Six-wave Interactions Research Articles

Six-wave interaction in multimode waveguides with Kerr nonlinearity with allowance for the Gaussian structure of pump waves

The quality of wavefront conjugation in the case of six-wave interaction in two-dimensional multimode waveguides with Kerr nonlinearity is analyzed under the condition that one of the pump waves excites a zero waveguide mode and the amplitude distribution of the other pump wave at the waveguide end facet varies according to the Gauss law. It is shown that in a waveguide with infinitely conducting walls, the half-width of the modulus of the point spread function of a six-wave radiation converter is completely determined by the transverse size of the waveguide and weakly depends on the width of the Gaussian pump wave. In a parabolic-index profile waveguide, a decrease in the width of the Gaussian pump wave at the waveguide ends commonly leads to a monotonic decrease in the half-width of the point spread function modulus.

Double wavefront reversal during six-wave interaction on Kerr nonlinearity in a waveguide with infinitely conducting surfaces

Background. Generation of a wave with a double reversed wavefront in multimode waveguides increases the efficiency of six-wave radiation converters and expands the possibilities of its use in adaptive optics problems and the conversion of complex spatially inhomogeneous waves. Aim. The quality of double wavefront reversal during six-wave interaction in a waveguide with infinitely conducting surfaces with Kerr nonlinearity is analyzed for the ratio of the wave numbers of the pump waves equal to 2 and 0,5, and the condition that one of the pump waves excites the zero mode of the waveguide, and the amplitude distribution of the other pump wave excites the edges of the waveguide are described by a Gaussian function. Methods. The influence of pump wave parameters on the half-width and contrast of the amplitude modulus of the object wave was studied using numerical methods. A wave from a point source located on the front face of the waveguide was used as a signal wave. Results. The dependences of the half-width and contrast of the amplitude modulus of the object wave on the ratio between the width of the waveguide and the width of the Gaussian pump wave are obtained. Conclusion. It is shown that the maximum change in the characteristics of a wave with a double reversed wavefront is observed when the width of the Gaussian pump waves changes in the range from 0,3 to 2 half-widths of the waveguide.

Six-wave interaction with double wavefront reversal in multimode waveguides with Kerr and thermal nonlinearities

Spatial selectivity of six-wave radiation converters, which perform double wavefront conjugation of a signal wave in long multimode waveguides with both Kerr and thermal nonlinearities, is studied. Waveguides with infinitely conductive surfaces, with a parabolic refractive index profile, were used. It is shown that the spatial structure of the first pump wave does not affect the quality of doubled wavefront conjugation in a waveguide with Kerr nonlinearity, but only slightly affects the quality of doubled wavefront conjugation in a waveguide with thermal nonlinearity. A decrease in the radius of the second Gaussian pump wave on the back face of the waveguide leads to an improvement in the quality of the doubled wavefront reversal both in the case of six-wave interaction in the Kerr and thermal nonlinearities. In a parabolic waveguide, when the zero mode of the waveguide is excited by pump waves at a constant frequency of the second pump wave, an increase in the frequency of the first pump wave worsens the quality of the double wavefront conjugation.

EXACT SOLITON SOLUTIONS FOR CONFORMABLE FRACTIONAL SIX WAVE INTERACTION EQUATIONS BY THE ANSATZ METHOD

In this paper, a conformable fractional time derivative of order [Formula: see text] is considered in view of the Lax-pair of nonlinear operators to derive a fractional nonlinear evolution system of partial differential equations, called the Fractional-Six-Wave-Interaction-Equations, which is derived in terms of one temporal plus one and two spatial dimensions. Further, an ansatz consisting of linear combinations of hyperbolic functions with complex coefficients is utilized to obtain an infinite set of exact soliton solutions for this system. Certain numerical examples are introduced to show the effectiveness of the ansatz method in obtaining exact solutions for similar systems of nonlinear evolution equations.

