Selection and generation of multipass modes in an open resonator.

The original numerical wave model of the open resonator has been employed in the investigation of conditions for multipass mode generation. It is shown that for Fresnel numbers larger than unity, multiple reflections of radiation from the stable resonator mirrors lead to sustained quasi-stationary oscillations which are indicative of multipass mode generation. Various types of ray trajectories have been considered at the paraxial resonance conditions. Trajectory selecting techniques are suggested to provide the high quality output beams at large Fresnel numbers. The results of numerical experiments on amplitude-phase distribution of output radiation are presented for the suggested schemes.

Formation of transverse mode in axially symmetric lasers.

The developed iteration algorithm for simulation of lasers with an open resonator was employed in the study of transverse mode formation. The simulations of an axially symmetrical resonator rely on an analytical description of radiation diffraction from a narrow ring. Reflection of an incident wave with a specified amplitude-phase distribution from the mirror is calculated by the Green-function method. The model also includes an active medium homogeneous along the resonator axis that is represented by the formula for saturating gain. The calculations were performed for two types of lasers: with on-axis and off-axis gain maximum. In the first type of laser one can obtain either a principal mode or "multimode" generation. The latter means quasi-stationary generation with regular or chaotic oscillations. In the second type of laser high order single-mode generation is possible. Experimental results obtained on a fast axial flow 4 kW CO(2) laser are also presented. They are in good agreement with the calculations.

Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer.

A principal scheme for an external cavity technique for changing the polarization of a laser beam based on a modified Sagnac interferometer is proposed. The modified Sagnac interferometer includes standard optical components: a displacement polarizing beam splitter, an angle reflector, and a Dove prism. The radially polarized beams, obtained with the help of the developed scheme, allow the generation of a longitudinally polarized electric field by sharp focusing. The phase correction of radially polarized modes of higher orders leads to increasing the longitudinal field in the focus of the beam.

Vector solution of the diffraction task using the Hertz vector.

A large class of diffraction problems can be solved on the basis of the Huygens principle. However, methods of solving diffraction problems based on this principle exhibit narrow boundaries of applicability. The goal of the present work is to offer a relatively simple physically based and mathematically strict "dipole wave" vector theory of non-paraxial diffraction of electromagnetic radiation which allows analytical solutions of typical diffraction problems. The suggested theory logically retains the wave approach used in the Kirchhoff method and does not exhibit strict limitations to applicability inherent in the Kirchhoff integral. The diffraction problem is solved by using the Hertz vector in the Kirchhoff integral instead of the field vector. The method efficiency is illustrated in several examples. Analytical solutions of diffraction base problems have been obtained for linearly polarized radiation on an infinite slit and on various-shaped holes at an arbitrary angle of incidence and polarization. It was shown the possibility of vector addition particular solutions to obtain diffraction patterns from several holes. The diffraction of radiation with azimuthal and radial directions of polarization on a ring slit is also considered. The main qualitative feature of the obtained solutions is the presence of "poles" one or two points of zero field in the diffraction pattern which are superimposed on the common system of light and dark fringes. The poles are located along electrical field vector directions. The vector analytical formulas describing the propagation of some laser beams in the free space have been obtained too. The solutions of the diffractive problems satisfy the Maxwell equations and the reciprocity principle.