## What is/are Nonlinear Effects?

Nonlinear Effects - Recently, a technique independent of nonlinear effects called dispersive Fourier transform (DFT) (6, 7) has made it possible to real-time detect spectral evolution in complex ultrafast systems (8, 9).^{[1]}Under simplifying hypotheses, these nonlinear effects are analyzed for the nonlinear vibrations under harmonic excitation, also considering the effects of an initial camber.

^{[2]}Originality/value Findings reveal the nonlinear effects of focused and multi-focus searches on RIE performance and clarify the dispute over the mechanism of KS on performance by proposing the different moderating role of C&E.

^{[3]}Recent milestones in power-scaling of ultrafast fiber-based lasers were achieved by the simultaneous mitigation of thermal and nonlinear effects through the coherent combination of ultrafast pulses [1].

^{[4]}On the other hand, for mitigating the nonlinear effects of the VLC system, an artificial neural network equalizer is designed and implemented in offline digital signal processing.

^{[5]}For relatively small liquid-depth, nonlinear effects shift the resonant sloshing frequency.

^{[6]}A significant cancellation of linear and nonlinear effects results a bright optical soliton in the coherent atomic medium.

^{[7]}Wave propagation in metamaterials with different structure scales is analyzed with account of nonlinear effects.

^{[8]}38), were identified to have nonlinear effects on tourism.

^{[9]}Compared to linear regressions, interactions and nonlinear effects enhance the predictive performance substantially.

^{[10]}Furthermore, we extend the standard definition of the scan element pattern (SEP) to the active SEP (ASEP) that accounts for nonlinear effects of PAs on the AiUC performance.

^{[11]}The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions.

^{[12]}In this paper, we numerically investigate and evaluate the requirements of a photonic RC using an active silicon micro-ring resonator as a photonic integrated circuit (PIC) based reservoir system to compensate for transmission impairments such as chromatic dispersion and nonlinear effects occurring in optical transmission systems.

^{[13]}Decreased power and nonlinear effects make bulk modification become usually achievable [2].

^{[14]}Above this altitude we solve Maxwell’s equations self-consistently including the nonlinear effects of heating and ionization/attachment of the electrons.

^{[15]}Nonlinear effects have been considered as the major limitations in coherent optical (CO) fiber transmission system.

^{[16]}At times significantly less than the characteristic flame burning time, the flame front deforms as an inert interface due to the Richtmyer–Meshkov instability with nonlinear effects becoming noticeable.

^{[17]}A single quantum emitter can possess a very strong intrinsic nonlinearity, but its overall promise for nonlinear effects is hampered by the challenge of efficient coupling to incident photons.

^{[18]}The nonlinear effects on the gluon distribution improve the behavior of the longitudinal structure function in comparison with the H1 data and CT18 at low values of Q.

^{[19]}Regression results indicate that a cubic S-curve relationship between board independence and IC efficiency exists, and firm size moderates the nonlinear effects.

^{[20]}The output power of fiber-based single-frequency amplifiers is typically limited by nonlinear effects (e.

^{[21]}Nonlinear effects of the near-seabed interference are found to be particularly significant when the relative clearance ratio (clearance beneath tunnel / height of tunnel element) is smaller than 0.

^{[22]}A comparison to the existing network-based risk measures reveals that our approach offers a new perspective on systemic risk due to the focus on the lower tail and to the allowance for nonlinear effects.

^{[23]}This confinement is not only being exploited for miniaturisation but also allows the concentration of electromagnetic energy, allowing for strong coupling18,19 and nonlinear effects20–22.

^{[24]}Linear and nonlinear effects of the equilibrium radial electric field on the ion temperature gradient (ITG) instability in the scrape-off layer (SOL) of a field-reversed configuration have been studied using gyrokinetic particle simulations for a single toroidal mode.

^{[25]}We then use a generalized additive model (GAM) to discern both linear and nonlinear effects, and include 5 random effect covariates to account for potential differences in testing and reporting that can bias the estimated R0.

^{[26]}Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to the nanoscale-based enhancement of nonlinear effects.

^{[27]}This raises the question that, given the small number of samples and the high number of variables in many spectroscopic datasets, are nonlinear effects significant enough to justify the additional model complexity? In the present study, we empirically investigate this question in relation to lactate, an important biomarker.

