[PDF]    http://dx.doi.org/10.3952/physics.v56i2.3302

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 56, 67–78 (2016)
CONDITIONS FOR REDUCING SPHERICAL THERMAL ABERRATIONS IN TRANSVERSALLY PUMPED YAG RODS
Dominykas Bričkus and Aleksandr S. Dement’ev
Center for Physical Sciences and Technology, Savanorių 231, LT-02300 Vilnius, Lithuania
E-mail: aldement@ktl.mii.lt

Received 7 March 2016; revised 18 April 2016; accepted 21 June 2016

Temperature dependences of the thermal conductivity and thermo-optic coefficient are often neglected when thermal lensing in laser crystals is investigated, though their influence is very significant. In this paper, the general solution of heat transfer equation with temperature dependent thermal conductivity is found in an integral form, which is very convenient for analytical and numerical analysis. Using this solution, the possibility to eliminate spherical aberration by a proper choice of the pump parabolicity parameter is investigated in detail. The inaccuracies in the definition of optical path differences used in a few previous works for the case of temperature dependent thermo-optic coefficient are explained. It is shown that the use of a correct definition increases the value of the parabolic coefficient at which the elimination of spherical aberrations may be realized as compared with the original work of Hodgson and Weber. It is also found that nearly the same shapes of pumping are required for elimination of spherical aberrations for both radial and tangential polarization.
Keywords: solid-state laser, thermal effect, spherical aberration
PACS: 42.25.Lc, 42.55.Xi, 78.20.hb

SĄLYGOS MAŽINTI ŠILUMINES SFERINES ABERACIJAS IŠ ŠONO KAUPINAMUOSE YAG STRYPUOSE
Dominykas Bričkus, Aleksandr S. Dement’ev
Fizinių ir technologijos mokslų centras, Vilnius, Lietuva

Šiluminio laidumo ir termooptinio koeficiento dn/dT temperatūrinės priklausomybės yra vienas pagrindinių veiksnių, lemiančių šiluminių aberacijų atsiradimą, tačiau jos ne visada yra įskaitomos nagrinėjant šiluminius lęšius kietojo kūno lazeriuose. Šiame darbe rastas šiluminės lygties su temperatūriškai priklausančiu šiluminio laidumo koeficientu bendras integralinės išraiškos pavidalo sprendinys, patogus naudoti tiek analitinei, tiek skaitinei analizei. Pasitelkus šį sprendinį detaliai išnagrinėta galimybė panaikinti šilumines sferines aberacijas parenkant tam tikros formos parabolinį kaupinimo pasiskirstymą.
Aptarti optinio kelio skirtumo apibrėžimų, naudojamų ankstesniuose darbuose, netikslumai, kai termooptinis koeficientas priklauso nuo temperatūros. Parodyta, kad naudojant teisingą apibrėžimą parabolinio koeficiento vertė, kai pasiekiamas sferinių aberacijų panaikinimas, padidėja, palyginti su gaunama naudojant Hodgsono ir Weberio išraišką. Taip pat rasta, kad tiek radialinės, tiek tangentinės poliarizacijos sferinėms aberacijoms panaikinti reikalinga beveik ta pati kaupinimo forma.
References / Nuorodos

