Nonlinear Regime Research Articles

Collective coherent emission of electrons in strong laser fields and perspective for hard x-ray lasers

Coherent motion of particles in a plasma can imprint itself on radiation. The recent advent of high-power lasers—allowing the nonlinear inverse Compton-scattering regime to be reached—has opened the possibility of looking at collective effects in laser–plasma interactions. Under certain conditions, the collective interaction of many electrons with a laser pulse can generate coherent radiation in the hard x-ray regime. This perspective paper explains the limitations under which such a regime might be attained.

Probing nonlinear excitation conditions: photoluminescence and nonlinear absorption studies in laser-irradiated dielectrics

Understanding the fundamentals of laser-matter interactions is crucial for developing and optimizing ultrafast laser processing strategies. In optically transparent solids, the key event by which energy is deposited in the material is through the generation of an electron–hole plasma via nonlinear excitation mechanisms. As the energy stored in the plasma relaxes, local distortions of the lattice may occur, such as point defects. These defects give rise to new discrete energy states located in the bandgap. In this study, we investigate how the presence of these energy states influences the transmission of ultrashort near-infrared laser pulses in fused silica. Experimental results of laser pulse transmission and photoluminescence from defects are correlated with optical microscopy of the irradiated spots, allowing us to identify different nonlinear interaction regimes. Numerical simulations indicate that photo-induced defects influence the nonlinear losses of ultrashort laser pulses and explain why a non-destructive damage regime with detectable excitation is only observed for a narrow intensity range in multipulse experiments.

Torque wiggles – a robust feature of the global disc–planet interaction

ABSTRACT Gravitational coupling between planets and protoplanetary discs is responsible for many important phenomena such as planet migration and gap formation. The key quantitative characteristic of this coupling is the excitation torque density – the torque (per unit radius) imparted on the disc by planetary gravity. Recent global simulations and linear calculations found an intricate pattern of low-amplitude, quasi-periodic oscillations in the global radial distribution of torque density in the outer disc, which we call torque wiggles. Here, we show that torque wiggles are a robust outcome of global disc–planet interaction and exist despite the variation of disc parameters and thermodynamic assumptions (including β-cooling). They result from coupling of the planetary potential to the planet-driven density wave freely propagating in the disc. We developed analytical theory of this phenomenon based on approximate self-similarity of the planet-driven density waves in the outer disc. We used it, together with linear calculations and simulations, to show that (a) the radial periodicity of the wiggles is determined by the global shape of the planet-driven density wave (its wrapping in the disc) and (b) the sharp features in the torque density distribution result from constructive interference of different azimuthal (Fourier) torque contributions at radii where the planetary wake crosses the star–planet line. In the linear regime, the torque wiggles represent a weak effect, affecting the total (integrated) torque by only a few per cent. However, their significance increases in the non-linear regime, when a gap (or a cavity) forms around the perturber’s orbit.

Intrinsic dichroism in amorphous and crystalline solids with helical light

Amorphous solids do not exhibit long-range order due to the disordered arrangement of atoms. They lack translational and rotational symmetry on a macroscopic scale and are therefore isotropic. As a result, differential absorption of polarized light, called dichroism, is not known to exist in amorphous solids. Using helical light beams that carry orbital angular momentum as a probe, we demonstrate that dichroism is intrinsic to both amorphous and crystalline solids. We show that in the nonlinear regime, helical dichroism is responsive to the short-range order and its origin is explained in terms of interband multiphoton assisted tunneling. We also demonstrate that the helical dichroism signal is sensitive to chirality and its strength can be controlled and tuned using a superposition of OAM and Gaussian beams. Our research challenges the conventional knowledge that dichroism does not exist in amorphous solids and enables to manipulate the optical properties of solids.

One Stone, Two Birds: Using High Electric Fields to Enhance the Mobility and the Concentration of Point Defects in Ion-Conducting Solids.

