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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  1. J. D. Mansell, J. Hennawi, E. K. Gustafson, M. M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. ReitzeEvaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensorAppl. Opt.200140366
  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. ReitzeAdaptive control of laser modal propertiesOpt. Lett.200631217
  3. Z. Liu, P. Fulda, M. A. Arain, L. Williams, G. Mueller, D. B. Tanner, and D. H. ReitzeFeedback control of optical beam spatial profiles using thermal lensingApp. Opt.2013526452
  4. W. KoechnerSolid-state laser engineeringChapter 7Springer-Verlag1998
  5. V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H ReitzeAnalysis of thermal aberrations in a high average power single-stage Ti: sapphire regenerative chirped pulse amplifier: Simulation and experimentRev. Sci. Instrum.200677103103
  6. B. Neuenschwander, R. Weber, and H. P. WeberDetermination of the thermal lens in solid-state lasers with stable cavitiesIEEE J. Quantum Electron.1995311082
  7. G. Wagner, M. Shiler, and V. WulfmeyerSimulations of thermal lensing of a Ti:Sapphire crystal end-pumped with high average powerOpt. Express2005138045
  8. G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. TannerMethod for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometersClassical Quantum Gravity2002191793
  9. M. Adier, F. Aguilar, T. Akutsu, and et al.Progress and challenges in advanced ground-based gravitational-wave detectorsGen. Relativ. Gravitation2014461749
  10. E. Wyss, M. Roth, T. Graf, and H. P. WeberThermooptical compensation methods for high-power lasersIEEE J. Quantum Electron.2002381620
  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. ReitzeAdaptive beam shaping by controlled thermal lensing in optical elementsAppl. Opt.2007462153
  12. R. Lawrence, D. Ottaway, M. Zucker, and P. FritschelActive correction of thermal lensing through external radiative thermal actuationOpt. Lett.2004222635
  13. S. SatoLiquid-crystal lens-cell with variable focal lengthJpn. J. Appl. Phys.1979181679
  14. J. Schwarz, M. Geissel, P. Rambo, J. Porter, D. Headley, and M. RamseyDevelopment of a variable focal length concave mirror for on-shot thermal lens correction in rod amplifiersOpt. Express20061410957
  15. K. Dobek, M. Baranowski, J. Karolczak, D. Komar, K. Kreczmer, and J. SzuniewiczThermal lens in a liquid sample with focal length controllable by bulk temperatureAppl. Phys. B2016122151
  16. T. A. MeyersEncyclopedia of analytical chemistryJohn Wiley & Sons Ltd2010
  17. J. Moreau and V. LorietteConfocal thermal-lens microscopeOpt. Lett.2004291488
  18. W. KoechnerThermal lensing in a Nd:YAG laser rodAppl. Opt.197092548
  19. U. O. Farrukh, A. M. Buoncristiani, and C. E. ByvikAn analysis of the temperature distribution in finite solid-state laser rodsIEEE J. Quantum Electron.1998242253
  20. M. Innocenzi, H. Yura, C. Fincher, and R. FieldsThermal modeling of continuous-wave end-pumped solid-state lasersAppl. Phys. Lett.1990561831
  21. A. CousinsTemperature and thermal stress scaling in finite-length end-pumped laser rodsIEEE J. Quantum Electron.1992281057
  22. M. Schmid, T. Graf, and H. P. WeberAnalytical model of the temperature distribution and the thermally induced birefringence in laser rods with cylindrically symmetric heatingJ. Opt. Soc. Am. B2000171398
  23. H. S. Carslaw and J. C. JaegerConduction of heat in solidsOxford Univ1948
  24. J. Lee and D. H. ReitzeAnalytic spatial and temporal temperature profile in a finite laser rod with input laser pulsesOpt. Express2015232591
  25. F. Kreitha and M. S. BohnPrinciple of heat transfer6th edBrooks/ColeCA, USA2001
  26. G. P. Kwon and J. LeeSelf-adaptive thermal-lensing compensation for a high-power laserJ. Korean Phys. Soc.2016691531
  27. R. Lausten and P. BallingThermal lensing in pulsed laser amplifiers: an analytical modelJ. Opt. Soc. Am. B2003201479
  28. A. H. Farhadian, H. Saghaffier, and M. DehghanbaghiCalculation of thermal lensing in end-pumped YVO4/Nd:YVO4 composite crystals in view of the temperature distributionJ. Russ Laser Res.201536350
  29. M. N. OzisikBoundary value problems of heat conductionDover Publications, INC1968457
  30. M. Sameti and A. KasaeianHeat diffusion in an anisotropic medium with central heat sourceInt. J. Partial Differ. Equations Appl.2014223
  31. S. Ito, H. Nagaoka, T. Kobayashi, A. Endo, and K. TorizukaMeasurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laserAppl. Phys. B200274343

