Nonlinear Propagation Research Articles

A p-Multigrid Hybrid-Spectral Model for Nonlinear Water Waves

AbstractTo improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and $${\mathcal {O}}(n \log n)$$ O ( n log n ) -scalable solution of a hybrid-spectral model for the simulation of highly nonlinear and highly dispersive water waves, the accurate calculation of wave kinematics and taking into account varying water depth. To achieve low numerical dispersive and dissipate errors, a high-order hybrid-spectral collocation scheme is implemented to solve the fully nonlinear potential flow (FNPF) equations, and utilizing a p-multigrid iterative solver scheme for solving the Laplace problem. Hereby, the numerical scheme combines the high accuracy of spectral methods, high efficiency of the fast Fourier transform (FFT) algorithm, and multigrid methods. Numerical analysis is performed to evaluate the performance and confirm the spectral accuracy of the scheme. Numerical experiments are considered for steady nonlinear wave propagation. A Fourier-continuation technique is used to extend the scheme from a periodic domain setup to perform benchmarks in a finite domain setup for numerical wave tanks utilizing conventional techniques for wave generation and absorption, and with results in excellent agreement with experimental measurements.

Orbital angular momentum and rotational properties of off-axis vortex beams in two-dimensional media with anisotropic nonlocal nonlinearity.

By introducing anisotropy into nonlinear propagations, off-axis vortex beams exhibit significantly different characteristics compared to the isotropic case. The orbital angular momentum (OAM) is non-conservative and can periodically change between positive and negative values. Accordingly, the rotation of phase singularity can transit between clockwise and counterclockwise directions. Furthermore, the phase singularity can move to infinity when the OAM approaches zero. By using the Ehrenfest theorem, the motion of the beam center is obtained. Its trajectory can be circular and parabolic or follow other complex shapes, depending closely on the anisotropy of the nonlinearity. The rotational velocity of the beam center can be modulated by the nonlinearity anisotropy and can far exceed the initial value during its propagation. These results may find potential applications in beam shaping and optical manipulation.

Analytical model for sound of explosives and firearms.

An analytical model is presented for approximate prediction of the waveform and the sound level spectrum of blast waves generated by explosives and firearms. The model is based on numerical results for spherical blast waves, with overpressures between 10 kPa and 100 MPa, and a nonlinear propagation theory for blast waves. The matching of the numerical results and the nonlinear propagation theory is investigated, and compared with results from the literature and results of calculations with a nonlinear propagation model. The analytical model presented here assumes a Friedlander waveform, from which formulas are derived for the 1/3-octave band spectrum of the sound exposure level. The formulas take into account the nonlinear effect of pulse broadening, and the corresponding frequency shift. For firearms, the muzzle blast levels vary in general with the emission direction, and the model takes into account an empirical directivity correction. Apart from the directivity correction, the model has no empirical parameters. The waveform and the spectrum follow directly from the explosion energy or the explosive charge mass. Model predictions are in good agreement with measurement results of explosives and firearms, with the explosive charge mass ranging from 0.4 g to 4 kg TNT.

Study of complex dynamics and novel soliton solutions of the Kraenkel-Manna-Merle model describing saturated ferromagnetic materials

This paper introduces a framework for nonlinear short wave propagation in an external field for saturated ferromagnetic materials with zero conductivity: the Kraenkel-Manna-Merle system. New solutions are produced via the G′/(bG′+G+a)-expansion technique. The suggested method is easier to understand, more precise, and simpler to compute. Specifically, a set of singular-periodic and kink-shaped exact soliton solutions is produced. Contour plots, 3D, and 2D visualizations with suitable parametric values are employed to present the computed solutions, which are derived through constraint conditions. For the development of certain novel soliton structures, the arbitrary functions in the solutions are selected. Moreover, bifurcation and chaos theory are applied to the primary dynamical system in order to provide a qualitative analysis of the system under study. Phase portraits of bifurcation are presented at fixed locations to illustrate different situations about parameter values in the dynamic system. However, adopting techniques for identifying chaos in a dynamical system and applying an external force verifies the occurrence of chaotic behavior in system. These results offer new perspectives that can enhance understanding of the dynamics of the KMM system.