Improving the ionic conductivity of outstanding, composition-optimized crystalline electrolytes is a major challenge. Achieving increases of orders of magnitude requires, conceivably, highly nonlinear effects. One known possibility is the use of high electric fields to increase point-defect mobility. In this study, we investigate quantitatively a second possibility that high electric fields can increase substantially point-defect concentrations. As a model system, we take a pyrochlore oxide (La2Zr2O7) for its combination of structural vacancies and dominant anti-Frenkel disorder; we perform molecular-dynamics simulations with many-body potentials as a function of temperature and applied electric field. Results within the linear regime yield the activation enthalpies and entropies of oxygen-vacancy and oxygen-interstitial migration, and from three independent methods, the enthalpy and entropy of anti-Frenkel disorder. Transport data for the nonlinear regime are consistent with field-enhanced defect concentrations and defect mobilities. A route for separating the two effects is shown, and an analytical expression for the quantitative prediction of the field-dependent anti-Frenkel equilibrium constant is derived. In summary, we demonstrate that the one stone of a nonlinear driving force can be used to hit two birds of defect behavior.

Photonic Floquet Skin-Topological Effect.

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

Statistics of modal condensation in nonlinear multimode fibers

Optical pulses traveling through multimode optical fibers encounter the influence of both linear disturbances and nonlinearity, resulting in a complex and chaotic redistribution of power among different modes. In our research, we explore the phenomenon where multimode fibers reach stable states marked by the concentration of energy into both single and multiple sub-systems. We introduce a weighted Bose-Einstein law, demonstrating its suitability in describing thermalized modal power distributions in the nonlinear regime, as well as steady-state distributions in the linear regime. We apply the law to experimental results and numerical simulations. Our findings reveal that, at power levels situated between the linear and soliton regimes, energy concentration occurs locally within higher-order modal groups before transitioning to global concentration in the fundamental mode within the soliton regime. This research broadens the application of thermodynamic principles to multimode fibers, uncovering previously unexplored optical states that exhibit characteristics akin to optical glass.

Numerical MHD simulations of solar flares and their associated small-scale structures

ABSTRACT Using numerical simulations, we study the formation and dynamics of solar flares in a local region of the solar atmosphere. The magnetohydrodynamics (MHD) equations describe the dynamic evolution of flares, including space-dependent and anomalous magnetic resistivity and highly anisotropic thermal conduction on a 2.5 D slice. We adopt an initial solar atmospheric model in magnetohydrostatic equilibrium, with a magnetic configuration consisting of a vertical current sheet, which helps trigger the magnetic reconnection process. Specifically, we study three scenarios, two with only resistivity and the third with resistivity plus thermal conduction. The main results of the numerical simulations show differences in the global morphology of the flares, including the post-flare loops and the current sheet in three cases. In particular, localized resistivity produces more substructure around the post-flare loops that could be related to the Ritchmyer–Meshkov Instability (RMI). Furthermore, in the scenario of anomalous resistivity, we identify the formation of a plasmoid and a jet at coronal heights. On the other hand, in the scenario with resistivity plus thermal conduction, the post-flare loops are smooth, and no apparent substructures develop. Besides, in the z-component of the current density for the Res + TC case, we observe the development of multiple magnetic islands generated due to the Tearing instability in the non-linear regime.

Multichannel Linear and Nonlinear Information Encryptions with Malus Metasurfaces

AbstractThe superior capability of wavefront manipulation makes metasurfaces a promising platform for implementing high‐density information storage and multifold optical encryption. Although some metasurfaces have realized information encryption, it is still challenging to implement polarization‐encrypted grayscale images in both linear and nonlinear channels. Here, a novel approach to realize multichannel linear and nonlinear information encryptions is proposed based on nonlinear Malus metasurfaces composed of single‐sized meta‐atoms, in which the polarization states of the linear and nonlinear signals can be decoupled. As a proof of concept, two distinct grayscale images with different polarizations have been encrypted in the fundamental and second harmonic wave channels simultaneously. Besides, by further introducing the nonlinear Pancharatnam‐Berry phase, a tri‐channel polarization encrypted metasurface with a multi‐level grayscale image in the near field and two holographic images in the far field has been experimentally demonstrated at the second harmonic frequency. This work provides more degrees of freedom for multichannel information storage and opens an avenue for optical information encryption in both linear and nonlinear regimes.

Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model.

