Sopin M. Singularities of electromagnetic wave characteristics in waveguide optics and vector fields.

Investigation object: electromagnetic field. Investigation purpose: the singularities in behavior of electromagnetic waves in free space and waveguided corrugated films is studied. Investigation methods and apparatus: graph theory, differential topology, methods of mathematical physics. Theoretical and practical results, novelly: Novel approach for the analysis of singularities in vector fields has been proposed. The essence of this approach is scalar consideration of the phase vortices at the orthogonal field components. The new type of vortices is introduced, namely the phase-difference vortices. The relationship between the characteristics of the complete system of phase vortices associated with orthogonal field components, the behavior of the azimuth of a linearly polarized electrical field at a s-contour, and the polarization singularities are established. The diagram method for problem of gratings anomalies is proposed. A simple method is proposed for calculating the efficiency of coupling laser radiation into a corrugated dielectric waveguide when two coupled modes are excited in the second diffraction order. The angular dependences of coupling-in efficiency are calculated for various corrugation periods. The existence optical bistability for nonlinear corrugated dielectric waveguide when two coupled modes are excited in the second diffraction order is shown. It is founded that bistability interval depends on the perturbation Bragg's resonance condition. Degree of application: it is planned. Sphere (area) of application: singular optics, holography, integrated optics.