Effect of the Thermal Lensing on stable Region, Beam Waist and Astigmatic Compensation of Z-fold Cr4+ : YAG laser Cavity

Cr4+ : YAG 레이저에서 열 렌즈 효과에 따른 공진기의 안정영역과 빔 허리 및 비점수차의 보상

  • Lee, Bong-Yeon (Research institute of Basic Sciences, Chungnam National University)
  • 이봉연 (충남대학교 기초과학연구원)
  • Published : 2006.10.25


We obtained analytic solutions of boundary conditions to the stable region of Z-fold $Cr^{4+}$ : YAG laser cavity when the conditions are with and without thermal tensing effect. Also we investigated the influence of the thermal tensing effect on the stability of cavity, beam waist, and astigmatic compensation using aberration transformation matrices. The thermal tensing effect almost has no influence on the stable region of the cavity when the crystal is located in the middle of two concave mirrors and when the distances from the concave mirror to the reflecting mirror and the output coupler are the same. The beam waist, however, is affected more in a tangential plane than in a sagittal plane, and so it is difficult to have astigmatic compensation when the thermal tensing effect exists. This result means that the thermal tensing effect should be considered even for the Kerr-lens mode-locking.


  1. H. Daido, S. ninomiya, M. takagi, Y. Kato, and F. Koike, 'Wavelength measurement of the Ni-like soft-x-ray lasing lines and comparison to the atomic-physics calculation', J. Opt. Soc. Am. B16, pp. 296-300, 1999
  2. B. E. Lemoff, G. Y. yin, C. L. Gordon , C. P. J. Barty, and S. E. Harris, 'Demonstration of a 10-Hz Femtosecond-Pulse-Driven XUV Laser at 41.8nm in Xe IX Phys. Rev. Lett. 74, pp. 1574-1577, 1995
  3. S. Sebban, R. Haroutunian, Ph. Balcou, G. Grillon, A. Rousse, S. Kazamias, T. Marin, J. P. Rousseau, L. Notebaert, M. Pittman, J. P. Chambaret, A. Antonetti, D. Hulin, D. Ros, A. Klisnick, A. Carillon, P. Jaegle, G. Jamelot, and J. F. Wyart, 'Saturated Amplification of a Collisionally Pumped Optical-Field-Ionization Soft X-Ray Laser at 41.8 nm', Phys. Rev. Lett. 86, No. 14, pp. 3004-3007, 2001
  4. Y. P. Tong, P. M. W. French, J. R. Taylor, and J. G. Fujimoto, 'All-solid-state femtosecond sources in the near infrared', Opt. Commun. 136, pp. 235-238, 1997
  5. D. J. Ripjn, C. Chudoda, J. T. Gopinath, J. G. Fujimoto, and E. P. Ippen, U. Morgner, F. X. Kartner, V. Scheuer, G. Angelow, and T. Tschudi, 'Generation of 20-fs pulses by a prismless Cr4+:YAG laser', Opt. Lett. vol. 27, no. 1, pp. 61-63, 2002
  6. 조원배, 이상민, 김종두, 전민용, 서호성, '수동 모드 잠금된 100 MHz $Cr^{4+}:YAG$ 레이저에서의 펨토초 펄스 발생', 한국광학회지, 제16권 제6호, pp. 535-541, 2005
  7. L. I. Krutova, N. A. Kulabin, V. A. Sandulenko, and A. V. Sandulenko, 'Electronic state and positions of chromium ions in garnet crystals', Sov. Phys. Solid State, 31, 1193, 1989
  8. 이봉연, 이동한, 이치원, 윤석범, 추한태, '극초단 펄스 $Cr^{4+}:YAG$ 레이저의 제작 및 동작특성', 한국광학회지, 제15권 제5호, pp. 455-460, 2004
  9. J. E. Geusic, H. M. Marcos, and L. G. Van Uitert, 'Laser oscillations in Nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets', Appl. Phys. Lett., 4, 182, 1964
  10. G. M. Zverev and A. V. Shestakov, 'Tunable near-infrared oxide crystal lasers', in OSA proceedings on tunable Solid-State Lasers, Optical Society of America, Washington, D. C., 5, p. 66, 1989
  11. W. Jia, B. M. Tissue, L. Lu, K. R. Hoffman, and W. M. Yen, 'Near-infrared luminescence in Cr, Ca-doped yttrium aluminum garnet', in OSA proceedings on advanced Solid-State Lasers, G. Dube and L. Chase, eds., Optical Society of America, Washington, D. C., 10, p. 87, 1991
  12. S. Kuck, L. Petermann, and G. Huber, 'Spectroscopic investigation of the $Cr^{4+}-center$ in YAG', in OSA proceedings on advanced Solid-State Lasers, G. Dube and L. Chase, eds., Optical Society of America, Washington, D. C., 10, p. 92, 1991
  13. F. A. Jenkins and H. E. White, Fundamentals of Optics, McGraw-Hill Inc., 1976
  14. P. W. Milonni, and Joseph H. Eberly, Lasers, A Wiley Interscience Publication, Chap. 14
  15. X. G. Huang, W. K. Lee, S. P. Wong, S. Y. Zhang, and Z. X. Yu, 'Stable properties of Ti:sapphire laser', in Solid State Laser and Nonlinear Optics, G. J. Quarles, L. Esterowitz, L. K. Cheng, and M. S. Sobey, eds., Proc. SPIE 2379, 73-82, 1995
  16. X. G. Huang, W. K. Lee, S. P. Wong, S. Y. Zhang, and Z. X. Yu, 'Effects of thermal lensing on stability and astigmatic compensation of a Z-fold laser cavity', J. Opt. Soc. Am. B, 13, 2863, 1996
  17. D. Georgiev, J. Herrmann, and U. Stamm, 'Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers', Opt. Commun. 92, 368-375, 1992
  18. A. Sennaroglu, 'Continuous wave thermal loading in saturable absorbers : theory and experiment', Applied Optics, Vol. 36, No. 36, 9528-9535, 1997
  19. A. Yariv, Quantum Electronics, Wiley, New York, 1988
  20. H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, 'Astigmatically compensated cavities for CW dye lasers', IEEE J. Quantum Electron., QE-8, 373, 1972