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.
The unfolded universe of elementary particles. A geometric explanation of the standard model structure
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold the lagrangian of Einstein and Dirac in dimension twelve. The main mechanism which gives birth to the standard model is a certain gauge fixing of triality, which permits to identify the multiplicity of fermions, as seen from the four dimensional world, with the eight unseen dimensions of the generating universe. In this way we get the known tables of particles, explaining the series of fermions and the gauge bosons. We suggest that the Higgs field dynamics could appear through a bosonization of the right handed neutrino and correspond to a displacement in the unseen dimensions. We also propose hypotheses for dark matter, and perhaps dark energy. Then we suggest predictions to go beyond the standard model.