Higher-order Nonlinear Effects Research Articles

The higher-order nonlinearity and parametric effects on dust-ion-acoustic shock waves

In the case of obliquely propagated small-amplitude shock waves, in this study, we investigate the impacts of higher-order nonlinearity as well as various parameters (such as dust concentrations, viscosity, trapping parameters, etc) on the shock wave structures. The considered magnetized plasma system consists of three components, such as inertial positive ions (mobile), trapped electrons, and immobile negatively charged dust particles. The modified Burgers equation with a dominating dissipative term (in which the viscous effect is significant) is derived initially to examine the lower-order nonlinear and dissipative effects, and then, to the best of our knowledge, the modified Burgers-type linear inhomogeneous equation is derived for the first time to observe the higher-order nonlinear effects on shock waves while the plasma contains trapped electrons. The reductive perturbation method is used for the derivation of the equations, whereas the Abel’s theorem and the method of variation of parameters are used for adding the higher-order effect. From the theoretical investigation, we observe that the higher-order nonlinearity has an increasing effect on the shock amplitude. Furthermore, the viscosity and dust concentration increase the shock width and the phase speed, respectively.

Nth-order smooth positon and breather-positon solutions for the generalized integrable discrete nonlinear Schrödinger equation

In this paper, we investigate the smooth positon and breather-positon solutions of the generalized integrable discrete nonlinear Schrödinger (NLS) equation by the degenerate Darboux transformation (DT). Starting from the zero seed solution, the Nth-order smooth positon solutions are obtained by degenerate DT. The breather solutions including Akhmediev breather, Kuznetsov-Ma breather and space-time periodic breather are derived from the nonzero seed solution. Then the breather-positon solutions are constructed by gradual Taylor series expansion of the eigenfunctions in breather solutions. We study the effect of the coefficient of nonlinear term on these discrete smooth positon solutions and breather-positon solutions, which demonstrates that the interacting region of soliton-positon and breather-positon are highly compressed by higher-order nonlinear effects, but the distance between the two positons has an opposite effect in two waveforms.

Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects

We study the propagation dynamics of extremely short light pulses in an optical fiber medium exhibiting a plethora of higher-order dispersive and nonlinear effects of different nature. The wave propagation in such nonlinear media is described by an extended nonlinear Schrö dinger equation incorporating both even and odd higher-order terms. We introduce an appropriate nonlinear equation which enables us to achieve analytical shape-preserved and periodic wave solutions for the model. A new dark solitary wave is identified for the first time in the presence of all physical processes. In addition, we show that moving fronts or optical shock-type soliton solutions exist for the considered model. The periodic wave solutions are also found together with the parametric conditions for their existence. Results in this study may be useful for experimental realization of shape-preserved pulses in optical fibers and further understanding of their optical transmission properties.

100 kW ultra high power fiber laser

Based on the self-developed non-photodarkening large mode field gain fiber and the 976 nm wavelength-locked high-power and high-brightness pump source, and using the secondary fiber power combining technology, a high-performance 100kW fiber laser in China was built, realizing high-order mode and non-linear effect suppression. The maximum output power of the laser can reach 101.65 kW, the center wavelength is 1080 ± 5 nm, the spectral bandwidth is (3dB) 5-8 nm, the output fiber core diameter is 400µm, the beam quality BPP is 19.28 mm*mrad, and the laser power instability is ±1.1%. Its laser non-destructive cladding stripping technology, distortion-free taper technology, inclined multi-die beam combining technology and circular inner cladding modification design have all reached the international advanced level.

Study on the regulation of amplitude for the optical soliton through nonlinear effects in the optical communication system

Optical communication system is a kind of communication system using the light wave as the carrier. It has been widely used in recent years with the advantages of the long distance. Optical solitons have some merits for high stability, amenable to generate and low cost, it is an ideal carrier of optical communication system. In this paper, the regulation of pulse characteristics of the optical soliton is studied theoretically. The influence of high-order dispersion and high-order nonlinear effects on the amplitude, shape and other transmission characteristics of the optical soliton is studied by using the bilinear method with the high-order variable coefficient nonlinear Schrödinger (NLS) equation in the nonuniform fibers, and the regulation problems such as the maintenance and excitation of the optical soliton are analyzed. The waveform and amplitude control of the optical soliton and the change of optical soliton characteristics with the dispersion management are studied profoundly, and the nonlinear dynamic processes in their respective intracavity are analyzed. A feasible scheme for avoiding and utilizing the optical soliton is proposed, which has the significance for the investigation of the parameter regulation and dynamic control of the optical soliton in practical inhomogeneous optical fiber communication systems.

