Nonlinear Regime Research Articles

Engineering dynamical photon blockade with Liouville exceptional points.

We investigate the dynamical blockade in a nonlinear cavity and demonstrate the connection between the correlation function g(2)(t) and system parameters in the entire nonlinear region. Utilizing the Liouville exceptional points (LEPs) and quantum dynamics, a near-perfect single-photon blockade (1PB) can be achieved. By fine-tuning system parameters to approach the second-order LEP (LEP2), we improved single-photon statistics in both weak and strong nonlinearity regimes, including a significant reduction of g(2)(t) and a pronounced increase in the single-photon occupation number. In the strong nonlinearity region, the maximum photon population may correspond to stronger antibunching effect. Simultaneously, the time window and period of blockade can be controlled by selecting detuning based on the LEP2. Furthermore, the 1PB exhibits robustness against parameter fluctuations, and this feature can be generalized to systems for implementing single-photon sources with nonharmonic energy levels.

High-efficiency all-optical switching based on broadband coherent perfect absorption in an atom-cavity system

We propose an ultrahigh-efficiency and broadband all-optical switching scheme based on coherent perfect absorption (CPA) in linear and nonlinear excitation regimes in a cavity quantum electrodynamics (CQED) system. Two separate atomic transitions are excited simultaneously by two signal fields coupled from two ends of an optical cavity under the collective strong coupling condition. Three polariton eigenstates are produced which can be tuned freely by varying system parameters. The output field intensities of multiple channels are zero when the CPA criterion is satisfied. However, destructive quantum interference can be induced by a free-space weak control laser when it is tuned to be resonant to the polariton state. As a consequence, the CQED system acts as a coherent perfect light absorber/transmitter as the control field is turned on/off the polariton resonances. In particular, the proposed scheme may be used to realize broadband multi-throw all-optical switching in the nonlinear excitation regime. The proposed scheme is useful for constructing all-optical routing, all-optical communication networks and various all-optical logic elements.

Twist-Angle-Controlled Nonlinear Circular Dichroism on Gold-Crystal Hybrid Metasurfaces.

Optical chirality, which plays important roles in liquid crystal display and biological and chemical detection, has been attracting scientists' attention due to its potential applications in optical information processing. Usually, the chiral optical response of natural molecules is very weak. However, the emergence of metasurfaces offers a promising solution to solve this issue. By judiciously designing the geometry of meta-atoms, we have realized strong optical circular dichroism (CD) in both linear and nonlinear optical regimes. However, tuning of the CD with a metasurface remains challenging. Here, we propose the twist-angle-controlled nonlinear CD effect by using the second-harmonic generation process on a gold-crystal hybrid metasurface. The CD effect of the second-harmonic waves can be tuned well by controlling the twist angle between the two constituent materials. The proposed hybrid metasurface may open new avenues for developing ultracompact and multifunctional nonlinear optical devices.

230-fold Enhancement of second-harmonic generation by coupled double resonances in a dolmen-type gold metasurface

Optical metasurfaces, artificial planar nanostructures composed of subwavelength meta-atoms, have attracted significant attention due to their ability to tailor optical nanoscale properties, making them a versatile platform for shaping light in both linear and nonlinear regimes. This paper reports on the realization of second harmonic generation (SHG) enhancement based on a dolmen-type gold metasurface containing two resonances. Nonlinear scattering theory is employed to numerically investigate the SHG enhancement phenomenon in the resonant metasurface. The periodic dolmen-type gold metasurface introduces a diffraction coupling effect between Fano resonance and surface lattice resonance (SLR), providing strong local-field enhancement and significantly enhancing the nonlinear effect. We analyze the influence of the coupling between Fano resonance and SLR on the SHG intensity and achieve a 230-fold enhancement in SHG intensity compared to the single resonance case by adjusting the periodicity of the metasurface. The SHG-enhanced gold metasurface may find applications in sensing, imaging, optical computing, and integrated nonlinear optics.