Difference Squeezing in Degenerate Three-Photon Absorption Six-Wave Interaction Process

: In this paper, difference squeezing in the degenerate three-photon absorption six-wave interaction process is examined. The difference squeezing in fields between the pump and Stokes modes can be converted to normal squeezing in the signal mode, and vice versa. It is demonstrated that in the pump mode, amplitude-cubed squeezing is directly turned into normal squeezing in the signal mode. The squeezing in the stimulated interaction, which reduces the depth of classicality of the field amplitude, is seen to be larger than the corresponding squeezing in the spontaneous interaction, despite having the same number of pump photons. Difference squeezing is observable only in certain domain values of pump photons. It is deduced that the multi-photon absorption nonlinear optical approach is the best way to generate optimal squeezed laser light in any optical system.

Difference squeezing of the optical fields in degenerate six-wave interaction process

Difference squeezing of the optical fields in degenerate six-wave interaction process

Six-wave interaction with double wavefront reversal on thermal nonlinearity in a medium with a nonlinear absorption coefficient

The spatial selectivity of a six-wave radiation converter w1 + w1 + w2 – w1 – w1 = w2 on thermal nonlinearity with allowance for the nonlinear absorption coefficient was studied. Relationships for the half-bandwidths of the spatial frequencies of object waves that are related both directly to the thermal nonlinearity and to the nonlinear character of variation of the absorption coefficient with varying signal wave divergence, nonlinear medium thickness, and pump wave intensity were analyzed. It was shown that for a highly diverging signal wave, the half-bandwidths of the spatial frequencies of object waves with a double-reversed wavefront are several times different.

Intermittency in generalized NLS equation with focusing six-wave interactions

We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrödinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic “fat tail” decaying with amplitude |Ψ| close to ∝exp⁡(−γ|Ψ|), where γ>0 is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.

Route to thermalization in the α-Fermi–Pasta–Ulam system

We study the original α-Fermi-Pasta-Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ(8), where ϵ is the small parameter in the system. The wave-wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed.

On the nonintegrability of the free surface hydrodynamics

The integrability of the compact 1D Zakharov equation has been analyzed. The numerical experiments show that the multiple collisions of breathers (which correspond to envelope solitons in the NLSE approximation) are not pure elastic. The amplitude of six-wave interactions for the compact 1D Zakharov equation has also been analyzed. It has been found that the six-wave amplitude is not canceled for this equation. Thus, the 1D Zakharov equation is not integrable.

Weak turbulence of Kelvin waves in superfluid He

The physics of small-scale quantum turbulence in superfluids is essentially based on knowledge of the energy spectrum of Kelvin waves, Ek. Here we derive a new type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature which describes a step-by-step energy cascade over scales resulting from five-wave interactions. This approach replaces the earlier six-wave theory, which has recently been shown to be inconsistent owing to nonlocalization Solving the four-wave kinetic equation, we found a new local spectrum with a universal (curvature-independent) exponent, Ek∝k−5∕3, which must replace the nonlocal spectrum of the six-wave theory, Ek∝k−7∕5 in any future theory, e.g., when determining the quantum turbulence decay rate, found by Kosik and Svistunov under an incorrect assumption of locality of energy transfer in six-wave interactions.

Frequency transformation of optical vortices upon nondegenerate multiwave interaction in dye solutions

A method for inverting the topological charge of singular light beams with their simultaneous frequency transformation under multiwave interaction in media with resonant and thermal nonlinearities is proposed. Frequency-nondegenerate four-wave and six-wave interactions of optical vortices are experimentally implemented using an ethanol solution of a polymethine dye 3274U as a nonlinear medium.

Modeling Kelvin Wave Cascades in Superfluid Helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the latter and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in $k$-space via a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and the closeness of the numerics for the higher-order DAM to the analytical predictions for the lower-order DAM .

Bifurcations and the stability of the surface envelope solitons for a finite-depth fluid

The dynamics of the quasi-monochromatic surface gravitational waves in a finite-depth fluid is studied for the case where the product of the wavenumber by the depth of the fluid is close to the critical value kcrh ≈ 1.363. Within the framework of the Hamiltonian formalism, the general nonlinear Schrodinger equation is derived. In contrast to the classical nonlinear Schrodinger equation, this equation involves the gradient terms to the four-wave interaction, as well as the six-wave interaction. This equation is used to analyze the modulation instability of the monochromatic waves, as well as the bifurcations of the soliton solutions and their stability. It is shown that the solitons are stable and unstable to finite perturbations for focusing and defocusing nonlinearities, respectively.