[1] A.V. Mezenov, L.N. Soms, and A.I. Stepanov, Thermooptics of solid-state lasers, J. Russ. Laser Res. 8(5), 427–549 (1987),
http://dx.doi.org/10.1007/BF01120583
[2] N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer, Berlin, 1997)
[3] N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer, Berlin, 2005),
http://dx.doi.org/10.1007/b106789
[4] W. Koechner, Solid-State Laser Engineering, 6th revised and updated ed. (Springer, Berlin, 2006),
http://dx.doi.org/10.1007/0-387-29338-8
[5] S. Chénais, F. Druon, S. Forget, F. Balembois, and P. Georges, On thermal effects in solid-state lasers: The case of ytterbium-doped materials, Prog. Quantum Electron. 30(4), 89–153 (2006),
http://dx.doi.org/10.1016/j.pquantelec.2006.12.001
[6] A.G. Rozanov, Nonlinear model of thermal effects in YAG:Nd laser crystals, Sov. J. Quantum Electron. 21(10), 1074–1075 (1992),
http://dx.doi.org/10.1070/QE1991v021n10ABEH004286
[7] N. Hodgson and H. Weber, Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers, IEEE J. Quant. Electron. 29(3), 2497–2507 (1993),
http://dx.doi.org/10.1109/3.247707
[8] W.A. Clarkson, Thermal effects and their mitigation in end-pumped solid-state lasers, J. Phys. D 34(16), 2381–2395 (2001),
http://dx.doi.org/10.1088/0022-3727/34/16/302
[9] S. Bjurshagen and R. Koch, Modeling of energy-transfer upconversion and thermal effects in end-pumped quasi-three-level lasers, Appl. Opt. 43(24), 4753–4767 (2004),
http://dx.doi.org/10.1364/AO.43.004753
[10] A.M. Bonnefois, M. Gilbert, P.Y. Thro, and J.M. Weulersse, Thermal lensing and spherical aberration in high-power transversally pumped laser rods, Opt. Commun. 259(1), 223–235 (2006),
http://dx.doi.org/10.1016/j.optcom.2005.08.041
[11] X. Song, B. Li, Z. Guo, S. Wang, D. Cai, and J. Wen, Influences of pump beam distribution on thermal lensing spherical aberration in an LD end-pumped Nd:YAG laser, Opt. Commun. 282(24), 4779–4783 (2009),
http://dx.doi.org/10.1016/j.optcom.2009.09.016
[12] A.M. Rodin, A. Michailovas, A.S. Dementjev, and A. Aleknavicius, Beam quality investigation in Nd:YAG crystal fiber amplifier pumped at >110 W, Proc. SPIE 9342, 934207 (2015),
http://dx.doi.org/10.1117/12.2079294
[13] A.S. Dement'ev, A. Jovaiša, K. Račkaitis, F. Ivanauskas, and J. Dabulytė-Bagdonavičienė, Numerical treatment of the temperature distribution in end-pumped composite laser rods, Lith. J. Phys. 47(3), 279–288 (2007),
http://dx.doi.org/10.3952/lithjphys.47316
[14] G.L. Bourdet and H. Yu, Longitudinal temperature distribution in an end-pumped solid-state amplifier medium: application to a high average power diode pumped Yb:YAG thin disk amplifier, Appl. Opt. 46(23), 6033–6041 (2007),
http://dx.doi.org/10.1364/AO.46.006033
[15] G.L. Bourdet and C. Gouédard, Simple analytical derivations of thermal lensing in longitudinally Q-CW pumped Yb:YAG, Appl. Opt. 49(22), 4160–4167 (2010),
http://dx.doi.org/10.1364/AO.49.004160
[16] M.M. Tilleman, Analysis of temperature and thermo-optical properties in optical materials. 1: Cylindrical geometry, Opt. Mater. 33(1), 48–57 (2010),
http://dx.doi.org/10.1016/j.optmat.2010.07.015
[17] M.H.M. Dindarlu, A. Maleki, H. Saghafifar, M.K. Tehrani, and S. Baghali, Analytical model for temperature, stress and strain distribution inside a side-pumped Nd:YAG laser rod having a Gaussian pump profile, Laser Phys. 25(4), 045001 (2015),
http://dx.doi.org/10.1088/1054-660X/25/4/045001
[18] H. Furuse, R. Yasuhara, and K. Hiraga, Thermooptic properties of ceramic YAG at high temperatures, Opt. Mater. Express 4(9), 1794–1799 (2014),
http://dx.doi.org/10.1364/OME.4.001794
[19] A.S. Dement'ev, Relationships between different expressions of thermo-optic and photoelastic coefficients of YAG crystal, Laser Phys. 25(9), 095004 (2015),
http://dx.doi.org/10.1088/1054-660X/25/9/095004
[20] B.S. Wang, H.H. Jiang, and S.T. Yin, Thermal conductivity of synthetic garnet laser crystals, Eur. Phys. J. Appl. Phys. 39(1), 23–26 (2007),
http://dx.doi.org/10.1051/epjap:2007091
[21] Y. Sato, J. Akiyama, and T. Taira, Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals, Opt. Mater. 31(5), 720–724 (2009),
http://dx.doi.org/10.1016/j.optmat.2008.10.040
[22] M. Polnau, P.J. Hardman, M.A. Kern, W.A. Clarkson, and D.C. Hanna, Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG, Phys. Rev. B 58(24), 16076–16092 (1998),
http://dx.doi.org/10.1103/PhysRevB.58.16076
[23] R.L. Aggarwal, D.J. Ripin, J.R. Ochoa, and T.Y. Fan, Measurement of thermo-optical properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range, J. Appl. Phys. 98, 103514 (2005),
http://dx.doi.org/10.1063/1.2128696
[24] D.C. Brown, Nonlinear thermal and stress effects and scaling behaviour of YAG slab amplifiers, IEEE J. Quant. Electron. 34(12), 2393–2402 (1998),
http://dx.doi.org/10.1109/3.736114
[25] D.C. Brown, Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers, IEEE J. Quant. Electron. 33(5), 861–873 (1997),
http://dx.doi.org/10.1109/3.572162
[26] B.A. Reznikov, Yu.I. Sirotin, and N.E. Voropaeva, Determination of the temperature dependence of the piezo-optical and elasto-optical coefficients of crystals, Phys. Status Solidi 33(2), 633–640 (1969),
http://dx.doi.org/10.1002/pssb.19690330217
[27] R.W. Dixon, Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners, J. Appl. Phys. 38(13), 5149–5153 (1967),
http://dx.doi.org/10.1063/1.1709293
[28] A.S. Dement'ev, A. Jovaiša, E. Stupak, and R. Kačianauskas, Thermal stresses and end-bulging in cylindrical laser rods under longitudinal diode laser pumping, J. Therm. Stresses 37(1), 73–92 (2014),
http://dx.doi.org/10.1080/01495739.2013.839462
[29] E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tzuk, and A. Meir, Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump-distribution control, in: Advanced Solid State Photonics 2005, OSA Trends in Optics and Photonics Series (Optical Society of America, 2005),
http://dx.doi.org/10.1364/ASSP.2005.MB45
[30] S. Radmard, A. Haghparast, S. Arabgari, and M.T. Mehrabani, High-power Yb:YAG/YAG microchip laser using octagonal-shape waveguide with uniform absorbed power distribution, Opt. Laser Technol. 48(1), 44–51 (2013),
http://dx.doi.org/10.1016/j.optlastec.2012.09.027