Current Optics and Photonics

Optical Society of Korea (한국광학회)
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Fully Analytic Approach to Evaluate Laser-induced Thermal Effects

  • Kim, Myungsoo (Department of Mechanical Design Engineering, Youngsan University) ;
  • Kwon, Gyeong-Pil (Department of Science Education, Gyeongin National University of Education) ;
  • Lee, Jinho (The Research Institute of Natural Science and Department of Physics Education, Gyeongsang National University)
  • Received : 2017.08.22
  • Accepted : 2017.09.27
  • Published : 2017.12.25
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Abstract

In this communication, we present an expression to determine thermal lensing in isotropic materials. The heat equation is analytically solved when a Gaussian spatial laser beam profile is introduced to a cylindrical geometry of optics using a complete set of Bessel functions. This expression permits explicit calculation of variation of focal length induced by thermal lensing and allows thermal effects for various material parameters on the optics. We applied our model to a high absorption material (Ti:sapphire) and also transparent material (thallium garnet or TGG) and found that the thermal lensing can be reduced more than 4 times by adjusting the laser beam waist and optics dimensions. Our analysis is completely general and applicable to any optical system.

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References

  1. J. D. Mansell, J. Hennawi, E. K. Gustafson, M. M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, "Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor," Appl. Opt. 40, 366 (2001). https://doi.org/10.1364/AO.40.000366
  2. V. Quetschke, J. Gleason, M. Rakhmanov, J. Lee, L. Zhang, K. Y. Franzen, C. Leidel, G. Mueller, R. Amin, D. B. Tanner, and D. H. Reitze, "Adaptive control of laser modal properties," Opt. Lett. 31, 217 (2006). https://doi.org/10.1364/OL.31.000217
  3. Z. Liu, P. Fulda, M. A. Arain, L. Williams, G. Mueller, D. B. Tanner, and D. H. Reitze, "Feedback control of optical beam spatial profiles using thermal lensing," App. Opt. 52, 6452 (2013).
  4. W. Koechner, Solid-state laser engineering (Springer-Verlag, 1998), Chapter 7.
  5. V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H Reitze, "Analysis of thermal aberrations in a high average power single-stage Ti: sapphire regenerative chirped pulse amplifier: Simulation and experiment," Rev. Sci. Instrum. 77, 103103 (2006). https://doi.org/10.1063/1.2360989
  6. B. Neuenschwander, R. Weber, and H. P. Weber, "Determination of the thermal lens in solid-state lasers with stable cavities," IEEE J. Quantum Electron. 31, 1082 (1995). https://doi.org/10.1109/3.387046
  7. G. Wagner, M. Shiler, and V. Wulfmeyer, "Simulations of thermal lensing of a Ti:Sapphire crystal end-pumped with high average power," Opt. Express 13, 8045 (2005). https://doi.org/10.1364/OPEX.13.008045
  8. G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, "Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers," Classical Quantum Gravity 19, 1793 (2002). https://doi.org/10.1088/0264-9381/19/7/376
  9. M. Adier, F. Aguilar, and T. Akutsu et al., "Progress and challenges in advanced ground-based gravitational-wave detectors." Gen. Relativ. Gravitation 46, 1749 (2014). https://doi.org/10.1007/s10714-014-1749-4
  10. E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermooptical compensation methods for high-power lasers," IEEE J. Quantum Electron. 38, 1620 (2002). https://doi.org/10.1109/JQE.2002.805105
