Interaction and fusion of light pulses at the dynamical four-wave mixing in photorefractive media
All-optical control of impulse parameters is realized via a dynamical transmission four-wave mixing. We show that the nonlinear system, which includes both coupled wave equations and an evolution equation for the dynamical grating amplitude, contains soliton-like solution for the intensity pattern formed in the medium. The nonlocality of the nonlinear response is the main important requirement to the soliton-like solution is established during the wave-mixing process. On some determined conditions the convergence of input pulses into one pulse takes place (i.e. the merge of the solitons) that lead to the dramatic changes of the output pulse shapes and intensities. The precise conditions, when the impulse output can be driven by another guiding pulse are obtained and discussed.
Analytic Structure of the Four-Wave Mixing Model in Photoreactive Material
In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\sqrt{z} exp(-t / tau), in which tau is the relaxation time.
Steady state and dynamic gratings in photorefractive four-wave mixing
The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.