Parametric Wave Interaction Research Articles

Controlled chaotic microwave generation under conditions of four-wave parametric interaction of surface spin waves

Controlled chaotic microwave generation under the conditions of four-wave parametric interaction of the surface spin waves has been experimentally studied in active resonance rings based on tangentially magnetized ferromagnetic films. It is shown that the chaotic microwave signal parameters can be effectively controlled.

Simulation of the random violation of the quasi-phase-matching condition in optical parametric process

The parametric interaction of light waves in a nonlinear photonic crystal (NPC) with the random violation of the quasi-phase-matching condition is considered. A model with correlated fluctuations of the width of adjacent domains is used which corresponds to NPCs fabricated, for example, by the repolarisation method. Both a numerical calculation algorithm and analytic stochastic approach taking into account the influence of fluctuations of the domain width are presented. The behaviour of the average intensity and dispersion of intensity fluctuations of parametrically interacting waves, including the strong energy exchange regime, is studied by the example of a LiNbO3 NPC. The obtained results can be used to estimate the required accuracy of manufacturing the nonlinear structure of the crystal.

Chaotic microwave self-generation in active rings based on ferromagnetic films

The phenomenon of chaotic microwave self-generation under conditions of a four-wave parametric spin wave interaction in active resonance rings based on ferromagnetic films has been studied for the first time. It is shown that microwave signals of various types—in particular, monochromatic, stationary soliton-like pulse trains, and dynamic chaos—can be generated by controlling the gain level in the active ring. Parameters characterizing the chaotic signal generated in the ring are determined.

Effects of ion temperature anisotropy on diffusion process in plasma with pump

On the basis of kinetic fluctuation theory, we consider the parametric interaction of lower and upper hybrid waves with ion-cyclotron oscillations in a plasma where the ion velocity distribution function is anisotropic. The turbulent diffusion coefficient is found to depend significantly on the ratio between the parallel and perpendicular ion temperatures. Our results can be of interest for the investigation of anomalous transport processes in space and laboratory plasma with ion temperature anisotropy.

Selection Theorem for Systems with Inheritance

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of natural selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t goes to infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of completely thin sets is introduced. Key words: Dynamics; Attractor; Evolution; Entropy; Natural selection

Inertial Alfvén-Wave-Driven Convective Cells in Low-Density Plasmas

The parametric interaction of inertial Alfven waves with large-scale convective cells in a low-density plasma is investigated. It is shown that, in plasmas where the Alfven velocity is comparable to or exceeds the speed of light, the parametric interaction is substantially suppressed. A compact expression for the optimal scale and instability growth rate of the fastest growing mode is obtained. The relevance of our theory to spacecraft measurements in the Earth’s ionosphere is discussed.

Periodically switched nonlinear structures for frequency conversion: theory and experimental demonstration

In this paper, we report on the analytical study of a first-order quasi-phase-matched structure based on a periodically switched nonlinearity. The general average equations describing parametric wave interaction for this structure are obtained. The theoretical results are then used to analyze the special case of a device based on a semiconductor Al/sub x/Ga/sub 1-x/As waveguide for efficient frequency doubling in the mid-infrared to the far-infrared range. The necessary conditions to obtain an optimal configuration are discussed in both continuous wave and femtosecond-pulse regimes. Our analysis indicates that the conversion efficiency obtained should significantly exceed the efficiency obtained with a periodically poled lithium niobate crystal at long wavelengths. Finally, we include the preliminary results of the experimental demonstration of a waveguide device based on alternating domains of GaAs and Al/sub 0.4/Ga/sub 0.6/As.

Consecutive Parametric Interactions of Light Waves with Nonmultiple Frequencies in Crystals with Irregular Poled Structure

A stochastic theory of quasi-phase-matched consecutive processes, which takes into account peculiarities of the method of creating a nonlinear lattice in crystals, is developed. The influence of aperiodicity of a certain type on the efficiency of the process of consecutive parametric interaction of light waves with nonmultiple frequencies in crystals with irregular poled structure is studied. It has been established that in aperiodically poled nonlinear crystals the regime of exponentially changing intensity of interacting waves can be implemented. A particular case of nondegenerate parametric amplification is also discussed.

Condensation in Hamiltonian parametric wave interaction.

In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states. This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the H theorem of entropy growth inherent to the random phase approximation approach. The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping. As a result, the lower the coherence of the initial state, the higher the coherence of the final state.

Quadratic Solitons

The experimental demonstration in 1995 of spatial soliton formation mediated by parametric wave interactions in crystals with quadratic nonlinearities, which had been theoretically predicted in the 1970s, opened a range of exciting new opportunities in the field of soliton science and its applications. For many years, second-order (or quadratic) nonlinearities had been associated only with the frequency conversion of laser light. A crucial step towards richer opportunities was the emergence of cascading, where cross-induced energy- and phase-shifts acquired by multiple light waves that parametrically interact in a material with a quadratic nonlinearity are exploited to perform all-optical operations on signals. To form a soliton, or in other words a self-sustained, localized, non-spreading light packet, such energy- and phase-shifts can also be used to dynamically counteract spreading caused by diffraction and by group-velocity dispersion.

Diffraction effects in the parametric interaction of acoustic waves: application to measurements of the nonlinearity parameter B/A in liquids.

