Three-wave Interaction Research Articles

Quantum mechanical rotations, information transfer and decoherence in the converter limit of parametric processes

In classical three-wave interaction there is a regime where only the phases move but no energy is exchanged. This is strictly valid for classical trajectories with sharp amplitudes and phases. Quantum mechanically, such a phase motion regime can be realized only approximately if all three waves start in coherent states because the states deform due to their initial uncertainties during rotation. In the limit of a strong signal or idler wave, what amounts to frequency conversion, we show that exact rotations of coherent states become possible. This completes our understanding of three-wave interaction. Different initial quantum states are exchanged periodically if the strong wave is treated classically and undepleted. This limit is investigated by numerical diagonalization of the exact Hamiltonian via nonclassical states in the pump and coherent states in the signal and idler. Classical phase motion turns out to be very helpful to understand the strong demands for the converter limit. In the converter, we consider the impurity of the two modes and show that the coherent state in one mode, which enables the no-energy transfer regime, has no influence on the impurity of the other wave and can be substituted by a vacuum state. Thus, the impurity in such a regime behaves exactly as under simple one-photon losses although the energy can be held constant. The different rotations are illustrated by calculating the Wigner functions via classical trajectories. In addition, we also consider the equivalent emission from a prepared atomic system (squeezed atoms) into one mode.

Three-wave interaction in dissipative systems: a new way towards secondary instabilities

We have identified a new mechanism of wave destabilization in nonlinear dissipative systems. This mechanism, which differs from the usual scheme of two complex Ginzburg–Landau equations, is associated with a three-wave interaction (TWI) process, in close analogy with nonlinear optics and plasma physics. We develop a paradigm from which we derive the wave number and threshold of the secondary instability. Numerically, we obtain a good agreement with the theoretical predictions. Moreover, we numerically investigate a model which describes a real experiment and exhibits a regime of parameter where this mechanism is involved.

Pattern formation in two-frequency forced parametric waves.

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with two commensurate frequencies. The spatiotemporal behavior of four qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different three-wave resonant interactions. They occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by four-wave interactions that arise when symmetry constraints rule out three-wave resonances.

Influence of external density fluctuations on parametric 3-wave interaction

Recent satellite observations seem to invalidate the classical scenario of Langmuir turbulence. Among the possible candidates which may play an important role to be taken into account are external density fluctuations. Parametric three-wave interaction is studied in the presence of quasi-monochromatic large-scale and low-frequency density fluctuations.

Frequency Spectrum of Plasma-Filled Free-Electron Laser Pumped by Electromagnetic Wave

The frequency spectrum of free-electron laser pumped by electromagnetic wave with magnetized and unmagnetized background plasma is analyzed by the theory of three-wave interaction and PIC simulation, respectively. The frequencies of PIC simulation are in agreement with the results of the three-wave interaction theory. The results show that the frequency spectrum is very plentiful.

The su q(2) algebra in the off-diagonal basis and applications to quantum optics

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the suq(2) algebra. The corresponding matrix elements of finite rotations (the q-deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate suq(2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques.

Nonlinear excitation of the second harmonic in a semiconductor superlattice placed into a magnetic field

The nonlinear interaction of waves in a periodic structure placed into a magnetic field is considered. The structure is comprised of alternate semiconducting and insulating layers. The three-wave interaction technique is applied to studying the nonlinear processes. It is shown that nonlinear phenomena in media with translational symmetry and in homogeneous media differ. Conditions for the resonant interaction between the first and second harmonics are analyzed. It is found that the second harmonic is generated when the interacting first spatial harmonics both co-and counterpropagate, which is possible only in periodic structures. Resonance events improving the generation efficiency are discussed.

