A.I. Illarionov - Dr.Sc. (Phys.-Math.), Professor, Department of Physics, Irkutsk National Research Technical University E-mail: illarionov.an1952@mail.ru M.S. Ivanov - Senior Lecturer,Department of Scientific and Engineering Disciplines, Zabaikalsky Institute of Railway Transport (Chita) E-mail: vanov.maks@mail.ru

The work considers the conversion of infrared radiation having a wavelength λ = 1064 nm in the second harmonic in a negative uniaxial crystal. IR radiation was focused into a nonlinear crystal of lithium iodate by lenticular lens having spherical aberration. For computer modeling of spatio-angular structure of the second optical harmonic it was necessary to define a mathematical expression that defines the focal length Ϝ for annular lens zones of different radii ρ and a coordinate χ fall focused by a lens (the distance from the optical axis of the system to the point of beam falling) on the front face of the nonlinear crystal IR rays of the incidence angle relative to the optical axis. For this work we used the method of tangents and normals in the geometric approximation spread of the falling on the lens infrared rays. This method greatly simplifies the derivation of necessary expressions. The resulting expression F(ρ) for the lenticular lens was graphically presented together with the corresponding dependencies for plano-convex and convex-plano lens which were considered in the early works of authors. The chartings are in good agreement with the theory of Born and Wolf of the spherical aberration of the focusing optical lenses of different shapes (M. Born, E. Wolf, Principles of Optics. M.: Science, 1973. 720 pp.), which confirms the reliability of the analytical expression F=F(ρ) made by the authors. Fair enough the resulting expression for χ=χ(α0), made by this method, which was built in the same coordinate system with the charts of χ=χ(α0), for plano and convex-plano lenses, comparison with which confirmed its authenticity, as presented graphs showed good agreement with the known experimental relations between χ for lenses of various shapes. These expressions allowed in conjunction with the theory of conversion of infrared radiation, which has a spherical aberration, first presented in the works of Stroganov V.I. and Illarionov A.I. (Stroganov V.I., Illarionov A.I. Optical system aberration effect in the second harmonic generation // Opt. Com. - 1980. - Vol. 35, No.3. - P. 455-461), to construct by using computer modeling, the spatial and angular structures of the second optical harmonic. These structures by their form and shape were similar to spatio-angular structures of the second harmonic while focusing IR radiation in a nonlinear negative crystal of lithium iodate by plano (Stroganov V.I., Illarionov A.I. Optical system aberration effect in the second harmonic generation // Opt. Com. - 1980. - Vol. 35, No. 3. - P. 455-461; Illarionov A.I., Goreva O.V., Ivanov M.S. Effect of optical lens parameters on the formation of the spatial-angular characteristics of the optical second harmonic // Proceedings of Universities. Physics. - 2011. - V.54, №2/2. - pp. 159-164) and convex-plano (Illarionov A.I., Ivanov M.S. Second harmonic generation in uniaxial crystals with the focus of the main radiation by real convex-flat lens // Scientific notes of the Zabaikal-sky Chernyshevsky State Humanitarian Pedagogical University. \"Natural sciences. Physics.\" Series. - 2011. - V.38, №3. - pp. 93-98) lenses with spherical aberration, which have been investigated previously by the authors. Space-angular structures of the second harmonic have on the output from the nonlinear crystal three curves representing the length of circles of different radii of curvature. The lower curve of the crystal has appeared due to the interaction of the crystal with collinear light waves of infrared radiation during the conditions of collinear synchronism (curve determines the direction of the collinear phase matching in the crystal). This curve has no information of the nature of the spherical aberration. This information is transferred by two curves intersecting curve of collinear phase matching. These curves are the result of the interaction of light waves under the conditions of the vector matching in nonlinear crystal in the areas with the largest concentration of infrared rays (focus on the axis and the ring focus). Spatial-angular structures were built for different distances of the nonlinear crystal from the focusing biconvex lens and different parameters as geometric (diameter, thickness on the optical axis, the radius of curvature) and optical (refractive index material) lenses characteristics. The analysis of IR radiation converted into the visible part of the spectrum showed a high sensitivity of the processes of transformation to changing of these parameters, which manifested itself in the change of the angular size of the second harmonic structures. Mentioned above allows us to offer the results obtained in this work for the development of nonlinear-optical method for mea-suring the spherical aberration of the focusing IR lens.

 

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