Bugaychuk S. Dissipative solitons of wave-mixing in dynamic nonlinear optical media.

TThe dissertation is devoted to the first comprehensive studies of dissipative solitons of wave-mixing (DSWM). They represent a new kind of spatial dissipative solitons that arise in dynamic holographic systems operating on reversible nonlinear-optical materials. We found that the basic prerequisites for the formation of DSWMs are self-diffraction of interacting waves, accompanied by the effect of energy transfer between the interacting waves, and relaxation of nonlinearity in the medium. Detailed theoretical studies of the DSWMs are carried out, including the study of various types of DSWMs and their dependence on the parameters of a nonlinear system. We show that a nonlinear system of the self-diffraction reduces to a single nonlinear evolutionary equation, which is (i) the parametric nonlinear Schrödinger equation (pNLS) (for reflective self-diffraction geometry) or the parametric Ginzburg-Landau equation (pCGLE) (for transmission self-diffraction geometry). The obtained pNLS and pCGLE explicitly contain the real parameters of the original nonliner system, namely, the gain of a nonlocal dynamic grating, and the grating period. In addition, both of these equations contain an exponential decay factor depending on the relaxation time constant of the medium. The equations are derived for the case of the formation of a nonlocal dynamic phase grating. This case corresponds to the conditions of maximum energy transfer and the absence of phase transfer between the interacting waves. The pNLS and pCGLE describe the nonlinear dynamics of two coupled lattices, which are an intensity lattice for light interference and a dynamic grating for photoinduced refractive index. We also show that the initial nonlinear system can be reduced to a sine-Gordon equation (for transmission geometry) or to a tangent-Gordon equation (for reflective geometry). These equations contain a relaxation term along the longitudinal coordinate z of wave propagation. We obtain analytical solutions for DSWM in steady state. The solution is a single bright soliton for transmission geometry and a dark soliton (a kink) for reflective geometry. The solution describes a stable spatially localized profile for the interference intensity of the interacting waves along the longitudinal direction z. The envelope of the amplitude of the dynamic grating has a similar soliton-like profile. The first experimental studies of the formation of an inhomogeneous spatial profile of the amplitude of a phase dynamic grating upon self-diffraction of laser beams in a bulk photorefractive crystal are described. It was found experimentally that the envelope of the dynamic grating amplitude takes a soliton-like form in accordance with the prediction of the theory. We show that formation of different types of DSWM solutions can lead to new effects that arise from self-diffraction of laser beams in dynamic media. We consider theoretically new possibilities for manipulating laser pulses as a result of DSWMs formation during the interaction of these pulses in a nonlinear optical material. Among such effects are: compression and amplification of laser pulses as a result of complex nonlinear dynamics in the system; light-control-light mirrors with high amplification, which can be created in fiber Bragg gratings or in photonic crystals; development of a holographic amplifier, which includes a set of matched thin phase gratings; optimization of optical phase conjugation schemes that provide high gain coefficients; optical logic elements, and others. We have also obtained breathers solutions for DSWM. We have shown that the breathers arise for conditions when the nonlinear system is unstable. Then under the influence of random phase fluctuations for interacting waves, the DSWM becomes in the form of periodic pulsations. All these effects can be promising for applications in modern optoelectronic information systems. We have developed a theoretical model of self-diffraction of laser beams on thin materials in the Raman-Nath regime. Analytical solutions of our model allow using Raman-Nath self-diffraction as a method for determining nonlinear-optical coefficients in thin materials. We have applied this method to study the nonlinear optical properties of many new materials. Among them, we first have proposed and prepared hybrid liquid crystal cells containing a photonic crystal made on one of the cell substrates. The results of the provided studies can be extended to other nonlinear systems, which involve the nonlinear interaction of coupled lattices (coupled chains). Our research also prove that dynamic holographic systems demonstrating the energy transfer between interacting waves can be used as model theoretical and experimental systems to study the fundamental properties of dissipative solitons in other, more complex nonlinear systems that are studying in neural networks, in nonlinear models of chemistry, biology, climate, cosmology, etc.