Strong third-and higher-order nonlinear optical studies on femtosecond laser ablated Germanium metalloid nanoparticle colloid in the wide spectral domain (450–1500 nm)

Wide spectral region higher-order optical nonlinearities are hereby reported for ultrashort pulsed laser ablated germanium nanoparticle (Ge NPs) colloidal solutions. The Ge NPs colloids are studied for optical nonlinearities under a wide spectral domain (∼450–1550 nm) utilizing the femtosecond laser (120 fs, 1 kHz) pulses. The results of the nonlinear absorption indicate a strong dominance of multi-photon absorption phenomena (two-, three- and four-photon absorptions), involving band-to-band and defect induced energies of the quantum confined Ge NPs. The intensity-dependent [(4–8) × 1015 W m−2] nonlinear absorption exhibits a monotonically decremental trend with the increase in excitation intensity, suggesting the involvement of higher-order nonlinear optical effects. Moreover, the obtained presented results also depict strong nonlinear contribution evidenced by two orders of higher magnitude nonlinear refraction in the infrared (IR) region, 1000–1550 nm. The enhanced optical nonlinearities in the IR region propound the capabilities of these Ge NPs as a potential substitute for silicon in IR photonics-related applications.

Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation

In this paper, a Lakshmanan-Porsezian-Daniel equation, which describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction, is investigated. With respect to the coherent amplitude of the spin deviation operator for the ferromagnetic spin chain in the coherent state, we construct a modified generalized Darboux transformation in which the multiple spectral parameters are involved, and the Nth-order semirational solutions in the determinant form, where N is a positive integer. Then, we obtain and analyze three types of the semirational solutions: Type-I degenerate soliton solutions which describe the degenerate solitons; Type-II degenerate soliton solutions which describe the interaction among the solitons and degenerate solitons; Type-III degenerate soliton solutions which describe the bound states among a set of the degenerate solitons. Generation conditions of the above semirational solutions are discussed. When the multiple solitons have the equal velocity, bound-state solitons are also constructed. Influence of β on the type-I degenerate solitons are graphically illustrated, where β denotes the strength of the higher-order linear and nonlinear effects in the equation.

Raman-induced frequency shift of pure quartic solitons in optical fiber with quartic dispersion.

We investigate the impact of Raman scattering on pure quartic solitons (PQSs) in an optical fiber with quartic dispersion. An analytical expression of the Raman-induced frequency shift (RIFS) of a PQS is obtained by using the variational approach with the Gaussian function ansatz. We find the RIFS of a PQS is inversely proportional to the sixth power of pulse width, when the fiber is short enough. The RIFS of a PQS is more sensitive to the pulse width, compared with that of a conventional soliton which is inversely proportional to the fourth power of pulse width. The theoretical predictions show good agreement with numerical results. In addition, we also discuss the RIFS of the other three typical pulses with the same peak power and pulse width as the PQS. These results provide a thorough understanding of the role of higher-order nonlinear effects on the propagation dynamics of PQSs.

Dust Acoustic Dressed Solitons in Jovian Magnetosphere

In this investigation, the evolution of dust acoustic solitons (DASs) and dust acoustic dressed solitons (DADSs) have been examined in the Jovian magnetosphere. A five components plasma in which positive dust grains interact with solar wind protons, superthermally distributed electrons, ions as well as solar wind electrons is considered to explore the formation of different kinds of nonlinear structures in the Jovian magnetosphere. The Korteweg-de Vries (KdV) and inhomogenous KdV-type equations encompassing the higher-order (HO) nonlinear and dispersion (N&D) effects are derived by employing the reductive perturbation technique (RPT). With the incorporation of HO effects, a new kind of DADSs are evolved. The influence of various plasma parameters viz., superthermality of ions as well as electrons, temperature, and concentration of different species on the salient features of DASs and DADSs has been encapsulated. The findings of this work may be useful to elucidate the formation of nonlinear dust acoustic coherent structures in the Jovian magnetosphere.

Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

In the present study, the quintic-septic nonlinear modulation of a longitudinal wave propagating to contribute the dispersive and higher-order nonlinear effects in a generalized cubically nonlinear elastic medium is considered. In recent work, for the modulation of a longitudinal wave, a cubic nonlinear Schrödinger equation with a third-order dispersive term is obtained by using a multi-scale expansion of quasi-monochromatic wave solutions. The third- quintic-septic longitudinal wave, by choosing specific values of material constants and wave number for which some coefficients of nonlinear terms are disappeared. In this case, a new perturbation expansion is needed to balance nonlinear effects with dispersive effects. As a result, a quintic-septic nonlinear Schrödinger equation with a third-order dispersion term is obtained as a new model that balances quintic-septic nonlinearity with a third-order dispersion term.

