Oded Yaakobi

Spatially autoresonant stimulated Raman scattering in nonuniform plasmas

New solutions to the coupled three-wave equations in a nonuniform plasma medium are presented that include both space and time dependence of the waves. By including the dominant nonlinear frequency shift of the material wave, it is shown that if the driving waves are sufficiently strong in relation to the medium gradient, a nonlinearly phase-locked solution develops that is characteristic of autoresonance. In this case, the material electrostatic wave develops into a front starting at the linear resonance point and moving with the wave group velocity in a manner such that the intensity increases linearly with the propagation distance. The forms of the other two electromagnetic waves follow naturally from the Manley‐Rowe relations.

Autoresonant four-wave mixing in optical fibers

A theory of autoresonant four-wave mixing in tapered fibers is developed in application to optical parametric amplification (OPA). In autoresonance, the interacting waves (two pump waves, a signal, and an idler) stay phase-locked continuously despite variation of system parameters (spatial tapering). This spatially extended phase-locking allows complete pump depletion in the system and uniform amplification spectrum in a wide frequency band. Different aspects of autoresonant OPA are described including the automatic initial phase-locking, conditions for autoresonant transition, stability, and spatial range of the autoresonant interaction.

Multidimensional, autoresonant three-wave interactions

The theory of autoresonant three-wave interactions is generalized to more than one space and/or time variation of the background medium. In the most general case, the three waves propagate in a four-dimensional (4D) slowly space-time varying background, with an embedded 3D linear resonance hypersurface, where the linear frequency and wave-vector matching conditions of the three waves are satisfied exactly. The autoresonance in the system is the result of weak nonlinear frequency shifts and nonuniformity in the problem and is manifested by satisfaction of the nonlinear resonance conditions in an extended region of space-time adjacent to the resonance surface despite the variation of the background. The threshold condition for autoresonance is found and further discussed in application to stimulated Raman scattering in a 1D, time-dependent plasma case. Asymptotic description of the autoresonant waves far away from the resonance surface is obtained. The theory is illustrated and tested in 2D numerical simula...

Equal energy phase space trajectories in resonant wave interactions

Adiabatic evolution of two and three resonantly interacting wave systems with nonlinear frequency/wave vector shifts is discussed. The corresponding Hamiltonian, depending on the coupling, detuning, and nonlinear frequency shift parameters may have a variable number of fixed points, i.e., the system can experience a topological change of phase space when these parameters vary in time or space. It is shown that the oscillation periods of two equal energy trajectories in these wave systems are equal and the difference between the action integrals of such trajectories is obtained analytically as a function of the system parameters. Based on these findings, a scheme of simultaneous adiabatic variation in the parameters is designed, such that any pair of initially equal energy trajectories continues to have the same energy at later times. These results are generalizations of a previous work [O. Polomarov and G. Shvets, Phys. Plasmas 13, 054502 (2006)] for a single, resonantly driven wave.

Autoresonance of coupled nonlinear waves

Resonant three‐wave interactions (R3WIs) and their dynamical counterpart, three‐oscillator interactions (R3OIs) play a fundamental role in many fields of physics. Consequently, controlling R3WI/R3OIs is an important goal of both basic and applied physics research. We have developed new control schemes based on a recent approach of wave autoresonance. This approach is based on the intrinsic property of many nonlinear waves and oscillations to stay in resonance (phase‐lock) even when parameters of the system vary in time and/or space. We review autoresonance in several new coupled wave systems including externally driven R3OI systems and multidimensional R3WIs. Particularly, we have focused on autoresonant stimulated Raman scattering in nonuniform plasmas. This research comprises an important step toward understanding of adiabatic synchronization of nonlinear waves in space‐time varying media with a potential of many new applications in plasma physics and related fields, such as fluid dynamics, nonlinear op...