Temperature compensation through kinetic regulation in biochemical oscillators

Nearly all circadian clocks maintain a period that is insensitive to temperature changes, a phenomenon known as temperature compensation (TC). Yet, it is unclear whether there is any common feature among different systems that exhibit TC. From a general timescale invariance, we show that TC relies on the existence of certain period-lengthening reactions wherein the period of the system increases strongly with the rates in these reactions. By studying several generic oscillator models, we show that this counterintuitive dependence is nonetheless a common feature of oscillators in the nonlinear (far-from-onset) regime where the oscillation can be separated into fast and slow phases. The increase of the period with the period-lengthening reaction rates occurs when the amplitude of the slow phase in the oscillation increases with these rates while the progression speed in the slow phase is controlled by other rates of the system. The positive dependence of the period on the period-lengthening rates balances its inverse dependence on other kinetic rates in the system, which gives rise to robust TC in a wide range of parameters. We demonstrate the existence of such period-lengthening reactions and their relevance for TC in all four model systems we considered. Theoretical results for a model of the Kai system are supported by experimental data. A study of the energy dissipation also shows that better TC performance requires higher energy consumption. Our study unveils a general mechanism by which a biochemical oscillator achieves TC by operating in parameter regimes far from the onset where period-lengthening reactions exist.

Interfacial rheological properties of pepsin-hydrolyzed lentil protein isolate at oil-water interfaces

Lentil protein isolate (LPI) was investigated for its potential as a plant protein-based emulsifier. LPI consists mainly of globulins with high molecular weights which are relatively slow to adsorb and stabilize oil-water interfaces. Smaller proteins, such as whey protein, can stabilize the interface much faster, quickly forming a viscoelastic film that slows down the rate of droplet recoalescence, leading to smaller droplets. To increase the rate of adsorption, LPI was enzymatically hydrolyzed by pepsin at 1.5% and 4.5% degree of hydrolysis (DH), to obtain small peptides. The behavior of these peptides was studied at the oil-water interface in comparison to whey protein isolate (WPI) and native lentil protein isolate (LPI). Interfacial properties were investigated using dilatational and interfacial shear rheology in the linear viscoelastic regime (LVE) and nonlinear viscoelastic regime (NLVE) and these were related to protein characteristics and emulsion formation. The 1.5% and 4.5%DH LPI showed high surface hydrophobicity, and consisted mainly of low molecular weight peptides, which contributed to faster adsorption kinetics and consequently covered the interface faster than LPI. In dilatation, the native and hydrolyzed LPI-stabilized interfaces had comparable stiffness and were clearly weaker than WPI-stabilized interfaces, which contrasts with the results in shear deformations, where the former both had higher stiffness than WPI. Both hydrolyzed LPI and WPI formed more brittle and less stretchable interfaces compared to native LPI in both dilatational and shear rheology. In emulsification tests, native LPI produces the largest droplets, and the 4.5% DH LPI and WPI have the smallest droplet size. But, bridging flocculation was observed when emulsions were prepared with both hydrolyzed LPI, which may be attributed to inter-droplet hydrophobic interactions between small polypeptides. This can be linked to an increase in the surface hydrophobicity of hydrolyzed LPI. Thus, the use of native LPI as a stabilizer in emulsion preparation is preferable over the hydrolyzed samples, despite its larger droplet size.

Quantifying flow regime impacts on hydrodynamic heat transfer in rough-walled rock fractures

Hydrodynamic heat transfer in rock fractures is crucial for many geophysical processes and engineering activities, notably in harnessing geothermal energy. Despite extensive research, characterizing hydrodynamic heat transfer in rock fractures, complicated by their geometric heterogeneity, remains a formidable challenge. To address this challenge, we experimentally investigated the hydrodynamic heat transfer in rock fractures with diverse geometric features at steady-state elevated temperatures. We found that both heterogeneous fracture geometry and elevated temperatures promote the transition of fracture flow from a linear to nonlinear regime. This flow regime transition enhances the heterogeneity of heat transfer intensity within the fracture and exacerbates the increase in heat transfer efficiency with flow rate. At a fortyfold increase in flow rate, the heat transfer coefficient in the most heterogeneous fracture rises by approximately 72 times, compared to about 28 times in the least heterogeneous one. Leveraging experimental data, we developed parametric models linking heat transfer coefficients, outflow temperature, and heat recovery rate to flow rate and geometric features, yielding a theoretical formulation for the maximal heat recovery rate. By introducing the concept of an energy conversion rate, we quantitatively evaluated the effect of nonlinear flow resistance on heat extraction feasibility, revealing that energy conversion rates in highly heterogeneous fractures can be up to 452 times lower than in less heterogeneous ones. This highlights the pivotal role of flow resistance in heat extraction feasibility. Our findings are instrumental for understanding and predicting the hydrodynamic heat transfer within fractured geothermal reservoirs and analogous hydro-thermal systems.