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates

Abstract Topological states have been widely investigated in different types of systems and lattices. In the present work, we report on topological edge states in double-wave (DW) chains, which can be described by a generalized Aubry-André-Harper (AAH) model. For the specific system of a driven-dissipative exciton polariton system we show that in such potential chains, different types of edge states can form. For resonant optical excitation, we further find that the optical nonlinearity leads to a multistability of different edge states. This includes topologically protected edge states evolved directly from individual linear eigenstates as well as additional edge states that originate from nonlinearity-induced localization of bulk states. Extending the system into two dimensions (2D) by stacking horizontal DW chains in the vertical direction, we also create 2D multi-wave lattices. In such 2D lattices multiple Su–Schrieffer–Heeger (SSH) chains appear along the vertical direction. The combination of DW chains in the horizonal and SSH chains in the vertical direction then results in the formation of higher-order topological insulator corner states. Multistable corner states emerge in the nonlinear regime.

Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity—streamfunction and shock-capturing simulations

Two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations [M. Latini and O. Schilling, “A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth,” Physica D 401, 132201 (2020)] are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment [J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005)]. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

Towards the generation of mechanical Kerr-cats: awakening the perturbative quantum Moyal corrections to classical motion

The quantum to classical transition is determined by the interplay of a trio of parameters: dissipation, nonlinearity, and macroscopicity. Why is nonlinearity needed to see quantum effects? And, is not an ordinary pendulum quite nonlinear already? In this manuscript, we discuss the parameter regime where the dynamics of a massive oscillator should be quantum mechanical in the presence of dissipation. We review the outstanding challenge of the dynamical generation of highly quantum mechanical cat states of a massive ‘pendulum’, known as Kerr-cats. We argue that state-of-the-art cold atom experiments may be in a position to reach such a nonlinear regime, which today singles out superconducting quantum circuits. A way to stabilize Schrödinger cat superpositions of a mechanical atomic oscillator via parametric squeezing and further protected by an unusual form of quantum interference is discussed. The encoding of a neutral atom Kerr-cat qubit is proposed.

On the importance of heavy fields in pseudo-scalar inflation

Pseudo-scalar inflation coupled with U(1) gauge fields through the Chern-Simons term has been extensively studied. However, new physics arising from UV theories may still influence the pseudo-scalar field at low-energy scales, potentially impacting predictions of inflation. In the realm of effective field theory (EFT), we investigated axion inflation, where operators from heavy fields are also present, in addition to the axion and gauge fields. The integrated out fields have two significant effects: the non-linear dispersion regime and coupling heavy modes to the Chern-Simons term. The first effect changes the propagation of the curvature fluctuation, while the second one results in additional operators that contribute to curvature fluctuation via inverse decay. We derived the power spectrum and magnitude of equilateral non-Gaussianity in this low-energy EFT. We found that the second effect could become significant as the mass of heavy fields approaches Hubble scale.

Extended Darcy–Forchheimer law including inertial flow deflection effects

Recent advances in manufacturing techniques are providing porous media with both high permeability, necessary for effective passive flow control, and high structural strength, essential for engineering applications. We therefore examine the predictive accuracy of the standard Darcy–Forchheimer (DF) law, which is often used to model porous media flows, for inclusion Reynolds numbers (Re) ranging from the low linear regime to the high nonlinear regime where unsteady effects such as vortex shedding become evident. We consider two different inclusion shapes, square and circular, and three different arrangements of the inclusions – inline, staggered and random. The numerical simulations show that the DF law performs well for low-Re flows, irrespective of the inclusion configuration. For intermediate/high-Re flows, the DF law is adequate only when the arrangement is highly random. However, for the regularly arranged topologies or less random geometries at intermediate/high-Re flows, the DF-law performance diminishes significantly due to flow sheltering and redirection (‘inertial flow deflection’) effects that arise from flow inertia, separation and vortex shedding in the wake of the inclusions. It is shown that the standard DF law, in which the nonlinear permeability tensor is independent of orientation, does not capture such effects. We modified the DF law to capture flow redirection effects by allowing the Forchheimer permeability tensor to depend on the flow orientation with respect to the principal geometrical directions of the porous geometry, and examined this extended DF law for these flows.

Nonlinear instability and solitons in a self‐gravitating fluid

We study a spherical, self‐gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity‐induced dispersion, the emergence of solitons becomes possible. We thus employ a multiscale expansion method to study, in the weakly nonlinear regime, the evolution of small‐amplitude perturbations around the equilibrium state. This way, we derive a spherical nonlinear Schrödinger (NLS) equation that governs the envelope of the perturbations. The effective NLS description allows us to predict a “nonlinear instability” (occurring in the nonlinear regime of the system), namely, the modulational instability, which, in turn, may give rise to spherical soliton states. The latter feature a very slow (polynomial) curvature‐induced decay in time. The soliton profiles may be used to describe the shape of dark matter halos at the rims of the galaxies.