Experimental study of intramodal XPM reduction by intramodal dispersion in weakly coupled FMF.

The understanding of nonlinear propagation effects in low-crosstalk few-mode fiber is crucial for a weakly coupled mode-division multiplexed system. In this Letter, we report the first, to the best of our knowledge, experimental verification of the advantage of intramodal dispersion on mitigating intramodal cross-phase modulation in a weakly coupled few-mode fiber transmission. The experimental system is established over a 70-km multiple-ring-core few-mode fiber accommodating 6 linearly polarized modes, based on which the influences of intramodal cross-phase modulation on transmission performances of each linearly polarized mode are evaluated. Experimental results show that the intramodal cross-phase modulation of degenerate linearly polarized modes with much larger intramodal dispersion values are significantly weaker than those of non-degenerate linearly polarized modes, in which the maximum suppression of intramodal cross-phase modulation noise is up to 9.7 dB. We believe that this work would be beneficial to practical applications of weakly coupled mode-division multiplexing technologies.

Optical solitons and their propagations in a time-varying coefficient modified nonlinear Schrödinger equation with non-zero boundary conditions via Riemann–Hilbert method

In this article, a time-varying coefficient modified nonlinear Schrödinger equation (tvcmNLSE) with non-zero boundary conditions (NZBCs) at infinity, phase term of which contains time-varying coefficients, is proposed to describe the nonlinear propagation behavior of optical pulses in non-uniform optical fibre. Meanwhile, the Riemann–Hilbert method (RHM) for the tvcmNLSE with NZBCs is presented for the first time. Specifically, a special transformation is constructed to convert the tvcmNLSE with NZBCs into the case with constant NZBCs, and the associated asymptotic spectral problem (ASP) is obtained. By introducing a suitable two-piece Riemann surface to map the original spectral parameter into a single-valued one, and analyzing the ASP, we construct the corresponding Jost solutions and spectral matrix, and sequentially analyze their analytical, symmetric, and asymptotic properties. Then, a generalized Riemann–Hilbert problem (RHP) is established that relates to the converted tvcmNLSE with constant NZBCs. Using the reconstruction formula, we further derive N-soliton solution with NZBCs in the absence of reflection potential, and analyze the dynamic characteristics of single and double solitons. Most notably, by modulating discrete spectral points (DSPs) and time-varying coefficients, we discover some previously unreported new waveforms, such as parabolic and periodic solitons with NZBCs. These waveforms have important implications in both theory and practice. In addition, the influences of different time-varying coefficients, NZBCs, and DSPs on soliton solutions are also discussed and analyzed. This study shows that the selection of time-varying coefficients, distribution of DSPs, and constraints from NZBCs all have significant impacts on the properties of soliton solutions.

Unseeded one-third harmonic generation in optical fibers

We propose a new concept to generate efficient one-third harmonic light from an unseeded third harmonic process in optical fibers. Our concept is based on the dynamic constant (Hamiltonian) of the nonlinear third harmonic generation in optical fibers and includes a periodic array of nonlinear fibers and phase compensation elements. We test our concept with a simulation of the nonlinear interaction between the fundamental and third harmonic modes of a realistic optical fiber, demonstrating high-efficiency one-third harmonic generation. Our work opens a new approach to achieving the so far elusive one-third harmonic generation in optical fibers.