^{[28]}Special attention is paid to the influence of nonlinear effects on the displacement state and axial forces.

^{[29]}Our work directly demonstrates that when the excited laser photon energy exceeds the material bandgap, photon drag effect would be the main mechanism of THz wave radiation rather than nonlinear effects.

^{[30]}Both linear and nonlinear functions were used for the strain-stress relation of the IMM fragment, with nonlinear effects more important at large IMM stretching strains.

^{[31]}Afterwards, we build the PIN diode model with these mathematical equations, making it compatible with implementing co-simulation between the passive electromagnetic model and the active element of PIN diodes and, particularly, the nonlinear effects can be considered.

^{[32]}However, inductive ITs, which are still the most widely used, suffer from both a filtering behavior due to their dynamics and from nonlinear effects due to their iron core.

^{[33]}Although the developed method incorporates the elastic constitutive relation, it enables the effective modeling of these nonlinear effects.

^{[34]}The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with weakening of the lift-up mechanism, which is known to dominate the linear operator.

^{[35]}Along with the Stokes line narrowing reasoned by the reduction of spectral broadening via nonlinear effects due to the enlargement of effective mode area in the multicore fiber with coupled cores in comparison with a standard singlemode fiber Raman laser, the additional line narrowing effect induced by the multicore random FBG array has been also revealed.

^{[36]}We illustrate how regression splines can be used to test for nonlinear effects of cross-language similarity in form as well as for controlling experimental trial effects.

^{[37]}Yet, such simulations are challenging mainly due to the large size of the finite-element model used to describe the system, the existence of random mistuning created by manufacture tolerances, and the nonlinear effects arising from the different components and their coupling.

^{[38]}Soliton technique is used to compensate the dispersion and balanced with nonlinear effects.

^{[39]}With judicious designs of refractive index, modal coupling and gain–loss distribution, unconventional control and manipulation of light flow and nonlinear effects could be achieved.

^{[40]}Nearly all nonlinear effects were practically insignificant in magnitude (mean incremental R2 =.

^{[41]}Despite the recent studies on the combination of these two techniques, nonlinear effects of devices have been ignored.

^{[42]}The reference region is estimated nonparametrically and the nonlinear effects of continuous covariates via polynomial kernel smoothers in additive models.

^{[43]}The medical application of the nonlinear effects of time-reversal acoustics is provided such as for the application to blood pressure measurement in heat chamber and application to assessment of the human calcaneus.

^{[44]}This paper proposes a sliding mode control for a heaving point absorber that includes the nonlinear effects of the dynamic and static Froude-Krylov forces.

^{[45]}Nonlinear effects are studied.

^{[46]}At high launch power levels, which are required for the long-haul transmission over hundreds of km, these nonlinear effects become more severe which imposes a challenge to achieve satisfactory transmission performance.

^{[47]}The nonlinear effects of respondents’ current age at birth at the time of survey showed the older women have higher potential to attain higher utilization levels than the younger ones.

^{[48]}We study the nonlinear effects of raw material prices measured by that of cotton product on the economic growth of a sample of African countries for the period of 1991–2019.

^{[49]}We demonstrate the ability of the spin-noise spectroscopy to access the nonlinear effects related to the renormalization of the spin states by strong electromagnetic fields.

^{[50]}

## self phase modulation

A mechanism to achieve the required spectral bandwidth is to broaden the output of a femtosecond laser source in nonlinear media such as highly nonlinear fibers (HNLF) utilizing a combination of nonlinear effects such as self-phase modulation (SPM) and four-wave mixing (FWM).^{[1]}The stretching stage prior the amplification stage is required to decrease the pulse intensity, and thereby to reduce a detrimental impact of the nonlinear effects (such as stimulated Raman scattering, self-phase modulation) on pulse.

^{[2]}Supercontinuum generation in transparent bulk media results from femtosecond filamentation, which involves a complex interplay among linear (diffraction and GVD) and nonlinear effects (self-focusing, self-phase modulation, pulse-front steepening, generation of optical shocks, multiphoton absorption/ionization, free-electron plasma generation, etc.

