Two-wave Interaction Research Articles

Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation

Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation

Two-wave interaction solutions of perturbation and CKdVE integrability for (2+1)-D CDGKS equation

By the Hirota bilinear method, some new interaction solutions with the complex perturbation for CDGKS equation are obtained. Meanwhile, with the help of the classical nonlinear KdV equation, many new exact solutions of CDGKS equation are derived through the CKdVE method, since it satisfies the CKdVE solvability. Two typical examples also show the local geometric characteristics of the parameter perturbation of these exact solutions.

Weakly nonlinear models of stochastic wave propagation in two-layer hydrodynamic systems

The paper discusses three-dimensional models of the propagation of stochastic internal waves in hydrodynamic systems: ’half-space - half-space’, ’half-space - layer with rigid lid’, and ’layer with solid bottom - layer with rigid lid’. In constructing the models, the layers are considered to be ideal fluids separated by a contact surface. The main objective of the modeling is to obtain a dynamic equation for the stochastic amplitude of surface waves. A comparative analysis of the obtained results has been conducted. In order to control the contribution of nonlinear terms, a dimensionless non-numerical parameter has been introduced. The models are distinguished by boundary conditions that determine the general form of solutions. As a result, a dynamic equation for the stochastic amplitude of internal waves has been derived. After ensemble averaging of the amplitudes, the dynamic equation is formulated in integral form using Fourier-Stieltjes integrals. The dynamic equation reveals two-wave and three-wave interactions, as well as the contribution of dispersion to wave dynamics. An investigation of the boundary case of the transition of internal waves in the ’half-space - half-space’ system to surface waves in the absence of an upper liquid layer confirms the validity of the results.

Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schrödinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1$$\\end{document}, k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_2$$\\end{document}) and of the spectral index κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} values, leads to enhance MI of the interacting wave pair. To the best of our knowledge, the dynamics of two co-propagating wavepackets in a plasma described by a fluid model with κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-distributed electrons is investigated thoroughly with respect to their MI properties as a function of κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} for the first time, in the framework of an asymmetric CNLS system whose coefficients present no obvious symmetries for arbitrary k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1$$\\end{document} and k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_2$$\\end{document}. Although we have focused on electrostatic wavepacket propagation in non-thermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where MI is relevant.

Взаємодія плоских пружних хвиль. Врахування квадратичної та кубічної нелінійності

The interaction of elastic plane harmonic waves in the material, the nonlinear properties of which are described by the elastic potential of Murnaghan, is investigated theoretically. The displacement vector is depended of only one spatial variable and time, a record of the complete system of equations for plane waves moves along the abscissa axis is recorded and used. The interaction of longitudinal waves with a separate considering cubic nonlinearity is investigated. On the basis of the cubic equation of motion, the interaction of four harmonic waves is studied. The method of slowly variable amplitudes is used. Firstly the two-wave interaction is investigated, then the interaction of four waves is described. Shorten and evolutionary equations are obtained, the first integrals of these equations and the record of the law of conservation for a set of four interacting waves are obtained. An analogy is made between the triplets studied when taking into account the interaction of three waves and the triplets investigated in the case under consideration, taking into account the four-wave interaction, quadruplets.

Solutions of the Two-Wave Interactions in Quadratic Nonlinear Media

In this paper, we propose a reliable treatment for studying the two-wave (symbiotic) solitons of interactions in nonlinear quadratic media. We investigate the Schauder’s fixed point theorem for proving the existence theorem. Additionally, the uniqueness solution for this system is proved. Also, a highly accurate approximate solution is presented via an iteration algorithm.

Fractional thermal transport and twisted light induced by an optical two-wave mixing in single-wall carbon nanotubes

Photothermally-activated energy transfer effects were analyzed by a vectorial two-wave mixing technique. Single-wall carbon nanotubes in thin film form were experimentally evaluated by nanosecond pulses at 532 nm wavelength. Significant changes in the heat conduction derived by equivalent incident energy from single-beam and two-wave optical interactions in the sample were promoted by different participation of quantum and nonlinear optical phenomena. Fractional analysis was carried out for studying the thermal behavior exhibited by the sample in a nonlinear regime. The fractional dynamics in the thermal transport was employed for describing the interferometric effects that correspond to optical phase-changes induced in nanoscale systems. This report can be a base for future research related to twisted light and photothermally-controlled functions.