  11. M. A. Arain, V. Quetschke, J. Gleason, L. F. Williams, M. Rakhmanov, J. Lee, R. J. Cruz, G. Mueller, D. B. Tanner, and D. H. Reitze, "Adaptive beam shaping by controlled thermal lensing in optical elements," Appl. Opt. 46, 2153 (2007). https://doi.org/10.1364/AO.46.002153
  12. R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, "Active correction of thermal lensing through external radiative thermal actuation," Opt. Lett. 22, 2635 (2004).
  13. S. Sato, "Liquid-crystal lens-cell with variable focal length," Jpn. J. Appl. Phys. 18, 1679 (1979). https://doi.org/10.1143/JJAP.18.1679
  14. J. Schwarz, M. Geissel, P. Rambo, J. Porter, D. Headley, and M. Ramsey, "Development of a variable focal length concave mirror for on-shot thermal lens correction in rod amplifiers," Opt. Express 14, 10957 (2006). https://doi.org/10.1364/OE.14.010957
  15. K. Dobek, M. Baranowski, J. Karolczak, D. Komar, K. Kreczmer, and J. Szuniewicz, "Thermal lens in a liquid sample with focal length controllable by bulk temperature," Appl. Phys. B 122, 151 (2016).
  16. T. A. Meyers, Encyclopedia of analytical chemistry (John Wiley & Sons Ltd 2010).
  17. J. Moreau and V. Loriette, "Confocal thermal-lens microscope," Opt. Lett. 29, 1488 (2004). https://doi.org/10.1364/OL.29.001488
  18. W. Koechner, "Thermal lensing in a Nd:YAG laser rod," Appl. Opt. 9, 2548 (1970). https://doi.org/10.1364/AO.9.002548
  19. U. O. Farrukh, A. M. Buoncristiani, and C. E. Byvik, "An analysis of the temperature distribution in finite solid-state laser rods," IEEE J. Quantum Electron. 24, 2253 (1998).
  20. M. Innocenzi, H. Yura, C. Fincher, and R. Fields, "Thermal modeling of continuous-wave end-pumped solid-state lasers," Appl. Phys. Lett. 56, 1831 (1990). https://doi.org/10.1063/1.103083
  21. A. Cousins, "Temperature and thermal stress scaling in finitelength end-pumped laser rods," IEEE J. Quantum Electron. 28, 1057 (1992). https://doi.org/10.1109/3.135228
  22. M. Schmid, T. Graf, and H. P. Weber, "Analytical model of the temperature distribution and the thermally induced birefringence in laser rods with cylindrically symmetric heating," J. Opt. Soc. Am. B 17, 1398 (2000). https://doi.org/10.1364/JOSAB.17.001398
  23. H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids (Oxford Univ. 1948).
  24. J. Lee, and D. H. Reitze, "Analytic spatial and temporal temperature profile in a finite laser rod with input laser pulses," Opt. Express 23, 2591 (2015). https://doi.org/10.1364/OE.23.002591
  25. F. Kreitha and M. S. Bohn, Principle of heat transfer, 6th ed. (Brooks/Cole, CA, USA, 2001).
  26. G. P. Kwon and J. Lee, "Self-adaptive thermal-lensing compensation for a high-power laser," J. Korean Phys. Soc. 69, 1531 (2016). https://doi.org/10.3938/jkps.69.1531
  27. R. Lausten, and P. Balling, "Thermal lensing in pulsed laser amplifiers: an analytical model," J. Opt. Soc. Am. B 20, 1479 (2003). https://doi.org/10.1364/JOSAB.20.001479
  28. A. H. Farhadian, H. Saghaffier, and M. Dehghanbaghi, "Calculation of thermal lensing in end-pumped $YVO_4$/ Nd:$YVO_4$ composite crystals in view of the temperature distribution," J. Russ Laser Res. 36, 350 (2015). https://doi.org/10.1007/s10946-015-9509-9
  29. M. N. Ozisik, Boundary value problems of heat conduction (Dover Publications, INC 1968), pp. 457.
  30. M. Sameti and A. Kasaeian, "Heat diffusion in an anisotropic medium with central heat source," Int. J. Partial Differ. Equations Appl. 2, 23 (2014).
  31. S. Ito, H. Nagaoka, T. Kobayashi, A. Endo and K. Torizuka, "Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser," Appl. Phys. B 74, 343 (2002). https://doi.org/10.1007/s003400200812