^{[3]}

## four wave mixing

In this paper, four kinds of nonlinear effects are investigated to realize all-optical multicast, including cross-gain modulation (XGM), cross-phase modulation (XPM), four-wave mixing (FWM) and cascaded sum frequency generation (SFG)/difference frequency generation (DFG).^{[1]}In DWDM, Four Wave Mixing is the most critical of nonlinear effects in fibre optics communication.

^{[2]}In the normal dispersion region, other nonlinear effects have broadened the spectra before four-wave mixing.

^{[3]}

## harmonic mode locking

Using a cascaded long-period fiber grating as a spectral filter, several modes of passively harmonic mode-locking including passive high-order harmonic mode-locking, passive multiple-pulse harmonic mode locking and passive large-pulse-width harmonic mode locking (over 300 ns ) were obtained by adjusting the tunable CW semiconductor laser (pumping source in the experiment) and polarization controller, in which the intense nonlinear effects, large fiber dispersion and phase bias played an important role.^{[1]}

## Order Nonlinear Effects

Second-order nonlinear effects, such as second-harmonic generation, can be strongly enhanced in nanofabricated photonic materials when both fundamental and harmonic frequencies are spatially and temporally confined.^{[1]}Both crystals possess high second-order susceptibility χ(2) and low loss, making them ideal for second-order nonlinear effects.

^{[2]}To launch LHOCS, the system mainly faces high order nonlinear effects.

^{[3]}An architecture based around a Ti:sapphire master comb in principle enables wavelengths across this range to be obtained by a combination of second- and third-order nonlinear effects.

^{[4]}35-μm pulses, we study high-order nonlinear effects in monocrystals.

^{[5]}We have studied the THz generation in DSTMS using a quasi-3D model that takes into account high-order nonlinear effects beyond the χ(2) nonlinearity.

^{[6]}01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects.

^{[7]}Photonic nanostructures simultaneously maximizing spectral and spatial overlap between fundamental and second-harmonic confined modes are highly desirable for enhancing second-order nonlinear effects in nonlinear media.

^{[8]}

## Different Nonlinear Effects

We also demonstrate the ability to generate different nonlinear effects in a wide spectral range in the visible region for monolayer MoS2, opening the possibility of using two-dimensional materials for nonlinear optoelectronic and photonic applications.^{[1]}We also demonstrate the ability to generate different nonlinear effects in a wide spectral range in the visible region for monolayer MoS2, opening the possibility of using two-dimensional materials for nonlinear optoelectronic and photonic applications.

^{[2]}However after travelling a certain distance the transmitted signal gets attenuated due to different nonlinear effects present in the fiber.

^{[3]}In addition, the influence of different nonlinear effects, the ultrashort pulse evolution in the CSAD-TMF with the anomalous dispersion (AD) zones and the normal dispersion (ND) zones were analyzed based on the generalized nonlinear Schrodinger equations (GNLSE) modelling.

^{[4]}A phenomenological pulse propagation model is employed that incorporates the experimentally obtained nonlinear absorption coefficients and different nonlinear effects exhibited by the system.

^{[5]}The different nonlinear effects of spin dynamics, ranging from homogeneous spin vibrations in small particles to the dynamics of solitons, domain walls, ferrimagnetic skyrmions, and vortices, are analyzed.

^{[6]}

## Strong Nonlinear Effects

To further explore their capabilities in such scenarios, it is crucial to be able to model their flight dynamics over the full envelope, which includes strong nonlinear effects and turbulence at high angles of attack.^{[1]}In shallow water, the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water, and the strong nonlinear effects are observed.

^{[2]}The economic infrastructure of these countries, often concentrated in a few cities, forces workers to travel from commuter cities and rural areas, which induces strong nonlinear effects on disease transmission.

^{[3]}The study of hysteresis loops and frequency response function showed strong nonlinear effects and vibration amplitude decrease up to 50%.

^{[4]}Tribological behaviour is characterized by the strong nonlinear effects in its response, which are hardly identified with standard signal processing methods.

^{[5]}Therefore, strong nonlinear effects are considered for the training of the ROM.

^{[6]}

## Optical Nonlinear Effects

Self-induced nonreciprocity based on optical nonlinear effects is a more appealing technique compared to other relevant nonreciprocal schemes due to the absence of any kind of external bias based on magnets, currents, or space and time modulation.^{[1]}Non-reciprocal phenomena generated by optical nonlinear effects without the requirement of external bias have important applications in modern photonics.

