategies to perfectly focus on the target in both cases are identified accordingly. In particular, in the latter case, optimal focusing requires at least two target displacements. Furthermore, for the case of dynamic complex media additionally featuring parasitic perturbers, a non‐invasive scheme to achieve optimal time‐averaged power delivery to a perturbation‐inducing target is established. In all cases, no assumptions about the unitarity of the system's scattering matrix or the perturbation strength are necessary. All results are experimentally demonstrated in the microwave regime using a strongly sub‐unitary lossy chaotic cavity as a complex medium. The experiments highlight that the target's “structural scattering” is irrelevant [must be negligible] in the case of target polarizability changes [displacements]. The presented results are expected to find applications in communications, cybersecurity, wireless bioelectronics, flow‐cytometry, and self‐propelled nano‐swimmers.

Time Delay Statistics for Chaotic Cavities with Absorption

Time Delay Statistics for Chaotic Cavities with Absorption

Multiscale model reduction for incompressible flows

We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.

A single-channel virtual receiving array using a time-reversal chaotic cavity.

Chaotic reverberation in a cavity, when coupled with time reversal acoustics, can be harnessed to build a perfect time-reversal mirror for transmitting and receiving highly focused sounds with a small number of transducers. In this article, a virtual receiving array, comprised of a single receiving transducer and a chaotic cavity, is developed based on time reversal processing of the reverberation inside the cavity. A prototype array, having 10 × 10 virtual receiving elements, is built and evaluated against a comparable physical array in terms of its localization and waveform reproduction capabilities. It turns out that the most crucial factor in the success of a virtual array is the ergodicity of its chaotic cavity, the exact mathematical expression for which is also derived. The virtual receiving array presented here may find some niche applications in reverberant environments, where a physical array turns out to be too costly or cumbersome to operate.

Chaotic-cavity surface-emitting lasers for optical wireless communication and low-speckle illumination

Though necessary and advantageous in many fields, the high coherence of lasers is detrimental to their performance in certain applications, including illumination, imaging, and projection. This is due to the formation of coherence artifacts, commonly known as speckles, resulting from the interference of randomly scattering spatially coherent photons. It is possible to resolve this issue by increasing the number of mutually incoherent modes emitted from the laser. In vertical-cavity surface-emitting lasers (VCSELs), this can be performed by designing them to have chaotic cavities. This paves the way toward their use in simultaneous illumination and communication scenarios. Herein, we show that chaotic-cavity broad-area VCSELs can achieve significantly broader modulation bandwidths (up to 5 GHz) and higher data rates (up to 12.6 GB/s) compared to other low-coherence light sources, with a lower speckle contrast. We further report a novel technique for lowering the speckle contrast by carefully designing the AC signal used for communication. We show that the apparent spatial coherence is dramatically decreased by inserting a short chirp signal between symbols. Using this method with a chaotic-cavity VCSEL, the number of apparent modes can be up to 450, compared to 88 modes measured from a conventional broad-area VCSEL (a fivefold increase). In light of the recent advances in visible-light VCSELs, this work shows the potential of low-coherence surface-emitting lasers (LCSELs) in simultaneous illumination and optical wireless communication systems since they combine the high speed of lasers with the excellent illumination properties of light-emitting diodes.

Modifying the coherence of vertical-cavity surface-emitting lasers using chaotic cavities

Vertical-cavity surface-emitting lasers (VCSELs) have been widely adopted in a variety of applications in recent years, with even more applications currently under research and development as a result of the emergence of visible-light VCSELs. Most of these applications make use of the ease of fabrication of large two-dimensional arrays of lasers, a feature unique to VCSELs that makes them scalable and versatile. However, applications that rely on the uniformity of the emitted beam in the transverse plane, such as illumination, projection, holography, and displays, suffer from the coherence artifacts (speckles) that reduce the quality of the formed images when coherent lasers are used. In this work, we show that, by using a chaotic-cavity D-shaped mesa, the coherence of broad-area VCSELs can be substantially reduced (the number of mutually incoherent modes is almost doubled, and the spectral full width at half-maximum is increased from ∼ 1.1 n m to ∼ 4.5 n m ), and the maximum achievable optical power is increased by up to 60%. The simplicity of implementing the reported design, which requires no additional fabrication steps, makes it a promising solution for applications that would benefit from the lower speckle density of the emitted light as well as those that rely on lower temporal coherence, such as time-domain optical coherence tomography and fiber-optic gyroscopes.