Analytical study of perturbed chirped solitons with triple-power law nonlinearity

In this work, a novel class of analytical chirped soliton solutions of the triple-power law nonlinear Schrödinger equation with perturbations are constructed. This model is used to describe the propagation of light waves in a nonlinear medium with the higher-order nonlinear optical effects including the triple-power law nonlinearity, self-frequency shift and self-steepening. The results shown that exact chirped plane wave, bright and kink solitons can exist in this physical setting when the degree of nonlinearity satisfy 2m=3n.

Multiscale numerical tool for studying nonlinear dynamics in solids induced by strong laser pulses.

Strong-field phenomena in solids exhibit extreme high-order nonlinear optical effects, which have triggered many theoretical and experimental investigations. However, there is still a lack of highly efficient numerical tools to simulate the relevant phenomena. In this paper, a versatile multiscale numerical tool set is developed for studying high-order nonlinear optical effects in solids, generated by ultrafast strong laser pulses. This tool is based on the tight-binding model approximation of the crystal structure, the related parameters of which are obtained from the density functional theory calculations. And the nonlinear effects are explored by solving the Maxwell equationscoupled with the semiconductor Bloch equations. Our numerical tool can provide not only basic electronic structures and optical responses of the crystal, but also the real-time evolution of the macroscopic electromagnetic fields and the current density. The high-performance parallel computing and the interpolation method in our tool make it possible to study the strong-field nonlinear responses and propagation effects on a large spatial and temporal scale. Finally, three theoretical or experimental results published recently are satisfactorily reproduced, showing a good performance of the current toolbox.

Nth-order smooth positon and breather-positon solutions of a generalized nonlinear Schrödinger equation

In this paper, we investigate smooth positon and breather-positon solutions of a generalized nonlinear Schrödinger (GNLS) equation which contains higher-order nonlinear effects. With the help of generalized Darboux transformation (GDT) method, we construct Nth-order smooth positon solutions of GNLS equation. We study the effect of higher-order nonlinear terms on these solutions. Our investigations show that the positon solutions are highly compressed by higher-order nonlinear effects. The direction of positons also get changed. We also derive Nth-order breather-positon (B-P) solution with the help of GDT. We show that these B-Ps are well compressed by the effect of higher-order nonlinear terms, but the period of B-P solution is not affected as in the breather solution case.

Transient Higgs oscillations and high-order nonlinear light-Higgs coupling in a terahertz wave driven NbN superconductor

We study the nonlinear optical response in a superconducting NbN thin film with a strong terahertz (THz) wave. In. addition to the expected third-harmonic generation, we observe a transient oscillation which softens in frequency with temperature increasing towards the superconducting transition temperature ${T}_{c}$. We identify this feature as transient Higgs oscillation. To verify this proposal, we introduce a time-frequency resolved technique, a spectrogram for visualizing the THz spectrum. The dynamic decaying behavior of the oscillation is observed, which is consistent with the theoretical expectation of intrinsic Higgs oscillation. Moreover, we observe a higher-order nonlinear optics effect, i.e., fifth-harmonic generation, which we assign to the higher-order coupling between the Higgs mode and electromagnetic field.

Influence of higher-order nonlinear effects on optical solitons of the complex Swift-Hohenberg model in the mode-locked fiber laser

The complex Swift-Hohenberg equation (CSHE) has been widely studied in recent years. It is a more real model in the mode-locked fiber laser with the saturable absorber due to the addition of the diffraction term compared with the complex Ginzburg-Landau equation. In this work, the dynamics process of the traditional soliton and M−type soliton pulses in the mode-locked fiber laser is demonstrated based on the CSHE model with higher-order nonlinear effects. The results show that with the increase of the small signal gain coefficient, the number of soliton molecules adds gradually. Under the same transmission conditions, the transmission of M−type solitons in the laser are more stable than that of single solitons. By adding the self-steepening effect, it can be found that the time-domain shift due to higher-order dispersion effects is compensated. The self-frequency shift effect caused by the Raman scattering can produce not only time domain shift, but also frequency domain shift. Moreover, the addition of higher-order diffraction term can describe the spectral response of multiple peaks, and makes the pulse spectrum show the asymmetric propagation in the transmission process. Finally, the increase of the length of the single-mode fiber on the right side of the gain fiber in the optical circuit will not only shift the center position of the output pulse backward, but also make the pulse energy show a ladder type downward trend.