^{[2]}Power scaling based on traditional ytterbium-doped fibers (YDFs) is limited by optical nonlinear effects and transverse mode instability (TMI) in high-power fiber lasers.

^{[3]}In this paper, we propose an all-optical modulation format conversion system between on-off keying, quadrature phase-shift keying, and 8-ary quadrature amplitude modulation using optical nonlinear effects in semiconductor optical amplifier and optical threshold device.

^{[4]}

## Detrimental Nonlinear Effects

Nevertheless, the high power density into the core of a fiber may induce detrimental nonlinear effects leading to spectral and temporal quality degradation of the optical pulses.^{[1]}One example is the use of a rod-type geometry with large core diameters to mitigate detrimental nonlinear effects.

^{[2]}Upscaling the mode area of fibers is the most effective approach to reduce the nonlinear interaction and, therefore, to allow for the confinement of high-power radiation without detrimental nonlinear effects.

^{[3]}Furthermore, the longer operation wavelength reduces the impact of detrimental nonlinear effects in fiber lasers, and allows for a larger mode field area with diffraction-limited beam quality as compared to the well-established ytterbium-doped fiber laser systems [4].

^{[4]}

## Variou Nonlinear Effects

Various nonlinear effects (modulation instability, formation of solitons, and acceleration of electrons) possibly take place in the localized region near the reflection height.^{[1]}The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions.

^{[2]}The core of the photonic crystal fibers and two-dimensional photonic crystal based on diverse geometries and the materials, permitting supercontinuum generation due to various nonlinear effects in an enormously broad spectral range.

^{[3]}Detail analysis of high power amplification of cladding-ring-up-doped ultra low NA single mode fiber amplifier has been presented, which includes various nonlinear effects and thermal effects.

^{[4]}

## Suppressing Nonlinear Effects

Compared with traditional uniform fiber, the long tapered fiber has the advantage of suppressing nonlinear effects and maintaining excellent beam quality.^{[1]}Suppressing nonlinear effects in fiber laser by special fiber gratings has attracted growing attentions.

^{[2]}Firstly, excellent performance of the Yb-doped T-DCF for suppressing nonlinear effects, including stimulated Brillouin scattering (SBS) effect and spectral broadening effects, is experimentally demonstrated and qualitatively analyzed.

^{[3]}Suppressing nonlinear effects in high-power fiber lasers based on fiber gratings has become a hotspot.

^{[4]}

## Multiple Nonlinear Effects

Second, in natural scene viewing, we model and isolate multiple nonlinear effects of saccade parameters on the FRP.^{[1]}To further increase the output brightness of single-channel fiber laser, high-brightness pump sources and high-power-handling passive components should be fabricated and utilized in the fiber laser systems, in addition to the advanced techniques for multiple nonlinear effects managements.

^{[2]}Ultrashort pulse propagation with complex modal interactions revealed new nonlinear dynamics and frequency conversion techniques such as cascaded Raman scattering [1] and supercontinuum generation by exploiting multiple nonlinear effects simultaneously [2,3].

^{[3]}

## Enhanced Nonlinear Effects

Indeed, the high confinement of the light in integrated waveguides allows for enhanced nonlinear effects.^{[1]}Such structures have ignited intensive research interests, as EIT produces enhanced transmission with an extremely strong dispersion, which shows great potentials for applications in slow light devices [25,26], optical buffers [27,28], ultrasensitive biosensing [29], and enhanced nonlinear effects [30].

^{[2]}Resonating structures such as ring resonators (RRs) experience enhanced nonlinear effects due to significant intensity buildup.

^{[3]}

## Account Nonlinear Effects

The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range.^{[1]}However, for heat transfer in rapid processes, heat transport on micro- and nanoscales, and heat transfer in materials with an internal structure (porous media and biological tissues), other models are required that take into account nonlinear effects, as well as temporal (memory) and spatial nonlocality.

^{[2]}The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range.