N-soliton solutions for the nonlocal two-wave interaction system via the Riemann–Hilbert method** Project supported by the National Natural Science Foundation of China (Grant Nos. 11331008 and 11522112).

In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann–Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann–Hilbert problem in both the regular and non-regular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover, the dynamical behaviour of the single-soliton solution is shown graphically.

Experimental and theoretical investigations of the gain dependence at two-wave interaction on the thickness and orientation angle of the Bi12GeO20 crystal

Experimental studies of the dependence of object wave gain at two-wave interaction on the effective thickness of cubic photorefractive optically active crystal Bi12GeO20 were performed using only one -cut crystal sample. It is shown that the obtained experimental results can be satisfactorily theoretically interpreted taking into account the inverse piezoelectric and the photo-elastic effects in addition to the traditionally considered electro-optical one.

Injection of 40 kHz-modulated electron beam from the satellite: I. Beam-plasma interaction near the linear stability boundary

Anomalous wave effects and stimulated charged particle fluxes were registered during 40kHz-modulated electron beam injection in active space experiment carried out in a double satellite system. To explain these effects, the beam-plasma instability for a two-wave longitudinal interaction has been considered. The growth of instability depends on the frequency and wavenumber detunings between these longitudinal waves one of them is a slow beam mode with negative or zero wave energy defined near the linear stability boundary.

Dynamically Configurable Nonlinear Optical Switching Based on Vertically Aligned Carbon Nanotubes

The modification of the third order nonlinear optical response exhibited by vertically aligned carbon nanotubes in two-wave mixing interactions was analyzed. All-optical switching effects were explored by using a vectorial optical Kerr gate with nanosecond pulses at 532 nm wavelength of excitation. The samples were prepared by a spray pyrolysis method. Morphological and structural characterization of the samples was conducted by Scanning Electron Microscopy, Transmission Electron Microscopy and Raman Spectroscopy studies. Important structural changes dependent on the temperature employed for the preparation of the carbon nanotubes were observed. It was highlighted a remarkable influence of nonlinear energy transference in spatially-resolved optical processes for designing ultrafast low-dimensional devices.

Optoelectronic switching in a microstructure containing Au nanoparticles

Photoconduction and nonlinear optical refraction effects exhibited by an array of separated Au microchannels are reported. The samples were constituted by Au thin solid films containing Au nanoparticles prepared by an evaporation method. The photoconductivity of the sample was measured with continuous illumination at 532 nm wavelength with 1 W average power. A vectorial two-wave interaction allowed us to explore the optical Kerr effect exhibited at 532 nm wavelength and 1 ns pulse duration. Z-scan experiments performed in a comparative Au thin solid film pointed out a saturated optical absorption as a dominant physical mechanism that originates the optical nonlinearity at 1064 nm wavelength with 150 ps pulses. The third-order optical nonlinearities measured in the studied cases with ps and ns pulses were estimated to be about = 10−10 esu. Microscopy observations were carried out to describe the morphology that is responsible for the noticeable optical Kerr effect. The optoelectronic switching behavior exhibited by the studied array was analyzed.

Using optical PT-symmetry for switching applications

This work introduces a new class of PT-symmetry grating assisted devices for switching or modulation applications. Their operation is based on a four-wave interaction, thus marking a step forward in the development of PT-symmetry devices which currently are essentially based on two-wave interactions. A remarkable feature of the new structure is that all its properties also hold in the case of imperfect PT-symmetry operation, corresponding to the important practical case of fixed losses.

Darboux transformation and dark rogue wave states arising from two-wave resonance interaction

Abstract Exact rogue wave solutions of the long wave–short wave resonance equation are obtained via Darboux transformations. Compared to the real long-wave field which always features a single hump structure, the short-wave field can be manifested as bright rogue wave, intermediate rogue wave, or dark rogue wave, depending on the subtle nonlinearity driven by the long-wave field.

