The three-dimensional (3D) theory of laser cutting is presented. The cutting efficiency determined by its ultimate parameters at different types of polarization is estimated. The physical reasons for limitations of ultimate cutting parameters at a plane P-polarized beam are displayed. In the case of cutting metals with a large ratio of sheet thickness to width of the cut, the laser cutting efficiency for a radially polarized beam is 1.5 - 2 times larger than for plane P-polarized and circularly polarized beams. The possibility of generating the radially polarized beam is discussed.
The analysis of the vector wave equation was conducted. The class of self-similar solutions with inhomogeneous polarization corresponding to the resonator modes is deduced. The modes with inhomogeneous polarization can be selected by a diffraction element with polarization selectivity used as one of the resonator mirrors. Diffraction elements with high polarization selectivity about 100% are necessary for generating "pure" radially polarized modes. The radially polarized beam provides higher energy efficiency (the product of the depth of the cut by cutting velocity) for laser cutting metals than the circular polarized main mode does under the same conditions. The two limiting cases of resonance absorption on the spherical plasma target could be realized using axially polarized beams: the resonance absorption is maximum in the case of radial polarization and doesn't occur in the case of azimuthal polarization.
Radially polarized radiation of 1.8 kW was first obtained in an industrial high-power CO 2 laser. Special reflective elements with an axial polarization selectivity of 22% were used as a rear mirror in the laser. The output radiation consisted mainly of an unpolarized mode TEM 00 and a radially polarized mode R-TEM 01 * .
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.
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.
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