A Simulation Code for Tempo-Spatial Analysis of Three-Wave Interaction with Ultrashort- and Ultrahigh-Intensity Laser Pulses

We have developed a simulation code that can be used for tempo-spatial analysis of three-wave interaction with ultrashort- and ultrahigh-intensity laser pulses. The code can be used to estimate conversion efficiency, tempo-spatial and spectral profiles and many transverse effects including diffraction, walk-off, phase modulations and self-focusing through the third-order nonlinear process. An application example of the code to second-harmonic generation is given in this short note.

Decay instability and Kolmogorov spectra of ion-drift waves in low-β dusty plasmas

The interaction of nonlinear ion-drift waves in a low β, that is me/mi≪β≪1, dusty plasma is investigated. The matrix elements of the three-wave interactions in an inhomogeneous plasma with uniform ion temperature are derived. The decay instability growth rates and weakly turbulent plasma wave spectra of the ion-drift waves are evaluated and analyzed.

Phase matching analysis of noncollinear optical parametric process in nonlinear anisotropic crystals

Phase matching for noncollinear optical parametric generation is investigated. All the possible phase matching configurations and existence conditions for general noncollinear three-wave mixing interactions are derived for propagation within the crystal principal planes. Numerical expressions for the critical phase matching angles are presented wherever possible. Finally, as an application of these expressions, several numerical calculations of the phase matching angles for general noncollinear phase matched optical parametric amplification in the nonlinear-optical crystals such as β-BaB 2O 4, LiB 3O 5 and KTiOPO 4 are completed, and the results are graphically presented.

Nonlinear Phase Shift by Parametric Amplification in Leaky Waveguides

In this article, the cascaded second-order nonlinear phase shifts induced in the signal wave are studied using the three-wave parametric interaction in a four-layered QPM leaky waveguide configuration in Z-cut LiNbO 3 . In this interaction, the pump-andsignal waves are guided modes and the idler is radiated into the substrate. We have analyzed the nonlinear phase shifts induced in the signal wave due to cascaded second-order effects, as a function of different waveguide parameters. These studies should find application in realizing practical all-optical signal processing devices.

A model of weakly nonlinear stages for the periodic structure formation on the charged surface of a conducting liquid

Effects of the four-wave processes on the dynamics of the charged boundary of a conducting liquid are compared for the cases of plane and square symmetry of the problem. Considering a slit liquid-metal electrode, whose special feature is a possible degeneration of the nonlinear three-wave interaction, we propose a model of the initial stage in the formation of a periodic system of cusps on its surface.

On wave turbulence in MHD

Abstract. We describe the fundamental differences between weak (wave) turbulence in incompressible and weakly compressible MHD at the level of three-wave interactions. The main difference is in the structure of the resonant manifolds and the mechanisms of redistribution of spectral densities along the applied magnetic field B0. Similar to pure acoustic waves, a three-wave resonance between collinear wave vectors is observed but, in addition, we also have a resonance through tilted planes and spheres. The properties of resonances and their consequences for the asymptotics are also discussed.

Nonadiabatic interaction of a propagating wave packet with localized parametric pumping.

The interaction of a propagating wave packet (carrier frequency omega, wave number k) with nonadiabatic parametric pumping, localized in a region of size the order of the carrier wavelength L approximately lambda=2pi/k, is studied experimentally in a system of dipolar spin waves in a ferrite film. It is shown that the three-wave parametric interaction omega+omega(')=omega(p) leads to the formation of both contrapropagating (k(')=-k) and copropagating (k(')=k) idle wave packets of carrier frequency omega('). A system of equations derived for the packet envelopes gives a quantitative description of the observed random modulation of the output signal caused by the interference of the input and copropagating idle wave packets.

Femtosecond Noncollinear Optical Parametric Amplification in the Mid-Infrared Range with 1.25 µm Pumping

We study noncollinear three-wave interaction in a traveling wave optical parametric amplifier operating in the mid-infrared spectral range between 6 and 8 µm using HgGa2S4 and AgGaS2 as nonlinear optical crystals. Calculations reveal that matching of the group velocities in both crystals is possible in a wider spectral (or angular) region for type-I interaction. High-power femtosecond pulses at 1.25 µm from a Cr:forsterite regenerative amplifier are used for pumping the optical parametric amplifier at a repetition rate of 1 kHz. Experimentally we verify the advantages of noncollinear interaction by increasing the conversion efficiency approximately sixfold in the saturation regime as compared to the collinear case. The maximum idler energy measured near 6 µm exceeds 4 µJ and typical pulse durations are about 300 fs.