Observation of nonlinear thermoelectric effect in MoGe/Y3Fe5O12

Thermoelectric effects refer to the voltage generation from temperature gradients in condensed matter. Although various power generators are made from them, all the known effects, such as Seebeck effect, require macroscopic temperature gradients; since the sign of the generated voltage is reversed by reversing the temperature gradient, the net voltage disappears when the temperature distribution fluctuates temporarily or spatially with a macroscopic temperature gradient of zero. It is impossible to utilize such temperature fluctuations in the conventional thermoelectric effects, a situation which limits their application. Here we report the observation of a second-order nonlinear thermoelectric effect; we develop a method to measure nonlinear thermoelectricity and observe that a superconducting MoGe film on Y3Fe5O12 generates a voltage proportional to the square of the applied temperature gradient. The nonlinear thermoelectric generation demonstrated here provides a way for making power generators that produce electric power from temperature fluctuations.

Isolated attosecond pulse generation in a semi-infinite gas cell driven by time-gated phase matching

Isolated attosecond pulse (IAP) generation usually involves the use of short-medium gas cells operated at high pressures. In contrast, long-medium schemes at low pressures are commonly perceived as inherently unsuitable for IAP generation due to the nonlinear phenomena that challenge favourable phase-matching conditions. Here we provide clear experimental evidence on the generation of isolated extreme-ultraviolet attosecond pulses in a semi-infinite gas cell, demonstrating the use of extended-medium geometries for effective production of IAPs. To gain a deeper understanding we develop a simulation method for high-order harmonic generation (HHG), which combines nonlinear propagation with macroscopic HHG solving the 3D time-dependent Schrödinger equation at the single-atom level. Our simulations reveal that the nonlinear spatio-temporal reshaping of the driving field, observed in the experiment as a bright plasma channel, acts as a self-regulating mechanism boosting the phase-matching conditions for the generation of IAPs.

TW-scale few-cycle short-wave infrared laser based on nonlinear compression in a large-core gas-filled hollow core fiber

In this Letter, we present the generation of terawatt-scale few-cycle short-wave infrared (SWIR) lasers using nonlinear compression in a large-core gas-filled hollow core fiber. Through the experimental verification, we investigate the energy scaling properties and nonlinear pulse propagation in the argon-filled hollow core fiber. At static pressure, the system delivers pulses with 5.55 mJ/9.04 fs at a central wavelength of 1.45 μm, resulting in a peak power of about 0.5 TW. Subsequently, based on the chirped input pulses and pressure gradient, the system delivers terawatt-scale two-cycle SWIR pulses with 9.52 mJ/10.65 fs, resulting in a record peak power of about 0.7 TW. This study marks a crucial advancement in the field of SWIR ultra-intense, ultrashort pulse nonlinear interaction platforms. This high-energy, few-cycle SWIR source has significant applications in high-intensity THz radiation, x-ray generation, and other fields of strong-field physics.

Electric Field-Manipulated Optical Chirality in Ferroelectric Vortex Domains.

Manipulating optical chirality via electric fields has garnered considerable attention in the realm of both fundamental physics and practical applications. Chiral ferroelectrics, characterized by their inherent optical chirality and switchable spontaneous polarization, are emerging as a promising platform for electronic-photonic integrated circuits applications. Unlike organics with chiral carbon centers, integrating chirality into technologically mature inorganic ferroelectrics has posed a long-standing challenge. Here, the successful introduction of chirality is reported into self-assembly La-doped BiFeO3 nanoislands, which exhibit ferroelectric vortex domains. By employing synergistic experimental techniques with piezoresponse force microscopy and nonlinear optical second-harmonic generation probes, a clear correlation between chirality and polarization configuration within these ferroelectric nanoislands is established. Furthermore, the deterministic control of ferroelectric vortex domains and chirality is demonstrated by applying electric fields, enabling reversible and nonvolatile generation and elimination of optically chiral signals. These findings significantly expand the repertoire of field-controllable chiral systems and lay the groundwork for the development of innovative ferroelectric optoelectronic devices.

Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws

Abstract Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F ( = − ( 1 / 4 ) F μ ν F μ ν ) . In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien’s displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well.

Ultrafast structured light through nonlinear frequency generation in an optical enhancement cavity.