Machine Learning-assisted spatiotemporal chaos forecasting

Long-term forecasting of extreme events such as oceanic rogue waves, heat waves, floods, earthquakes, has always been a challenge due to their highly complex dynamics. Recently, machine learning methods have been used for model-free forecasting of physical systems. In this work, we investigated the ability of these methods to forecast the emergence of extreme events in a spatiotemporal chaotic passive ring cavity by detecting the precursors of high intensity pulses. To this end, we have implemented supervised sequence (precursors) to sequence (pulses) machine learning algorithms, corresponding to a local forecasting of when and where extreme events will appear.

Blocky Diagonalized Scattering Matrices in Chaotic Scattering with Direct Processes

Scattering matrices that can be diagonalized by a rotation through an angle θ in 2×2 blocks of independent scattering matrices of rank N, are considered. Assuming that the independent scattering matrices are chosen from one of the circular ensembles, or from the Poisson kernel, the 2N×2N scattering matrix may describe the scattering through chaotic cavities with reduced symmetry in the absence, or presence, of direct processes, respectively. To illustrate the effect of such symmetry, the statistical distribution of the dimensionless conductance through a ballistic chaotic cavity in the presence of direct processes is analyzed for N=1 using analytical calculations. We make a conjecture for N=2 in the absence of direct processes, which is verified by numerical random-matrix theory simulations, and the first two moments are calculated analytically for arbitrary N.

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

The energy levels of a quasicontinuous spectrum in mesoscopic systems fluctuate in positions and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of a secondary gap that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime ${E}_{\mathrm{Th}}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$, with ${E}_{\mathrm{Th}}$ being the Thouless energy of the cavity and $\mathrm{\ensuremath{\Delta}}$ being the superconducting gap. We find that the distribution is determined by an intermediate energy scale ${\mathrm{\ensuremath{\Delta}}}_{g}$ with the value between the level spacing in the cavity ${\ensuremath{\delta}}_{s}$ and the quasiclassical value of the gap ${E}_{g}$. From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov et al. [Phys. Rev. Lett. 86, 874 (2001)] for the distribution of the minigap edge in the opposite limit ${E}_{\mathrm{Th}}\ensuremath{\ll}\mathrm{\ensuremath{\Delta}}$. This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum in agreement with the known random matrix models featuring a square root singularity in the density of states.

Exponentially small quantum correction to conductance

When time-reversal symmetry is broken, the average conductance through a chaotic cavity, from an entrance lead with N 1 open channels to an exit lead with N 2 open channels, is given by N 1 N 2/M, where M = N 1 + N 2. We show that, when tunnel barriers of reflectivity γ are placed on the leads, two correction terms appear in the average conductance, and that one of them is proportional to γ M . Since M ∼ ℏ −1, this correction is exponentially small in the semiclassical limit. We derive this term from a semiclassical approximation, generally expected to give only leading orders in powers of ℏ. Even though the theory is built perturbatively both in γ and in 1/M, the final result is exact.

Low-Complexity 3D InISAR Imaging Using a Compressive Hardware Device and a Single Receiver.