Integrability and multisoliton solutions of the reverse space and/or time nonlocal Fokas–Lenells equation

This paper studies reverse space and/or time nonlocal Fokas–Lenells (FL) equation, which describes the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered, by Hirota bilinear method. Firstly, we construct variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations. Secondly, the multisoliton and quasi-periodic solutions of the reverse space nonlocal FL equation are derived through Hirota bilinear method, and the soliton solutions of reverse time and reverse space-time nonlocal FL equations are given through variable transformations. Also, dynamical behaviors of the multisoliton solutions are discussed in detail by analyzing their wave structures. Thirdly, asymptotic analysis of two- and three-soliton solutions of reverse space nonlocal FL equation is used to investigate the elastic interaction and inelastic interaction. Finally, the infinite conservation laws of three types of nonlocal FL equations are found by using their lax pairs. The results obtained in this paper possess new properties that different from the ones for FL equation, which are useful in exploring novel physical phenomena of nonlocal systems in nonlinear media.

Higher-order nonlinear and dispersive effects on dust-ion-acoustic solitary waves in magnetized dusty plasmas

We deal with the theoretical investigation of the higher-order nonlinear and dispersive effects on the basic features of dust-ion-acoustic (DIA) solitary waves in a magnetized dusty plasma. Also, we examine the impacts of the external magnetic field and adiabaticity, obliquity, etc. in changing solitary wave structures. The waves of small but finite amplitude propagate obliquely through the dusty plasma where the system comprises adiabatic positively charged ions (mobile), negatively charged trapped light ions, Maxwellian distributed electrons and stationary dust particles with arbitrary charges. The reductive perturbation method is extensively used for incorporating the higher-order terms into the modified Korteweg-de Vries (mKdV) equation, and the procedure yields an inhomogeneous mKdV-type equation. It is observed that the inclusion of higher-order nonlinear and dispersion effects increases the wave’s amplitude and width. Furthermore, in the presence of higher-order effects, the magnetic field and adiabaticity have decreasing and increasing effects respectively on the wave features. It is expected that the results will be useful to describe higher-order effects on DIA solitary waves.

Evolution of Airy-Gaussian pulses in photonic crystal fiber with two zero-dispersion wavelengths

We numerically investigate the evolution of Airy-Gaussian (AiG) pulses in photonic crystal fiber with two zero-dispersion wavelengths. Firstly, in the absence of higher-order nonlinear effects, the effects of three essential parameters of AiG pulses (truncation coefficient, distribution factor, and initial chirp) on the pulse evolution are studied in detail. The results indicate that initial AiG pump pulses with a small truncation coefficient, small distribution factor, and positive chirp are beneficial for obtaining a wider supercontinuum spectrum. Moreover, we further take stimulated Raman scattering (SRS) and self-steepening (SS) effects into account, and find that SRS greatly broadens the output spectrum when AiG pulses with a small distribution factor (χ0 = 0.1), however, it also leads to obvious spectrum collapse and the collapse will be reduced to a certain extent due to SS.

Tip-enhanced two-photon-excited fluorescence of monolayer MoS2

High-order nonlinearity enables larger signal enhancements in two-photon spectroscopy compared to one-photon spectroscopy, which is important for conducting photoluminescence measurements at the single-molecule level. Herein, the two-photon-excited fluorescence (2pF) of monolayer MoS2 in various tip-enhanced spectroscopy configurations was theoretically investigated using the finite-difference time-domain method. Large enhancement factor for 2pF on the order of 105 was achieved by optimizing the radius and cone angle of the tip together with the distance between the tip and MoS2 film. The enhancement factor for 2pF is 40 times as much as that for one-photon-excited fluorescence because of the high-order nonlinear effect. Radiative and nonradiative decay rates were further calculated for determining quantum yields and elucidating the 2pF emission mechanism. These results provide a comprehensive understanding of 2pF behavior, which is highly useful for the design of MoS2-based optoelectronic devices.

On the construction of the general solution of the Fokas–Lenells equation

In this communication we consider the Fokas–Lenells equation which describes the propagation of the nonlinear optical pulses in mono mode fibers when higher-order nonlinear effects are taken into consideration. Based on the traveling wave ansatz, we construct the general solution for the envelope of the wave packet in terms of the Jacobi elliptic sine function. The special case of solitary wave solutions is shown to emerge when the arbitrary constant in the general solution is set to zero. Analytical forms of the solutions are studied for different values of parameters and qualitative features of the solutions are also described.