This paper deals with diffraction effects related to the determination of nonlinearity parameters B/A in liquids using the parametric interaction. A diffraction model, based on plane wave expansions, is applied to weak nonlinear interactions between two ultrasonic waves propagating in an absorbing medium. A validation of the model has been carried out with an experiment performed using an optical interferometer. A method is proposed to measure nonlinearity parameters with the parametric interaction of two waves with a high frequency ratio. With respect to diffraction effects, the parametric interaction can then be identified with a phase modulation of the high frequency wave. A prototype, using the interaction of a 30-MHz frequency continuous wave with an acoustic pulse of central frequency 2.5 MHz, has been designed. The proposed method is validated by nonlinearity parameters measurements in well-known liquids (water and ethanol). The uncertainty on absolute measurements is discussed, and a relative method is proposed to increase the accuracy. This method enables measurements without any transducer calibration.

Parametric amplification of vortex waves in an acoustically active medium

The parametric interaction of acoustic waves with vortex waves in a gaseous medium is considered. It is shown that the parametric increment may become exponential in a thermodynamically nonequilibrium medium.

Multipulses of Nonlinearly Coupled Schrödinger Equations

The capacity of coupled nonlinear Schrödinger (NLS) equations to support multipulse solutions (multibump solitary-waves) is investigated. A detailed analysis is undertaken for a system of quadratically coupled equations that describe the phenomena of second harmonic generation and parametric wave interaction in non-centrosymmetric optical materials. Utilising the framework of homoclinic bifurcation theory, and employing a Lyapunov–Schmidt reduction method developed by Hale, Lin, and Sandstede, a novel mechanism for the generation of multipulses is identified, which arises from a resonant semi-simple eigenvalue configuration of the linearised steady-state equations. Conditions for the existence of multipulses, as well as a description of their geometry, are derived from the analysis.

Generation of circularly polarized radio waves within magnetic holes of the solar wind

The possibility of nonlinear interaction between Langmuir waves and ion–acoustic waves in the solar wind has received considerable interest in the last years. However, little attention has been paid to the possibility of nonlinear coupling between Langmuir waves and whistler waves in the interplanetary medium. Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations within magnetic holes of the solar wind, we develop a nonlinear three-wave theory describing the parametric interaction of Langmuir waves, electromagnetic whistler waves with either right- or left-hand circularly polarized electromagnetic waves. We suggest that the nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind.

Parametric interaction of magnetostatic waves with a nonstationary local pump

A solution is obtained for the general problem of the nonstationary interaction of backward volume magnetostatic waves in films of yttrium-iron garnet with local parametric pumping. In the case of a large pump region, l≫λ, where λ is the wavelength of the backward volume magnetostatic waves, the problem reduces to a system of truncated equations for two packets of counter propagating waves. In the opposite case, l<λ, the exact problem of parametric interactions of the eigenmodes of a ferrite film (both counterpropagating and in the same direction) is solved numerically. Both cases are studied experimentally and good qualitative and quantitative agreement is obtained with the theory. For the first time, the reversal of a wave front and the time reversal of the shape of backward volume magnetostatic wave pulses are observed and a change in the propagation time for the peak of the signal pulse and a reduction in its width owing to pumping are recorded. Two operating regimes are identified for a nonstationary parametric backward volume magnetostatic wave amplifier with local pumping, which differ in the ratio of the duration of the pump pulse to the transit time for the wave through the local pump region, and the effect of the parametric excitation of two-dimensional spin waves on the interaction of backward volume magnetostatic waves with a local nonstationary parametric pump is determined.

Parametric interaction of volume magnetostatic waves in a ferrite film with spatiotemporal modulation of the magnetic field

Effects of the resonant Bragg scattering of magnetostatic backward volume waves on the periodic structure of a conductive meander pattern with an alternating current are analyzed theoretically and compared with experiment. It is shown that unlike a static grating, a dynamic grating causes a frequency shift of the scattered wave. It is proposed that this phenomenon be utilized for effective control of the intermodal conversion of magnetostatic waves.

Parametric interaction of surface waves guided by a plasma layer

We study the linear stage of the parametric instability of high-frequency surface waves guided by a homogeneous plasma layer on a metallic substrate when a TM-polarized plane electromagnetic wave is incident on the layer. The instability growth rate and the threshold value of the pumping wave amplitude are determined. It is shown that the instability can be thresholdless in a certain range of permittivities and thicknesses of the layer.

Frequency conversion by the parametric interaction of space-charge waves in thin-film semiconductor structures with negative differential conductivity

Frequency conversion by the parametric interaction of space-charge waves in thin-film semiconductor structures with negative differential conductivity

Walking Solitons in Quadratic Nonlinear Media.

We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications.

Elastic wave interactions as a principle of vibration measurement

It is known that ultrasound can be used to measure the constant in time deformations and residual stresses, through the acoustoelasticity effect. The method presented here is different from this principle. It is based on the non-resonant parametric interaction of elastic waves and enables measurement of the dynamic deformation in elastic media. The aim of this work is to investigate the interaction of waves in non-linear elastic media with the deformation fields in parametric approximation and to create a method that permits observation (in three-dimensions) of the dynamic stress-state of the opaque elements of a structure. In particular, interest in the solution of this problem arises for high-frequency non-stationary loading on the structure, when it is impossible to determine the internal stress-state of the elastic body by measurement of the vibration of its surface. The solution to this is found by using ultrasonic waves as a type of transducer that can freely penetrate the elastic body in the necessary direction.