An Interferometric Inverse SAR system is able to perform 3D imaging of non-cooperative targets by measuring their responses over time and through several receiving antennas. Phase differences between signals acquired with a spatial diversity in vertical or horizontal directions are used to localize moving scatterers in 3D. The use of several receiving channels generally results into a costly and complex hardware solution, and this paper proposes performing this multichannel acquisition using a single receiver and a hardware compressive device, based on a chaotic cavity which simultaneously multiplexes in the spectral domain signals acquired over different antennas. The radar responses of the scene are encoded in the spectral domain onto the single output of a leaky chaotic cavity, and can be retrieved by solving an inverse problem involving the random transfer matrix of the cavity. The applicability of this compressed sensing approach for the 3D imaging of a non-cooperative target using low-complexity hardware is demonstrated using both simulations and measurements. This study opens up new perspectives to reduce the hardware complexity of high-resolution ISAR systems.

Tunable Chaotic External-Cavity Semiconductor Laser With Time-Delay Signature Suppression Including a Broadband Chirped FBG

A wavelength tunable chaotic external cavity semiconductor laser (ECSL) composed by a distributed-feedback laser diode (DFB-LD) and a broadband chirped fiber Bragg grating (CFBG), is proposed and experimentally demonstrated for generating tunable chaos signals with time delay signature (TDS) suppression. The experimental results show that by using a CFBG with a 3-dB reflection bandwidth of approximately 30 nm and a low dispersion of approximately 1.25 ps/nm, the chaotic ECSL can be tuned over a wide wavelength range, and the generated chaos possesses a low TDS of about 0.04. With the increase of the bias current of the DFB-LD, the chaotic ECSL is tuned towards long-wavelength direction, the effective bandwidth of the chaotic signal is extended, and the TDS of the chaotic signal remains effectively suppressed. To highlight the advantages of the proposed scheme, relevant experiments for the DFB-LD under fiber mirror feedback and fiber Bragg grating feedback are also performed and compared.

Quantum transport in chaotic cavities with tunnel barriers

We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are present and the number of open channels, $M$, is small. In contrast to previous approaches, ours is non-perturbative in $M$; instead, we arrive at an explicit expression in the form of a power series in the barrier's reflectivity, whose coefficients are rational functions of $M$. For general moments we must require that the barriers are equal and time reversal symmetry is broken, but for conductance we treat the general situation. Our method accounts for exponentially small non-perturbative terms that were not accessible to previous semiclassical approaches. We also show how to include more than two leads in the system.

Bragg Scattering from a Random Potential.

A potential for propagation of a wave in two dimensions is constructed from a random superposition of plane waves around all propagation angles. Surprisingly, despite the lack of periodic structure, sharp Bragg diffraction of the wave is observed, analogous to a powder diffraction pattern. The scattering is partially resonant, so Fermi's golden rule does not apply. This phenomenon would be experimentally observable by sending an atomic beam into a chaotic cavity populated by a single mode laser.

Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities

Motivated by the phenomenon of coherent perfect absorption, we study the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. We show that it is largely determined by non-orthogonality factors O nn of the eigenmodes associated with the non-selfadjoint effective Hamiltonian. For cavities supporting chaotic ray dynamics we then use random matrix theory to derive, fully non-perturbatively, the explicit distribution of the non-orthogonality factors for systems with both broken and preserved time reversal symmetry. The results imply that O nn are heavy-tail distributed. As a by-product, we derive an explicit non-perturbative expression for the resonance density in a single-channel chaotic systems in a much simpler form than available in the literature.

Statistics of conductance and shot noise power in chaotic mesoscopic cavities with one ideal and one nonideal lead

Chaotic mesoscopic cavities with ideal leads have been studied extensively using the powerful formalism of random matrix theory. Consequently, the statistical behavior of quantum transport observables, such as Landauer conductance and shot noise power, is fairly well understood. However, these have been explored far less in cavities with nonideal leads, i.e. having tunnel barriers. Here, we consider chaotic mesoscopic cavities with one ideal and one nonideal lead, and investigate the statistics of conductance and shot noise power under the condition of broken time-reversal symmetry. We derive exact expressions for the average and variance for both conductance and shot noise power. Moreover, we provide exact characteristic functions of these quantities, which are subsequently Fourier-inverted using a simple yet effective numerical procedure to obtain the corresponding distributions. We examine these quantities by varying the tunneling probabilities. We also compare our analytical results with Monte Carlo simulations and find very good agreements.