Photoluminescent logic gate controlled by the optical Kerr effect exhibited by porous silicon

Abstract The magnitude of the third order optical susceptibility exhibited by porous silicon monolayers was measured by a non-degenerated vectorial two-wave interaction. Optical irradiations at 488 nm and 532 nm wavelengths were employed to carry out the nonlinear optical experiments. Compared to bulk silicon material, a noticeable enhancement in the third order nonlinear optical response was identified. Photoluminescence and photoconductive properties were evaluated for the two studied wavelengths. The photoluminescent logic gate function AND was experimentally demonstrated using as a control a reflective optical Kerr gate configuration. A perceptible contribution for the third order optical nonlinearities seems to be related to the optical Kerr effect originated by excited states population. A two-level model was considered in order to describe the observed optical behavior.

Identification of inhomogenous optical absorptive response by chaotic photonic signals in Au nanoparticles

A chaotic circuit allows us to identify with a high sensitivity the optical absorption associated with a highly transparent sample with Au nanoparticles embedded in a TiO2 thin film prepared by a sol–gel method. The measurements are based on a comparison of the correlation between a controlled optical irradiance that propagates through different zones of the sample. Nanosecond nonlinear optical measurements were obtained by monitoring the transmittance and the amplitude modification for the vectorial components of the electric fields in a two-wave mixing interaction. In addition, we theoretically study chaotic physical behavior exhibited by optical signals under nonlinear optical absorption. Our numerical results point out that small intensity fluctuations related to excitations of the absorptive nonlinearity can be described using a simple fractal model. Potential applications for developing sensors and instrumentation of the optical response of advanced materials are contemplated.

Engineering the optical and mechanical properties exhibited by a titanium dioxide thin film with gold nanoparticles

Thermo-optic and electrostrictive contributions to the nonlinear refractive index were observed in a titanium dioxide thin film with embedded gold nanoparticles. A sol–gel method was employed for preparing thin solid film samples. The nanosecond nonlinear optical properties and the Young’s modulus parameter were changed by shifting the optical absorption band associated with the localized surface plasmon of resonance of the gold nanoparticles with platinum. The third order nonlinear optical phenomena exhibited by the sample were induced by the second harmonic of a Nd-YAG laser with 532 nm wavelength; the nonlinear optical measurements were obtained by monitoring the transmittance and the amplitude modification for the vectorial components of the electric fields in a two-wave interaction. Optical evaluations were confirmed considering a straightforward measurement of the change in the refractive index of the sample when the sample was located in a Michelson interferometer.

Electron cyclotron maser based on the combination two-wave resonance

A mechanism of a combination two-wave cyclotron interaction between an electron beam and the forward/backward components of a far-from-cutoff standing wave is analyzed. This regime can be promising for the realization of high-power continuous-wave electron cyclotron masers operating in the THz frequency range.

Participation of the Third Order Optical Nonlinearities in Nanostructured Silver Doped Zinc Oxide Thin Solid Films

We report the transmittance modulation of optical signals in a nanocomposite integrated by two different silver doped zinc oxide thin solid films. An ultrasonic spray pyrolysis approach was employed for the preparation of the samples. Measurements of the third‐order nonlinear optical response at a nonresonant 532 nm wavelength of excitation were performed using a vectorial two‐wave mixing. It seems that the separated contribution of the optical nonlinearity associated with each film noticeable differs in the resulting nonlinear effects with respect to the additive response exhibited by the bilayer system. An enhancement of the optical Kerr nonlinearity is predicted for prime number arrays of the studied nanoclusters in a two‐wave interaction. We consider that the nanostructured morphology of the thin solid films originates a strong modification of the third‐order optical phenomena exhibited by multilayer films based on zinc oxide.

Effect of finite-amplitude acoustic wave nonlinear interaction on farfield directivity of sound source

The acoustic radiation pressure expression of a multi-frequency sound source is obtained on the basis of the Fenlon theory. Then using the solution method of a monochromatic source harmonic wave directivity, farfield directivity of second-order approximate is obtained in the case of the dual-frequency sound source interaction. Subsequently, the effect of two-wave interaction on the farfield of first-order and second-order wave of either wave is studied and discussed when the initial radiation pressures and frequencies are different. The conclusion is that there are some different effects of sound wave interaction on the farfield directivity of a sound source, when the relative initial radiation pressure and frequency between the sound waves is changed.