Plane-wave Modes Research Articles

Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

This Memoir concerns fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave is large and the independent variables ( x , t ) (x,t) are proportional to the order (the far-field limit). We first formulate a Riemann-Hilbert representation of these solutions that allows the order to vary continuously rather than by integer increments. The intermediate solutions in this continuous family include also soliton solutions for zero boundary conditions spectrally encoded by a single complex-conjugate pair of poles of arbitrary order, as well as other solutions having nonzero boundary conditions matching those of the rogue waves albeit with far slower decay as x → ± ∞ x\to \pm \infty . The large-order far-field asymptotic behavior of the solution depends on which of three disjoint regions C \mathcal {C} (the “channels”), S \mathcal {S} (the “shelves”), and E \mathcal {E} (the “exterior domain”) contains the rescaled variables. On the region C \mathcal {C} , the amplitude is small and the solution is highly oscillatory, while on the region S \mathcal {S} , the solution is approximated by a modulated plane wave with a highly oscillatory correction term. The asymptotic behavior on these two domains is the same for all continuous orders. Assuming that the order belongs to the discrete sequence characteristic of rogue-wave solutions, the asymptotic behavior of the solution on the region E \mathcal {E} resembles that on S \mathcal {S} but without the oscillatory correction term. Solutions of other continuous orders behave quite differently on E \mathcal {E} .

An application of a beamforming technique, linear acoustic array and robot for pipe condition localization

Pipe inspection robots with sensors significantly enhance the maintenance of water systems by enabling early defect detection and reducing the risks of leaks and environmental damage. This paper introduces a sparse representation acoustic beamformer designed to locate artefacts within pipes using a short linear microphone array on a robot. The primary contributions include: (i) a new acoustic beamforming approach based on sparse representation that accurately predicts pipe conditions with a localization error within 3 % of the sensing distance; (ii) an enhanced beamforming algorithm combining plane wave and first non-axisymmetric mode, extending the frequency range from < 1300 Hz to < 2200 Hz in a 150 mm diameter pipe (an increase by 1.69 times), effectively managing unwanted acoustic reverberations and distinguishing blockages from lateral connections; and (iii) a novel robust algorithm predicting pipe length with an error margin within 2 %. This research advances acoustic sensing technologies for autonomous mobile robots inspecting buried pipes.

Josephson diode effect in junctions of superconductors with band asymmetric metals

At interfaces connecting two superconductors (SCs) separated by a metallic layer, an electric current is induced when there is a disparity in the phases of the two superconductors. We elucidate this phenomenon based on the weights of the Andreev bound states associated with the states carrying currents in forward and reverse directions. Typically, current phase relation (CPR) in Josephson junctions is an odd function. When time reversal and inversion symmetries are broken at the junction, CPR ceases to be an odd function and the system may exhibit Josephson diode effect. This phenomenon has been studied in spin orbit coupled systems under an external Zeeman field wherein the magnetochiral anisotropy is responsible for the Josephson diode effect. Recently introduced the band asymmetric metal (BAM) model presents a novel avenue, featuring an asymmetric band structure. We investigate DC Josephson effect in SC-BAM-SC junctions and find that band asymmetry can lead to Josephson diode effect and anomalous Josephson effect. We explain the mechanism behind these effects based on interference of plane wave modes within the Bogoliubov de-Genne formalism. We calculate diode effect coefficient for different values of the parameters.

Broadband asymmetric acoustic vortex generator based on integrative meta-atoms

The significance of asymmetric acoustic vortices primarily derives from their distinctive influence on acoustic vortex applications, such as acoustic communication receiving and sending isolation. However, the existing asymmetric acoustic vortices suffer from strong narrow-band confinement. In this paper, we eliminate this constraint by proposing a novel asymmetric scheme based on integrative meta-atoms (IMs). The IM is assembled by a phase gradient metasurface (PGM) and a mode selection structure (MSS), which serve the mode conversion and selection functions respectively. The PGM is constructed by a coiling-up space, converting the incident plane wave mode into a first-order vortex mode. We introduce three mirror scatterers in a cylindrical waveguide to form the MSS, allowing the first-order vortex mode to pass but blocking the plane wave mode in the mode band gap. The mode selection mechanism of MSS is revealed by employing the dispersion relation of the unit cell and the mode transmission performance of the MSS. By coupling the acoustic modulation effects of PGM and MSS, the asymmetric generation for the first-order vortex mode is realized, and further demonstrated numerically and experimentally. Significantly, the designed IMs exhibit commendable performance in both broadband and mode purity. In detail, a relative bandwidth of 25.3 % and a purity metric of 0.88 can be achieved. Our study may offer an alternative approach to producing asymmetric acoustic vortex devices, paving the way for a myriad of advanced applications.