Other (31)

J. D. Mansell, J. Hennawi, E. K. Gustafson, M. M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. ReitzeEvaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensorAppl. Opt.200140366

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. ReitzeAdaptive control of laser modal propertiesOpt. Lett.200631217

Z. Liu, P. Fulda, M. A. Arain, L. Williams, G. Mueller, D. B. Tanner, and D. H. ReitzeFeedback control of optical beam spatial profiles using thermal lensingApp. Opt.2013526452

W. KoechnerSolid-state laser engineeringChapter 7Springer-Verlag1998

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H ReitzeAnalysis of thermal aberrations in a high average power single-stage Ti: sapphire regenerative chirped pulse amplifier: Simulation and experimentRev. Sci. Instrum.200677103103

B. Neuenschwander, R. Weber, and H. P. WeberDetermination of the thermal lens in solid-state lasers with stable cavitiesIEEE J. Quantum Electron.1995311082

G. Wagner, M. Shiler, and V. WulfmeyerSimulations of thermal lensing of a Ti:Sapphire crystal end-pumped with high average powerOpt. Express2005138045

G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. TannerMethod for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometersClassical Quantum Gravity2002191793

M. Adier, F. Aguilar, T. Akutsu, and et al.Progress and challenges in advanced ground-based gravitational-wave detectorsGen. Relativ. Gravitation2014461749

E. Wyss, M. Roth, T. Graf, and H. P. WeberThermooptical compensation methods for high-power lasersIEEE J. Quantum Electron.2002381620

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. ReitzeAdaptive beam shaping by controlled thermal lensing in optical elementsAppl. Opt.2007462153

R. Lawrence, D. Ottaway, M. Zucker, and P. FritschelActive correction of thermal lensing through external radiative thermal actuationOpt. Lett.2004222635

S. SatoLiquid-crystal lens-cell with variable focal lengthJpn. J. Appl. Phys.1979181679

J. Schwarz, M. Geissel, P. Rambo, J. Porter, D. Headley, and M. RamseyDevelopment of a variable focal length concave mirror for on-shot thermal lens correction in rod amplifiersOpt. Express20061410957

K. Dobek, M. Baranowski, J. Karolczak, D. Komar, K. Kreczmer, and J. SzuniewiczThermal lens in a liquid sample with focal length controllable by bulk temperatureAppl. Phys. B2016122151

T. A. MeyersEncyclopedia of analytical chemistryJohn Wiley & Sons Ltd2010

J. Moreau and V. LorietteConfocal thermal-lens microscopeOpt. Lett.2004291488

W. KoechnerThermal lensing in a Nd:YAG laser rodAppl. Opt.197092548

U. O. Farrukh, A. M. Buoncristiani, and C. E. ByvikAn analysis of the temperature distribution in finite solid-state laser rodsIEEE J. Quantum Electron.1998242253

M. Innocenzi, H. Yura, C. Fincher, and R. FieldsThermal modeling of continuous-wave end-pumped solid-state lasersAppl. Phys. Lett.1990561831

A. CousinsTemperature and thermal stress scaling in finite-length end-pumped laser rodsIEEE J. Quantum Electron.1992281057

M. Schmid, T. Graf, and H. P. WeberAnalytical model of the temperature distribution and the thermally induced birefringence in laser rods with cylindrically symmetric heatingJ. Opt. Soc. Am. B2000171398

H. S. Carslaw and J. C. JaegerConduction of heat in solidsOxford Univ1948

J. Lee and D. H. ReitzeAnalytic spatial and temporal temperature profile in a finite laser rod with input laser pulsesOpt. Express2015232591

F. Kreitha and M. S. BohnPrinciple of heat transfer6th edBrooks/ColeCA, USA2001

G. P. Kwon and J. LeeSelf-adaptive thermal-lensing compensation for a high-power laserJ. Korean Phys. Soc.2016691531

R. Lausten and P. BallingThermal lensing in pulsed laser amplifiers: an analytical modelJ. Opt. Soc. Am. B2003201479

A. H. Farhadian, H. Saghaffier, and M. DehghanbaghiCalculation of thermal lensing in end-pumped YVO4/Nd:YVO4 composite crystals in view of the temperature distributionJ. Russ Laser Res.201536350

M. N. OzisikBoundary value problems of heat conductionDover Publications, INC1968457

M. Sameti and A. KasaeianHeat diffusion in an anisotropic medium with central heat sourceInt. J. Partial Differ. Equations Appl.2014223

S. Ito, H. Nagaoka, T. Kobayashi, A. Endo, and K. TorizukaMeasurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laserAppl. Phys. B200274343

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