Selected fundamental and applied problems of laser mode formation

Abstract

Several problems are considered in this review. Using our dipole wave theory of diffraction the analytical formulas for diffraction from a narrow ring for different polarization were obtained. They were used in the new wave numerical model of an open resonator. A number of parameters of mode formation were investigated. It was shown that mUltipass geometrical "modes" win in competition with single pass Laguerre-Gaussian (LG) non-main modes during the relaxation oscillations. A method has been suggested for description of the azimuthally (A) and radially (R) polarized modes that excludes any inherent contradictions and unjustified approximations. It allows the analytical calculation of the field components for these modes, including the longitudinal one. Generation of high power beams with axial symmetric polarization in stable resonator of industrial COrlaser with diffraction gratings has been realized. The transformation of azimuthally polarized mode to R-polarized mode was demonstrated. R-polarized beam was successfully used for cutting metal. The principal scheme based on a modified Sagnac interferometer was proposed and investigated experimentally. This external cavity technique was used for generation of R-and A polarized laser beam.In many cases of modem research the classical approach of describing the transversal laser beam structure of the open resonators [1] is not enough. LG modes TEMpq belong to the self-reproducing solutions of the scalar wave equation. These solutions are in direct contradiction to Maxwell equationV·E=O. The longitudinal field is neglected at the describing laser beams in paraxial approximation. The solution of scalar wave equation relates to the homogenously polarized beams. The direction of the electric field in every point of the beam cross section remains the same for such beams. There are many other beams with inhomogeneous polarization. There also exists the problem of correlation between the wave and geometric optics in describing stable resonators. The report is devoted to these very problems. It is a review of our results in this field for the last years. Dipole-wave theory of diffraction.The Kirchhoff integral is scalar so it can be applied for strictly limited number of problems.If we have the initial field Eo Cr') on the given surface S ' , the field E(r) at the observation point can be calculated. Here n is a unit normal to the surface S ' , and G(r, r') is the Green's function of the scalar wave equation. Strictly saying the used iklr-r'l form of G (r,r') = I r-r'l is incorrect for the point source of vector electromagnetic wave.This integral can be used for obtaining vector solutions of diffractive problems by submission Hertz vector instead of electric field E.Then the fields can be found by the formulas: E=VxVxZ, H=ikVxZ. The main problem here is finding Zo if we know Eo.But for a widespread case of a plane polarized wave Eo(r ' ) andZo(r ' ) on S ' surface are related by a simple expression Eo (r') = _k 2 Zo(r') . Solutions obtained by this method automatically sat...