1 Compensation of Thermally Induced Birefringence in Active Medium Made of Polycrystalline Ceramics. Efim A. Khazanov Institute of Applied Physics, Nizhny Novgorod, Russia Mikhail A. Kagan Pennsylvania State University, University Park, PA, USA 2 Outline. Introduction Polycrystalline ceramics vs glass and a single crystal Thermally induced birefringence in polycrystalline ceramics Ceramics description Depolarization in single crystal and polycrystalline ceramics Birefringence compensation in polycrystalline ceramics Conclusion 3 Introduction. Structure of polycrystalline ceramics. 4 Polycrystalline ceramics vs glass and single crystal. Properties. 5 Depolarization in single crystal and ceramics. Thermo-induced birefringence. angle of declination of eigen polarizations r, phases delay between eigen polarizations r, L g Grain Jones matrix A g =A g (r, g g g, L g r e2e2 e 1 x y z k y x c, z x z x, a y, b x y z, c x y x y z r crystal/grain orientation Euler angles ( 6 Jones matrix of whole element (k realization) A(r, ,k A 1 (r, 1 1 1,L 1 A 2 (r, 2 2 2,L 2 A N (r, N N N,L N Local depolarization (r, ,k)= E out (r, ,k) /E in (r, ) Average (over realizations) local depolarization Integrated depolarization: k and its deviation : and Depolarization in single crystal and ceramics. Local and integrated. .. N E in (r, ) E out (r, ) 7 Mathematical statement of the problem. Assumptions. Nfixed 1.The number of grains, N within a beams path is fixed. orientationdoes not dependvicinal grains 2.The orientation of crystallographic axes in a certain grain does not depend on vicinal grains. fL g uniform angular partgaussianL g 3.The distribution function f(L g for a single grain is uniform with respect to the angular part and the gaussian with respect to L g 8 Ceramics description. Jones matrixes Quaternion formalism. Media without absorption is described by a unitary matrix U, That could be presented as 9 Ceramics description. Quaternion properties. (takes place for every imaginary unit) (takes place for two different imaginary units) Jones matrixes and quaternions for several typical optical elements - angle of declination, - phases delay between eigen polarizations 10 Difference between depolarization in single crystal and ceramics. List of parameters. - crystal constant p - normalized (unitless) heat power single crystal orientation , , 11 Difference between depolarization in single crystal and ceramics. Local depopolarization (r, ). J. Lu, Appl. Phys. Lett., 78, 2000 S. D. Sims, Applied Optics, 6, 1967 Analytical plot 0 1 12 Difference between depolarization in single crystal and ceramics. Integrated depopolarization . Integrated depopolarization, % ceramics N= [111] single crystal normalized heat power + N=30 o N=100 N=300 13 Birefringence compensation in active elements. Typical schemes active element active element 1a1a W.Scott, M. De Wit Appl. Phys. Lett. 18, 3, 1973 V.Gelikonov et al. JETF lett., 13, 775, 1987 Faraday mirror active element ll 45 0 uniaxial crystal active element 1b1b 1c1c ll active element /4 2a2a /2 active element active element 2b2b W.A. Clarkson. et al. Opt. Lett., 24, 820, 1999 E.Khazanov et al. JOSA B, 19, 667, 2002 14 at pN -1