Observation of instabilities due to three-wave interaction during nonlinear pump wave modulation

Instabilities due to three wave interaction, being just like explosive instabilities, are experimentally shown to occur during the nonlinear modulation of a pump wave (negative energy wave) externally excited in an ion-beam-plasma system. In this experiment, the pump wave is observed to be self-modulated above a threshold because of nonlinear mode coupling among three different waves (ω0,k0), (ω1,k1), and (ω2,k2) and to split into a series of wave packets. Spectral analyses of such evolving waves and identification of all three waves, based on wave pattern observations, make it possible to clarify the feature of the mode coupling characterized by ω0=ω2−ω1 and k0=k2−k1. Furthermore, spectral observations indicate that all the wave powers rapidly increase simultaneously with the increase of the pump power above the threshold described above, although they do not grow infinitely in a finite time. All the above results suggest the realization of instabilities due to three wave interaction, being like explosive instabilities, in the beam-plasma system. Finally, the frequency shifts, the threshold for the instabilities, and the saturation of the instabilities are discussed.

Energy conversion and all-optical switching in three-wave mixing in crystal with periodical modulation of χ(2) susceptibility

Three-wave interaction of fundamental optical field and its second harmonic in crystal with periodical modulation of χ (2) susceptibility is investigated. We use approach based on asymptotic expansion technique to study analytically evolution of the optical fields within the crystal with periodical modulation of second-order susceptibility. Results of the analytical approach are used in numerical calculations. We show that all-optical switching in interaction can be implemented in wide range of initial parameters.

Random Scattering and Anisotropic Turbulence of Shear Alfvén Wave Packets

A theoretical model is given of anisotropic magnetohydrodynamic turbulence in the interstellar medium and the solar wind. The model is motivated by observations that show significant deviations from the Kolmogorov power law. Dimensional and heuristic arguments are given and critically assessed. On the basis of the weak turbulence approximation in which three-wave interactions dominate, analytical and numerical results are obtained for the anisotropic energy spectrum produced by the random scattering of shear Alfven waves propagating parallel to a large-scale magnetic field. The energy spectrum is shown to be proportional to k, qualitatively consistent with some observations and wave kinetic theory.

Steady-state symmetric three-wave forward interaction in a cubic photorefractive crystal in an ac external electric field

An analysis of symmetric three-wave forward mixing in a cubic crystal with an applied ac external electric field is carried out for the case of a strong central wave and weak side waves. Numerical calculations are made for interaction in a Bi12SiO20 crystal in a square-wave electric field. It is shown that the dependence of the photorefractive grating amplitude on interaction length and grating spacing is qualitatively different for longitudinal and transverse electro-optic configurations. The effects of the energy exchange between interacting plane light waves that are not peculiar to two-wave interaction are described.

The Effect of Electromagnetically Induced Transparency in Classical Systems

We develop a classical model of the recently popular parametric effect of electromagnetically induced transparency (EIT), i.e., the formation of a “transparency window” inside a resonance absorption line of a three-level quantum system, which is accompanied by a record strong slowing of the probe wave. Based on this model, we consider the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma. The parametric (three-wave) interaction of two electromagnetic modes (the frequency of one of these modes is equal to the electron gyrofrequency) with the electrostatic mode is considered. It is shown that the resonance growth in the electron oscillations at the gyrofrequency can be damped due to the parametric coupling with the collective electrostatic oscillations. Similar to analogous quantum systems, the group slowing of the probe electron-cyclotron wave in the transparency window takes place in the case considered.