A machine learning architecture for including wave breaking in envelope-type wave models

Wave breaking is a complex physical process about which open questions remain. For some applications, it is critical to include breaking effects in phase-resolved envelope-based wave models such as the non-linear Schrödinger. A promising approach is to use machine learning to capture breaking effects. In the present paper we develop the machine learning architecture to model breaking developed by Eeltink et al. (2022) further, potentially enabling more detailed breaking physics to be captured. We show that this model can be trained on focused wave groups but can also capture breaking in random waves and modulated plane waves. Analysis of the model suggests that the machine learning has broken the problem into two—one part which detects whether the wave is breaking and another which captures the subsequent behaviour, consistent with the way human scientists routinely understand the breaking problem.

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

In this paper, we report existence of optical rogue waves in the focussing non—autonomous nonlinear Schrödinger equation (NLSE) through numerical studies of modulation instability (MI). The dynamics of non-autonomous rogue waves discussed and its associated modulation instability through linear stability analysis taken place followed by pulse splitting behaviour due to non—autonomous coefficient. We prove that the excitation of rogue waves with certain conditions in the base band modulation instability regime. The above analysis of complex dynamics in terms of MI processes has allowed to experiments to excite the nonlinear superposition of rogue wave solutions using a modulated plane wave optical field injected into optical fiber which offer the evidence for excitation of nonautonomous rogue waves in an inhomogeneous nonlinear medium. It is identified from the results frequency modulation on a wavefield induces modulation instability as a result of rogue waves. We analyze the dependence of parameters coefficient of group velocity dispersion(GVD) and nonlinearity (α(z)) and non—autonomous coefficient (β(z)) and the instability of rogue waves. Our work suggests that the presence of non-autonomous coefficients can have a significant impact on the emergence of extreme events, particularly in relation to their self—steepening nature.

Quantum electrodynamics with a nonmoving dielectric sphere: quantizing Lorenz–Mie scattering

We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case, we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong–Ou–Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for a dielectric sphere of arbitrary refractive index and size with a particular emphasis on the small-particle limit. As shown in Phys. Rev. A 108, 033714 (2023)PLRAAN1050-294710.1103/PhysRevA.108.033714, this work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational, and vibrational degrees of freedom of a dielectric sphere.

Simulations of modulated plane waves using weakly compressible smoothed particle hydrodynamics

Simulations of modulated plane waves using weakly compressible smoothed particle hydrodynamics

P-forms on the celestial sphere

We construct a basis of conformal primary wavefunctions (CPWs) for pp-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of pp-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension \Delta=pΔ=p, while shadow pp-forms of this weight are only pure gauge in the critical spacetime dimension value D=2p+2D=2p+2. We then provide a systematic technique to obtain the large-rr asymptotic limit near \mathscr Iℐ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In D=4D=4, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.

Anisotropic acoustics in dipolar Fermi gases

We consider plane wave modes in ultracold, but not quantum degenerate, dipolar Fermi gases in the hydrodynamic limit. Longitudinal waves present anisotropies in both the speed of sound and their damping, and experience a small, undulatory effect in their flow velocity. Two distinct types of shear waves appear, a ``familiar" one, and another that is accompanied by nontrivial density and temperature modulations. We propose these shear modes as an experimental means to measure the viscosity coefficients, including their anisotropies.

An Accelerated Time-Domain Iterative Physical Optics Method for Analyzing Electrically Large and Complex Targets

A local area coupling-based time-domain iterative physical optics (TD-LIPO) method for the analysis of the scattering from electrically large and complex targets is proposed in this study. A modulated Gaussian-pulse plane wave is taken as the incident wave. Initially, via a ray-tracing mechanism, the current radiation iteration is limited to the local area, and the iteration times are determined by the bounce times. This approach can lower the enormous computation time. In addition, GPU parallel technology is also applied to accelerate the method. Finally, the TD-LIPO method is used to obtain the scattering echo data matrix of the target under different radar observation angles. An inverse fast Fourier transform (IFFT) is performed on the matrix to obtain the ISAR image under a small bandwidth and small angle. Numerical examples and ISAR images show that the accelerated local area coupling technique can significantly improve computational efficiency and verify feasibility in radar imaging.