The generation of shaped laser beams, or structured light, is of interest in a wide range of fields, from microscopy to fundamental physics. There are several ways to make shaped beams, most commonly using spatial light modulators comprised of pixels of liquid crystals. These methods have limitations on the wavelength, pulse duration, and average power that can be used. Here we present a method to generate shaped light that can be used at any wavelength from the UV to IR, on ultrafast pulses, and a large range of optical powers. By exploiting the frequency difference between higher-order modes, a result of the Gouy phase, and cavity mode matching, we can selectively couple into a variety of pure and composite higher-order modes. Optical cavities are used as a spatial filter and then combined with sum-frequency generation in a nonlinear crystal as the output coupler to the cavity to create ultrafast, frequency comb structured light.

Excited‐State Dynamics and Optical Properties of Silica Under Ultrafast Laser Irradiation

AbstractExcited by intense infrared ultrafast light pulses, a wide bandgap material undergoes nonlinear ionization, generating a high density of free electrons in conduction states. As a result, the electronic band structure is critically modified and the bandgap shrinks. This induces rapid changes in optical properties, dramatically affecting the absorption spectrum during light coupling to the dielectric surface or during nonlinear propagation inside the bulk. This study analyzes the structural behavior and the modification of the optical properties of laser‐excited silica glass at the molecular cluster level through first‐principles simulations. Employing density functional theory and the GW approximations for band structure under nonequilibrium conditions, alongside the Bethe–Salpeter equation, the dynamics of the optical properties of fused silica are comprehensively explored. The behavior of excited fused silica in a wide photon energy range (from a few to 20 eV) is thus predicted. Laser‐induced electron excitation triggers a redistribution of charges between oxygen and silicon atoms, accompanied by a significant increase in electronic pressure, local atomic structure rearrangement, and material expansion. Molecular dynamics simulations offer a temporal perspective on the excited state dynamics, unveiling the intricate interplay between electronic and atomic effects on bandgap evolution. The analysis sheds light on excitonic resonances, intraband and interband transitions in fused silica under ultrafast laser irradiation, providing valuable insights into its excited state behavior and optical properties.

Unveiling the intricacies of nonlinear third-harmonic generation within a hyperstructure

Unveiling the intricacies of nonlinear third-harmonic generation within a hyperstructure

Self-Focused Pulse Propagation Is Mediated by Spatiotemporal Optical Vortices.

We show that the dynamics of high-intensity laser pulses undergoing self-focused propagation in a nonlinear medium can be understood in terms of the topological constraints imposed by the formation and evolution of spatiotemporal optical vortices (STOVs). STOVs are born from pointlike phase defects on the sides of the pulse nucleated by spatiotemporal phase shear. These defects grow into closed loops of spatiotemporal vorticity that initially exclude the pulse propagation axis, but then reconnect to form a pair of toroidal vortex rings that wrap around it. STOVs constrain the intrapulse flow of electromagnetic energy, controlling the focusing-defocusing cycles and pulse splitting inherent to nonlinear pulse propagation. We illustrate this in two widely studied but very different regimes, relativistic self-focusing in plasma and nonrelativistic self-focusing in gas, demonstrating that STOVs mediate nonlinear propagation irrespective of the detailed physics.