Deep-Learning Estimation of Complex Reverberant Wave Fields with a Programmable Metasurface

Electromagnetic environments are becoming increasingly complex and congested, creating a growing challenge for systems that rely on electromagnetic waves for communication, sensing, or imaging, particularly in reverberating environments. The use of programmable metasurfaces provides a potential means of directing waves to optimize wireless channels on demand, ensuring reliable operation and protecting sensitive electronic components. Here we introduce a technique that combines a deep-learning network with a binary programmable metasurface to shape waves in complex reverberant electromagnetic environments, in particular ones where there is no direct line of sight. We apply this technique for wavefront reconstruction and control, and accurately determine metasurface configurations based on measured system scattering responses in a chaotic microwave cavity. The state of the metasurface that realizes desired electromagnetic wave field distribution properties was successfully determined even in cases previously unseen by the deep-learning algorithm. Our technique is enabled by the reverberant nature of the cavity, and is effective with a metasurface that covers only approximately 1.5% of the total cavity surface area.

Chaotic cavity design of a UV-C disinfection chamber for uniform radiation distribution.

UV-C radiation has been used extensively for disinfection wherein the dosage of radiation varies with the microorganism concerned. The efficacy of disinfection largely relies on the radiation reaching uniformly across the chamber without simultaneously leaving out dark regions within the chamber. The regular geometries of the chambers, such as with circular or rectangular cross sections, invariably lead to hot spots accompanied by regions that remain dark, thereby severely limiting the germicidal effects of the UV-C radiation. We propose and demonstrate the use of a chaotic Bunimovich stadium design chamber that ensures uniform UV-C exposure without any accompanying "dark spots." The design incorporates the shape parameters of a chaotic Bunimovich stadium, wherein ray-tracing simulations confirm the space-filling nature of the photon trajectories, typical of chaotic dynamics. This leads to uniform radiation distribution across the whole volume. Experimental results are presented for a biosafety cabinet that can be used for UV-C disinfection wherein the UV-C light intensity distribution is more evenly distributed than the conventional regular (cuboidal) geometry. Adaptation of this simple design consideration is paramount for air disinfection, wherein dark regions in conventional air ducts can severely compromise the efficacy of the disinfection.

Analysis of time reversal cavity characteristics based on multipath channel model

The electromagnetic wave time reversal technology using time reversal cavity (TRC) has potential applications in many areas, such as pulse compression, power synthesis, perturbation detection, beamforming, etc. Microwave chaotic cavity with multi-path transmission characteristics is usually used in TRC. Based on diffraction theory, it can prove that this kind of cavity has spatiotemporal focusing characteristics and can be used for compressing pulses, but it cannot be used to analyze the reversal performance of the cavity. In order to obtain a suitable analysis method and guide the design of TRC, in this work, the scattering, diffusion and attenuation characteristics of electromagnetic wave propagation are analyzed and a multipath channel model of TRC is built by the channel theory. Moreover, the crosstalk characteristics between paths are studied, and the generation mechanism of time sidelobe, time sidelobe shift and interference are also investigated. In addition, under the assumption of random plane wave, the distribution characteristics of spatial focal spot are analyzed, which is consistent with the diffraction theory. Moreover, the actual focal spot size is not only limited by the diffraction limit, but also related to the initial focal spot size. The theoretical analysis results are basically consistent with the experimental and numerical simulation results.

Breakdown of quantum-classical correspondence and dynamical generation of entanglement

The {\it exchange} interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X \textbf{8}, 021026 (2018), and strengthen its statement.