The Aemulus Project. VI. Emulation of Beyond-standard Galaxy Clustering Statistics to Improve Cosmological Constraints

There is untapped cosmological information in galaxy redshift surveys in the nonlinear regime. In this work, we use the Aemulus suite of cosmological N-body simulations to construct Gaussian process emulators of galaxy clustering statistics at small scales (0.1–50 h −1 Mpc) in order to constrain cosmological and galaxy bias parameters. In addition to standard statistics—the projected correlation function w p(r p), the redshift-space monopole of the correlation function ξ 0(s), and the quadrupole ξ 2(s)—we emulate statistics that include information about the local environment, namely the underdensity probability function P U(s) and the density-marked correlation function M(s). This extends the model of Aemulus III for redshift-space distortions by including new statistics sensitive to galaxy assembly bias. In recovery tests, we find that the beyond-standard statistics significantly increase the constraining power on cosmological parameters of interest: including P U(s) and M(s) improves the precision of our constraints on Ωm by 27%, σ 8 by 19%, and the growth of structure parameter, f σ 8, by 12% compared to standard statistics. We additionally find that scales below ∼6 h −1 Mpc contain as much information as larger scales. The density-sensitive statistics also contribute to constraining halo occupation distribution parameters and a flexible environment-dependent assembly bias model, which is important for extracting the small-scale cosmological information as well as understanding the galaxy–halo connection. This analysis demonstrates the potential of emulating beyond-standard clustering statistics at small scales to constrain the growth of structure as a test of cosmic acceleration.

High-g-factor phase-matched second harmonic generation near photonic bandgap of polar cholesteric liquid crystals

ABSTRACT The discovery of polar liquid crystals, such as ferroelectric and helielectric liquid crystals, provides fascinating platforms for designing and modulating polarisation structures that generate strong second harmonic generation. Here, we report that the helielectric nematics, i.e. the polar cholesteric liquid crystals, realise an unprecedented phase-matching condition for the second harmonic generation in the photonic bandgap. Like the circular dichroism in the linear optical regime, the phase-matched second harmonic generation generated in a helielectric nematic medium exhibits a circular polarisation selectivity in the nonlinear optical regime. The maximum g-factor for the second harmonic generation is over ~ 1.95.

Strongly nonlinear antiferromagnetic dynamics in high magnetic fields

Antiferromagnetic (AFM) materials possess a well-recognized potential for ultrafast data processing thanks to their intrinsic ultrafast spin dynamics, absence of stray fields, and large spin transport effects. The very same properties, however, make their manipulation difficult, requiring frequencies in THz range and magnetic fields of tens of Teslas. Switching of AFM order implies going into the nonlinear regime, a largely unexplored territory. Here we use THz light from a free electron laser to drive antiferromagnetic NiO into a highly nonlinear regime and steer it out of nonlinearity with magnetic field from a 33-Tesla Bitter magnet. This demonstration of large-amplitude dynamics represents a crucial step towards ultrafast resonant switching of AFM order.

Polyethylene glycol regulates the pitch and liquid crystal behavior of cellulose nanocrystal-based photonic crystals

Inspired by iridescent color in natural creations, cellulose nanocrystal (CNC) photonic crystals artificially created by nanotechnology have great application prospects due to their potential to control light propagation in the linear and nonlinear regimes. One of the most important development directions of photonic crystals is the diversification of colors, usually by adjusting the pitch. However, few researchers notice the effect of polymer molecular weight and content on pitch regulation and the interaction between polymer and CNC liquid crystals. Polyethylene glycol (PEG) were used as polymers to regulate the pitch of CNC photonic crystals and investigate the changes in microstructure, crystal structure, thermal properties, and liquid crystal texture of the composites by changing the PEG content and molecular weight. Different photonic crystal construction systems show that when the molecular weight of PEG is 0.4 k, it can be filled between CNCs to regulate the pitch of photonic crystals, while when the molecular weight of PEG is 20 k, it cannot always be filled between CNCs in evaporation-induced self-assembly (EISA) process due to the depletion interaction, which cannot effectively regulate the pitch. This study reveals the relationship between PEG and CNC liquid crystals, which supports the development of photonic crystals and the pitch regulation.