Nonlocal meta-lens with Huygens’ bound states in the continuum

Meta-lenses composed of artificial meta-atoms have stimulated substantial interest due to their compact and flexible wavefront shaping capabilities, outperforming bulk optical devices. The operating bandwidth is a critical factor determining the meta-lens’ performance across various wavelengths. Meta-lenses that operate in a narrowband manner relying on nonlocal effects can effectively reduce disturbance and crosstalk from non-resonant wavelengths, making them well-suitable for specialized applications such as nonlinear generation and augmented reality/virtual reality display. However, nonlocal meta-lenses require striking a balance between local phase manipulation and nonlocal resonance excitation, which involves trade-offs among factors like quality-factor, efficiency, manipulation dimensions, and footprint. In this work, we experimentally demonstrate the nonlocal meta-lens featuring Huygens’ bound states in the continuum (BICs) and its near-infrared imaging application. All-dielectric integrated-resonant unit is particularly optimized to efficiently induce both the quasi-BIC and generalized Kerker effect, while ensuring the rotation-angle robustness for generating geometric phase. The experimental results show that the single-layer nonlocal Huygens’ meta-lens possesses a high quality-factor of 104 and achieves a transmission polarization conversion efficiency of 55%, exceeding the theoretical limit of 25%. The wavelength-selective two-dimensional focusing and imaging are demonstrated as well. This work will pave the way for efficient nonlocal wavefront shaping and meta-devices.

Thermoviscous dissipation of nonlinear acoustic waves in channels with wavy walls.

We derive a nonlinear acoustic wave propagation model for analyzing the thermoviscous dissipation of nonlinear acoustic waves in narrow pores with wavy walls using the boundary layer theory. As a nonlinear acoustic wave propagates in a pore, the wave-steepening effect competes with the bulk dissipation, as well as the thermoviscous heat transfer and shear from the pore walls. Due to thermoviscous dissipation, the wave thickness increases beyond the weak shock thickness scale. Using the weak shock thickness scale, we obtain dimensionless linear and nonlinear model wave equations governing the shock-wall interactions. We also perform two-dimensional shock-resolved direct numerical simulation of the wave propagation inside the pores and compare the results with model equations. The direct numerical simulation and model calculations show that, for flat walls and shock strength parameter ϵ, the dimensional wall heat-flux and shear scale as ϵ. For wavy walls, the scaling becomes ϵ3/2-n(k) where k is the wall-waviness wavenumber and the exponent n increases from 0.5 for k = 0 to n(k)≈0.65 for k = 10, n(k)≈0.75 for k = 20, and n(k)≈0.85 for k = 40. Furthermore, we show that both the dimensionless scaled wall shear and wall heat-flux decrease with increasing k.

Free Infragravity Waves on the Inner Shelf: Observations and Parameterizations at Two Southern California Beaches

AbstractNumerical predictions of nearshore waves and shoreline runup are usually initialized on the inner shelf, seaward of the surfzone, with sea‐swell (SS) waves from local wave buoys or regional wave models. Lower frequency infragravity (IG) waves are not reliably measured by buoys or included in regional models. Here, co‐located pressure and velocity observations are used to characterize IG waves in 10–15 m depth in southern California. Shoreward propagating IG waves are often dominated by free waves, with the boundwave energy fraction <30% for moderate and low energy incident SS waves. Only 5% of records, with energetic long swell, show primarily bound waves. The shoreline slope of concave beaches increases by ∼3 between spring high and low tides, and free seaward and shoreward IG energy in 10–15 m vary tidally. The observed linear dependency of free IG energy on SS energy and period is consistent with Ardhuin et al. (2014, https://doi.org/10.1016/j.ocemod.2014.02.006)'s parameterization (R2 = 0.71). Including the tide level as a proxy for beach slope and modifying the SS frequency dependency increases R2 to 0.91. The ratio of free seaward to shoreward propagating IG energy suggests between 50 and 100% of the energy radiated seaward in depths of 10–15 m is trapped offshore and redirected shoreward. Free (random phase) and bound (phase‐coupled) IG waves are combined to initialize the SWASH numerical model. SWASH predicted runup is only weakly influenced by waves at the offshore boundary. Nonlinear IG generation and dissipation in the shoaling and surfzone overwhelm the effects of shoreward propagating waves observed at the offshore boundary.

H 2-solutions for an Ostrosky–Hunter type equation

The Ostrosky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth, for the evolution of nonlinear propagation of optical pulses of a few oscillations duration in dielectric media, and for the evolution of the propagation of ultra-short light pulses in silica optical fibers. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.