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers via Nonlinear Boundary Region Equations

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number M∞, the shear layer thickness δ, the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer ΔV on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing ΔV and A decreases with increasing delta. It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure’s amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration.

Multi-GeV Electron Acceleration in Wakefields Strongly Driven by Oversized Laser Spots.

Experiments were performed on laser wakefield acceleration in the highly nonlinear regime. With laser powers P<250 TW and using an initial spot size larger than the matched spot size for guiding, we were able to accelerate electrons to energies E_{max}>2.5 GeV, in fields exceeding 500 GV m^{-1}, with more than 80pC of charge at energies E>1 GeV. Three-dimensional particle-in-cell simulations show that using an oversized spot delays injection, avoiding beam loss as the wakefield undergoes length oscillation. This enables injected electrons to remain in the regions of highest accelerating fields and leads to a doubling of energy gain as compared to results from using half the focal length with the same laser.

Stability of convective rolls in a horizontal layer rotating about an inclined axis

We present three results on stability of rolls in Boussinesq convection in a plane horizontal layer with rigid boundaries that is rotating about an inclined axis with the angular velocity Ω = ( Ω 1 , Ω 2 , Ω 3 ) . (i) We call the full problem the set of equations governing the temporal behaviour of the flow and temperature for an arbitrary Ω , and by the reduced problem the set of equations for the angular velocity ( Ω 1 , 0 , Ω 3 ) . Here x,y are horizontal Cartesian coordinates in the layer and z is the vertical one. We prove that a y-independent solution to one of the two problems is also a solution to the second one. (ii) We calculate the critical Rayleigh number for the monotonic onset of convection. The instability mode in the form of rolls (a flow independent of a horizontal direction) is assumed. Let β be the angle between the horizontal projection of Ω and the rolls axes. We show that β = 0 for the least stable mode. When the axis of rotation is horizontal, this is proven analytically, and for Ω 3 ≠ 0 , the result is obtained numerically. Taking i into account, we conclude that the critical Rayleigh number for the onset of convection is independent of Ω 1 and Ω 2 and the emerging flow are rolls with axis aligned with the horizontal component of the rotation vector. (iii) We study the behaviour of convective flows by integrating numerically the three-dimensional equations of convection for Ω = ( 0 , Ω 2 , Ω 3 ) and a range of the Rayleigh numbers, other parameters of the problem being fixed. We assume square horizontal periodicity cells, whose sides are equal to the period of the most unstable mode. The computations indicate that, in general, in the nonlinear regime convective rolls become more stable as Ω 2 increases. Namely, on increasing Ω 2 , the interval of the Rayleigh numbers for which convective rolls are stable increases.

Jets from shocked metal surfaces with grooves: Missing experiments

Many studies have investigated the mass outflows generated when a planar shock transits an imperfect (“defected”) metal surface, where the defects are symmetric triangular or sinusoidal grooves. Yet a fundamental question remains unanswered: how does the quantity of outflow mass and its maximum velocity vary as a function of the groove cross-sectional aspect ratio? We identify two sets of missing experiments that must be addressed to answer the question. The aspect ratio (groove depth over width) is equivalently represented by θ, the cross-sectional half angle, or by η0k, the amplitude multiplied by an effective wavenumber. Low θ (high η0k) grooves comprise the first set of missing experiments, which are necessary to determine the validity of theoretical predictions of the nonlinear regime (η0k≥1, θ&amp;lt;57.5°). The second set of missing experiments are those in which the volume of the groove (or equivalently, the axial cross-sectional area) has been held constant as θ or η0k are varied. Such experiments are necessary to independently measure the effects of variations in groove volume and groove aspect ratio on the resulting jets.