Unidirectional transmission of surface water waves based on evanescent wave modes

In this paper, the unidirectional transmission of surface water waves is experimentally observed by connecting the mode-selective channel and the spatial symmetry-breaking channel. The proposed mode-selective channel contains a symmetry structure but only allows the propagation of anti-symmetric modes in a specific frequency band, while the antisymmetric modes can be excited in the channel with spatial symmetry-breaking. Therefore, the surface water waves can only propagate through the channel when the fundamental plane wave mode is excited at the entrance of the spatial symmetry-breaking channel, but not vice versa. The results of theoretical and numerical analyses indicate that the evanescent wave mode caused by non-Bragg resonances is responsible for the emergence of the antisymmetric mode transmission. The non-Bragg evanescent wave mode, generated by the resonance between the fundamental and higher-order modes, widens the unidirectional transmission band of surface water waves. Limited by the small structure, the experimental observed unidirectional transmission has a wave extinction ratio of 20.49 dB. The simulations closer to the ocean situation show that the bandwidth can reach 0.18 Hz, and the extinction ratio is 46.09 dB. The realization of surface water wave transmission not only enriches our knowledge on ubiquitous wave phenomenon, but also benefits applications in ocean engineering, such as coastal protection, ocean wave control, green energy collection, and reef maintenance.

Numerical analysis of wave propagating in a periodic layered structure

Controlling sound fields is a key technology for noise removal, acoustic lenses, energy harvesting, etc. This study investigated the control of sound field by a periodic layered structure. At first, we formulated the wave propagation in a periodic layered structure and proved that the wave fields constructed by the periodic boundary conditions are limited to plane wave modes with discretely different propagation directions. Numerical calculations clarified that the desired plane wave mode can be obtained in the transmitted wave through an intermediate thin-plate stacked region in a periodic layered structure, in which Lamb waves travel in each plate at different phase velocities and create phase difference at the exit of the intermediate thin-plate region. Further numerical investigations revealed that tuning frequency and the length of the thin-plate region provides wave field more dominantly with a single wanted plane wave mode.

Hamilton energy, complex dynamical analysis and information patterns of a new memristive FitzHugh-Nagumo neural network

This paper presents and studies the dynamics of a single neuron, followed by the network of an improved FitzHugh-Nagumo model with memristive autapse. The investigation on the single neuron revealed that, for the set of the system parameters used for our study, the improved model experiences hidden dynamics. The Hamilton energy of the proposed model is established by exploiting the Helmholtz theorem. It is found that the external current has no effect on that energy and only the memristive autapse strength is able to affect the energy released by the considered neuron. The study of the dynamics of the proposed model revealed neuronal behaviors such as quiescent, bursting, spiking, and hysteretic dynamics characterized by the coexistence of firing patterns for the same set of parameters. The electronic circuit of the proposed model is constructed and simulated in the Pspice environment, and the obtained results match well with those obtained from the direct investigations of the mathematical model of the introduced neuron. Furthermore, a chain network of 500 identical neurons with memristive autapses is built and information pattern stability is investigated numerically via modulational instability under memristive autapse strength. It is found that with initial conditions taken as slightly modulated plane waves, the new network supports localized information patterns with traits of synchronization as a means of information coding. Also, by fixing the stimulation current, higher autaptic couplings resulted in new localized pattern formation, confirming the new information coding pattern and possible mode transition. This could provide a possible application in the building of artificial neurons.

A Method For Generating Plane Wave And Zero-Offet Vsp Synthetic Seismograms

Synthetic Vertical Seismic Profiles (VSP) seianograms are a useful aid to the interpretation of VSP re- conds, Plane wave VSP syntherics multiples and mode conversions can be computed rapldly n the frequency domain using a new recursive formulation. The method urilises the concept of "renultanz" phase related reflection and tranamission coefficients for a layer atack. High frequerncy signals can be handled with relative euse. The ability to control the order of the multiple avolds wraparound problems with the discrete Fourier transform. Several examples are used to lhustrate the method with relewance to seismic exploration.

Localization of plane waves in the stochastic telegrapher's equation.

