New physics and applications will be investigated theoretically and experimentally of optical spatial solitons in passive and active cavities, and Bragg gratings with cascaded second-order optical nonlinearity. The types and properties of the dissipative optical solitons in wide-aperture nonlinear cavities will be studied. The features, including polarization structure, of extremely narrow spatial solitons with sizes comparable with the light wavelength will be examined. The theory of parametric optical solitons for both three wave and frequency degenerate interactions in quadratic media will be developed. These phenomena will also be studied experimentally. The planar and vortex interaction of the dissipative optical solitons will be examined. Soliton bistability caused by the interference of second- and third-order nonlinearities will be analysed. For the first time, the experiments on quadratic spatial soliton self-trapping in single resonator cavities will be carried out. In these experiments properties of such solitons will be studied in detail. Important information on influence of cavity frequency detuning, phase mismatching, walk-off effect, diffraction and dispersion on formation and properties of chi-2 solitons will be obtained. The comparison of solitons excited in cavities and bulk media will provide a basis for developing of photonics using quadratic cavities.
Novel theoretical methods, computer codes will be developed. For extremely narrow and short (half-period) solitons, the analysis of nonlinear vector Maxwell's equations will be carried out. Nonlinear tunnelling of slow solitons in quadratic Bragg gratings will be studied employing two theoretical methods: quasi-standing wave amplitude diffusion and interaction of two counter-propagating waves. Localized optical structures will be examined in 1D and 2D gratings.
The transverse stability of wide-aperture solitons in cavities will be studied, and such phenomena as hysteresis and bistability will be considered. The investigation of planar and vortex interactions in cavities will be fulfilled with the help of variation and aberration-free approximation methods.
As a result, new physical conception of optical beam interactions in cavities with quadratic or quadratic-qubic nonlinearities will be elaborated. In quadratic cavities one can control following properties of spatial solitons: width, transverse shape, cleaning-up, hysteresis, bistability, switching and spiralling. Limitations of high-density spatial solitons packaging will be estimated. Parametric generation methods of extremely short (half-period) pulses are of vital importance for atto-second optics (including spectroscopy and interaction with matter). Quadratic Bragg gratings with low thresholds can be effectively used for generation of soliton trains at the first and second harmonic frequencies.
Thus, a novel field of nonlinear optics will be developed and new effective approaches to all-optical information processing will be proposed and tested.