Reconstruction of turbulence characteristics from fluctuation reflectometry measurements in the nonlinear regime

The nonlinear theory of radial correlation reflectometry (RCR) predicts that the cross correlation function of a signal follows a Gaussian distribution with a cutoff separation, where the correlation length is determined by both the turbulence amplitude and its radial correlation length. In contrast, phase spectrum analysis provides information solely on the turbulence amplitude. This work describes the possibility of applying both signal analysis methods and demonstrates that turbulence amplitude and radial correlation length can be simultaneously measured using RCR diagnostics in the nonlinear regime.

Dynamics of femtosecond lasers and induced plasma in non-Kerr nonlinear transparent materials: Competing effects of electron–hole radiative recombinations and single-electron diffusions

Modern laser micromachining utilizes ultrashort optical fields, such as femtosecond lasers, to perform high-precision processings on solid materials, including cutting, drilling, ablation, polishing, and scripturing. Femtosecond laser-based material processings can induce a plasma of free electrons whose density depends on physical phenomena such as single-electron diffusions, multiphoton ionization, and electron–hole radiative recombinations. In this work, we examine the dynamics of femtosecond lasers in transparent materials with non-Kerr nonlinearity, taking into account the generation of an electron plasma. In these specific materials, a balance between the nonlinearity and the group-velocity dispersion of the optical medium can favor the formation of optical filaments propagating with a permanent shape by virtue of their “solitonic” features. We are interested in the effects of the competition between electron–hole radiative recombination and single-electron diffusion processes on the spatiotemporal profiles of the propagating optical field and of the plasma density. The model features a complex Ginzburg–Landau equation with an optical nonlinearity of a general saturable form and a Kth-order nonlinearity term accounting for K-photon ionization processes, coupled to a rate equation for the electron plasma density where the present terms are representing avalanche ionizations, single-electron diffusion, and electron–hole radiative recombination processes. The modulational-instability analysis suggests that the continuous-wave regime will be stabilized by strong electron–hole radiative recombination processes for a fixed value of the single-electron diffusion coefficient, a stability enhanced by an increase in K. In the nonlinear regime, numerical simulations of the model equations for different combinations of the nonlinearity-saturation exponents and different values of the photon number K unveil soliton train structures forming from the laser field propagation and the time evolution of the plasma density. These structures turn out to be either dissipative soliton trains in the absence of electron–hole radiative recombinations or soliton crystals when electron–hole radiative recombination processes are taken into consideration to balance the damping effect caused by single-electron diffusions.

Magnetic-induced chiral dynamics in an extended two-leg bosonic ladder

The realization and detection of chiral physics with ultracold atomic gases provide a unique path for the exploration of topological phases. Here, we show that the interplay of magnetic field and interacting particles in an extended two-leg ladder leads to rich chiral Bloch dynamics. Considering both the on-site contact interaction and nearest-neighbor interactions, the ground state and Bloch dynamics of the system are studied analytically and numerically. When the system is in the ground state, the threshold and phase diagram for the transition between zero-momentum state and plane-wave state are analytically obtained, showing the nearest-neighbor interactions along the legs and rungs have opposite impact on the ground state transition, providing new opportunity to manipulate the ground state transition. When the ladder is perturbated under an external linear force, chiral dephasing of Bloch oscillations (BOs), i.e. symmetry breaking damped BOs (the damping rate of BOs on one leg is larger than the other), are observed. This chirality is absent for vanishing the magnetic field and atomic interaction. Particularly, the chirality of damped BOs is inversed when the magnetic field (chiral current) is inversed. In addition, the damping of BOs induced by different types of atomic interactions is different, and the strength and damping rate of BOs initialized in different ground states are distinct, offering dynamic ways to detect the different ground states. Furthermore, the persistent chiral Bloch oscillations observed in single particle case is predicted analytically, which is a crucial requirement for observation and application of chiral BOs in nonlinear regime. Our results provide an interesting path towards the exploration of topological atomic superfluids.

Simulations of non-integer upconversion in resonant six-wave scattering

Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [Malkin and Fisch, Phys. Rev. E 108, 045208 (2023)]. The high order resonance is a unique non-integer multiple of a driving pump frequency resulting in a frequency upshift by a factor of ≈3.73. We demonstrate the presence, unique requirements, and growth of this mode numerically. Through tuning waves to high amplitude, in a mildly underdense plasma, the six-photon process may grow more than other non-resonant but lower order processes. The growth of the high frequency mode remains below the nonlinear growth regime. However, extending current numerical results to more strongly coupled resonances with longer pulse propagation distances suggests a pathway to significant upconversion.