From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes are introduced. Then the time evolution of the plane-wave modes are analyzed when the absorption of energy in the telegrapher's equation has strong time fluctuations. We demonstrate that fluctuations in the loss of energy introduce a localized gap with a size that depends on the correlation timescale of the fluctuations. We prove that for a large time correlation the gap is strongly reduced, which means that there is delocalization in the plane-wave modes with respect to the plane waves in the ordinary telegrapher's equation. This result is of relevance in the study of the transport of electromagnetic waves in a conducting medium, and sheds light on the functional role of the fluctuations in the loss of energy in the telegrapher's dynamics.

Light propagation and magnon-photon coupling in optically dispersive magnetic media

Achieving strong coupling between light and matter excitations in hybrid systems is a benchmark for the implementation of quantum technologies. We recently proposed (Bittencourt, Liberal, and Viola-Kusminskiy, arXiv:2110.02984) that strong single-particle coupling between magnons and light can be realized in a magnetized epsilon-near-zero (ENZ) medium, in which magneto-optical effects are enhanced. Here we present a detailed derivation of the magnon-photon coupling Hamiltonian in dispersive media both for degenerate and nondegenerate optical modes, and show the enhancement of the coupling near the ENZ frequency. Moreover, we show that the coupling of magnons to plane-wave nondegenerate Voigt modes vanishes at specific frequencies due to polarization selection rules tuned by dispersion. Finally, we present specific results using a Lorentz dispersion model. Our results pave the way for the design of dispersive optomagnonic systems, providing a general theoretical framework for describing and engineering ENZ-based optomagnonic systems.

General relativity from $p$-adic strings

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$-adic strings, similar to the ordinary bosonic strings case. It turns out that certain $p$-adic automorphic forms are the plane wave modes of the bosonic fields on $p$-adic strings, and that the regularized normalization of these modes on the $p$-adic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.

Approaching the Fundamental Limit of Orbital-Angular-Momentum Multiplexing Through a Hologram Metasurface

Establishing and approaching the fundamental limit of orbital angular momentum (OAM) multiplexing are necessary and increasingly urgent for current multiple-input multiple-output research. In this work, we elaborate the fundamental limit in terms of independent scattering channels (or degrees of freedom of scattered fields) through angular-spectral analysis, in conjunction with a rigorous Green function method. The scattering channel limit is universal for arbitrary spatial mode multiplexing, which is launched by a planar electromagnetic device, such as antenna, metasurface, etc, with a predefined physical size. As a proof of concept, we demonstrate both theoretically and experimentally the limit by a metasurface hologram that transforms orthogonal OAM modes to plane-wave modes scattered at critically separated angular-spectral regions. Particularly, a minimax optimization algorithm is applied to suppress angular spectrum aliasing, achieving good performances in both full-wave simulation and experimental measurement at microwave frequencies. This work offers a theoretical upper bound and corresponding approach route for engineering designs of OAM multiplexing.

Past and Present Trends in the Development of the Pattern-Formation Theory: Domain Walls and Quasicrystals

A condensed review is presented for two basic topics in the theory of pattern formation in nonlinear dissipative media: (i) domain walls (DWs, alias grain boundaries), which appear as transient layers between different states occupying semi-infinite regions, and (ii) two- and three-dimensional (2D and 3D) quasiperiodic (QP) patterns, which are built as a superposition of plane–wave modes with incommensurate spatial periodicities. These topics are selected for the present review, dedicated to the 70th birthday of Professor Michael I. Tribelsky, due to the impact made on them by papers of Prof. Tribelsky and his coauthors. Although some findings revealed in those works may now seem “old”, they keep their significance as fundamentally important results in the theory of nonlinear DW and QP patterns. Adding to the findings revealed in the original papers by M.I. Tribelsky et al., the present review also reports several new analytical results, obtained as exact solutions to systems of coupled real Ginzburg–Landau (GL) equations. These are a new solution for symmetric DWs in the bimodal system including linear mixing between its components; a solution for a strongly asymmetric DWs in the case when the diffusion (second-derivative) term is present only in one GL equation; a solution for a system of three real GL equations, for the symmetric DW with a trapped bright soliton in the third component; and an exact solution for DWs between counter-propagating waves governed by the GL equations with group-velocity terms. The significance of the “old” and new results, collected in this review, is enhanced by the fact that the systems of coupled equations for two- and multicomponent order parameters, addressed in this review, apply equally well to modeling thermal convection, multimode light propagation in nonlinear optics, and binary Bose–Einstein condensates.