^{[3]}

## Mitigate Nonlinear Effects

The design of a microfluidic cell that mitigates nonlinear effects is presented, enabling enhanced diffusional effects and quasi-1D electrodeposition of patterns on the cathode.^{[1]}Assuming a wCDM model and equivalent scale cuts to mitigate nonlinear effects, this leads to $40\%$ increase in the figure of merit for the pair combinations of $\Omega_m$, $w$, and $\sigma_8$, and gains of $16\%$ in $\sigma_8$, $10\%$ in $\Omega_m$, and $12\%$ in $w$.

^{[2]}Simulation results indicate that the concave tapered structure can introduce high loss for high-order modes (HOMs) that is advantageous to achieve single-mode operation, whereas the convex tapered structure provides large effective mode area that can help to mitigate nonlinear effects.

^{[3]}

## Model Nonlinear Effects

Here, we develop and apply a new method to simultaneously model nonlinear effects of primary climate drivers, reconstructed tree diameter at breast height (DBH), and calendar year in generalized least squares models that account for the temporal autocorrelation inherent to each individual tree's growth.^{[1]}However, these methods tend not to outperform classical linear methods, leaving it an open question why this capacity to model nonlinear effects does not seem to result in better predictive capability.

^{[2]}However, these methods tend not to outperform classical linear methods, leaving it an open question why this capacity to model nonlinear effects does not seem to result in better predictive capability.

^{[3]}

## Potential Nonlinear Effects

We estimate panel data models with country and time fixed effects, and control for potential nonlinear effects of population aging on health expenditure.^{[1]}To depict the hyperspectral data, here a sturdy mixing model is implemented by employing various perfect spectral signatures mixture, which enhances the generally utilized linear mixture model (LMM) by inserting an extra term that describes the potential nonlinear effects (NEs), which are addressed as additive nonlinearities (NLs) those are disseminated without dense.

^{[2]}

## Minimize Nonlinear Effects

Optimal launch power is investigated to minimize nonlinear effects of transmission links.^{[1]}The paper makes various recommendations for experimental system identification procedures using linear structural models, which include developing empirical models for parameter shifts due to nonlinearities and using constant response tests to minimize nonlinear effects in the measured system response.

^{[2]}

## Geometric Nonlinear Effects

Two applications demonstrate the accuracy of the proposed numerical scheme and emphasize the importance of handling properly the geometric nonlinear effects into real engineering design.^{[1]}The geometric nonlinear effects were disregarded in these analyses.

^{[2]}

## Compensate Nonlinear Effects

In order to compensate nonlinear effects of piezoelectric actuators, a hysteresis operator is implemented.^{[1]}We proposed an extension of FlANN filter to compensate nonlinear effects in multi-bands CAP64 VLC system.

^{[2]}

## Consider Nonlinear Effects

Here we show that standard quantum mechanics actually allows for apparent high-order interference, if one considers nonlinear effects.^{[1]}It considers nonlinear effects of the machine, and determines the machine parameters such as the magnetic field distribution, flux linkage, electromagnetic torques, and flux density.

^{[2]}

## New Nonlinear Effects

Indeed, numerous new nonlinear effects have recently been observed including, for instance, Kerr beam self-cleaning, mode-locking by spatiotemporal filtering, or multimode parametric wave mixing, to name a few [1].^{[1]}Graded-index multimode optical fibers have recently attracted a renewed attention, thanks to the discovery of new nonlinear effects, such as Kerr beam self-cleaning.

^{[2]}

## Study Nonlinear Effects

We study nonlinear effects in synthetic space photonic topological insulators.^{[1]}In this work, a nonlinear transmission line model, which solves for the electromagnetic fields in the time domain, is coupled to a two-dimensional bulk plasma fluid model to study nonlinear effects in asymmetric cylindrical capacitive argon discharges.

^{[2]}

## Observed Nonlinear Effects

The PL exhibits a clear correlation with the observed nonlinear effects, which we attribute to the generation of excitons via degenerate and nondegenerate multiphoton absorption.^{[1]}Open aperture Z-scan results suggests that reverse saturable absorption is the predominant mechanism behind the observed nonlinear effects and it can be ascribed to enhanced triplet state population.

^{[2]}

## Enhancing Nonlinear Effects

Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing nonlinear effects and light-matter interactions in structured fibers.^{[1]}They exhibit intense and localized resonances that can be conveniently tuned in the near-infrared and are therefore ideal for enhancing nonlinear effects in this spectral range.

^{[2]}