A unified theory of the self-similar supersonic Marshak wave problem

We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity, and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat and does possess its common sharp characteristic; this characteristic is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer–Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non-sharp fronts. The solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.

Eigenmodes and eigenfunctions of high-power electromagnetic waves in inhomogeneous magnetized plasmas and their stability to stimulated Raman backscattering

Eigenmodes and eigenfunctions of high-power electromagnetic waves in inhomogeneous magnetized plasmas are investigated. Considering the dielectric permittivity in the presence of an external magnetic field and relativistic nonlinearity and considering the inhomogeneity of the electron density in the linear and rippled structures, two nonlinear wave equations are obtained. In the linear regime, eigenmodes and eigenfunctions of the electric field for two-electron densities are obtained. In the nonlinear regime, results indicate that by increasing the external magnetic field, the amplitude of the electric field increases, which affects the dielectric permittivity. The conditions of the stimulated Raman backscattering and the equation of the space-charge potential are obtained. Results also indicate that in the presence of the external magnetic field, plasma inhomogeneity, and relativistic nonlinearity, the stimulated Raman backscattering becomes unstable.

Continuous control of structural vibrations using hybrid deep reinforcement learning policy

An efficient active structural control scheme by utilizing the collective concepts of data-driven and physics-inspired reinforcement learning (RL) approaches is being introduced here. The controller is designed to deliver optimal feedback forces based on the full-state information, wherein the training process involves the use of deep neural networks (NNs) and a specially designed gradient descent-based sequence within the RL framework. This integration of algorithms results in a unique active control policy that accelerates the learning process, thereby demands considerably less computational resources to develop an optimal and stable controller as compared to existing data-driven approaches. Most importantly, the mentioned data-driven and physics-inspired approaches encompass deep deterministic policy gradient (DDPG) and an iterative gradient-based state feedback control (SFSC) algorithms, respectively, to establish the architecture of the hybrid control policy, referred to as hybrid RL-controller. Additional advantage of the hybrid RL-controller is its ability to operate in continuous state–action spaces, which allows the designed controller to address diverse structural control problems. The staggered performance of the hybrid RL-controller, both in continuous and discrete time, is evaluated in three case studies that involve structures in linear and nonlinear regimes. The outcomes include a detailed comparison of the hybrid RL-controller with the individually designed DDPG and SFSC RL control strategies, as well as the uncontrolled scenario. Furthermore, this study thoroughly investigates the real-life implementation concerns of control strategies, such as perturbations in model parameters and input forces, and time delays in the feedback loop. Finally, the results from this study corroborate that the designed RL-controller showcases superior performance and faster execution time in the feedback loop, making it suitable for the vibration control of multidimensional complex structures.

Wave–particle interactions in tokamaks

Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.

A weakly nonlinear Love hypothesis for longitudinal waves in elastic rods

When investigating nonlinear wave propagation in slender hyperelastic rods, the usual stance is to construct a reduced kinematics and then derive a system of coupled nonlinear PDEs for the unknown functions. To make further analytical progress, the linear Love hypothesis, that connects longitudinal and transversal strain, is often reverted to. The viability of this assumption, that was originally proposed within the framework of linear elasticity, remains uncertain. In this paper, a refined Love hypothesis is derived in the weakly nonlinear regime by slow-time perturbation of the motion equations. For the sake of illustration, the simplest two-modal setting is adopted. This refined Love assumption is not equivalent, not even in principle, to that derived by Porubov and Samsonov (1993) by accommodating for the free boundary conditions at the rod mantle. Besides, the perturbation process lends a uni-dimensional model equation which parallels that obtained by Ostrovskii and Sutin (1977) with the help of the linear Love hypothesis, with yet different coefficients in the dispersive term. The corresponding longitudinal motion is compared numerically against the solution of the bimodal nonlinear system and the transversal motion is contrasted with the linear Love hypothesis. For both motions, excellent agreement is found and the quality of the approximation extends to a wide range of values for the small parameter. Finally, within this setting, the corresponding unimodal Lagrangian is also derived, and it remains accurate regardless of the first correction terms to the linear Love hypothesis.