Resonators with Variable Internal Lenses

  • Norman Hodgson
  • Horst Weber


In solid state lasers the active medium exhibits the properties of a thermally induced lens when the material is pumped. The refractive power is brought about by a combination of heat generation due to absorption of pump and laser radiation and the flow of heat to the outer periphery due to cooling. For a laser rod this leads to a temperature distribution which is parabolic with respect to the radial position r if the thermal conductivity is constant and the medium is illuminated homogeneously by the excitation source (Fig 12.1). This results in a similar radial dependence of the index of refraction:
$$n(r) = {n_0}\;(1\; - \;\gamma {r^2})$$
where n 0 is the index of refraction at the center. A bundle of parallel rays incident on the laser rod is focused by the thermal lens for γ > 0 since the optical path length n(r)ℓ inside the medium is longer for rays being closer to the center of the rod.


Pump Power Beam Quality Stable Zone Beam Quality Factor Refractive Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 4.41
    H. Kogelnik, Imaging of optical modes-resonators with internal lenses, Bell Syst. Tech. J. 44, 455, 1965Google Scholar
  2. 4.42
    C.M. Stickley, Laser brightness gain and mode control by compensation for thermal distortion, IEEE J. Quantum Electron. 2, 511, 1966CrossRefGoogle Scholar
  3. 4.43
    L.M. Osterink, L.D. Foster, Thermal effects and transverse mode control in a Nd:YAG laser, Appl. Phys. Lett. 12, 128, 1968CrossRefGoogle Scholar
  4. 4.44
    W. Koechner, Absorbed pump power, thermal profile and stress in a cw-pumped Nd:YAG laser rod, Appl. Opt. 9, 1429, 1970CrossRefGoogle Scholar
  5. 4.45
    W. Koechner, Thermal lensing in a Nd:YAG laser rod, Appl. Opt. 9, 2548, 1970CrossRefGoogle Scholar
  6. 4.46
    J.D. Foster, L.M. Osterink, Thermal effects in a Nd:YAG laser, J. Appl. Phys. 41, 3656, 1970CrossRefGoogle Scholar
  7. 4.47
    F.A. Levine, TEM00 enhancement in cw Nd:YAG by thermal lensing compensation, IEEE J. Quantum Electron. 7, 170, 1971CrossRefGoogle Scholar
  8. 4.48
    J. Steffen, J.P. Lörtschner, G. Herziger, Fundamental mode radiation with solid state lasers, IEEE J. Quantum Electron. 8, 239, 1972CrossRefGoogle Scholar
  9. 4.49
    T.J. Gleason, J.S. Kruger, R.M. Curnutt, Thermally induced focusing in a Nd:YAG laser rod at low input powers, Appl. Opt. 12, 2942, 1973Google Scholar
  10. 4.50
    J.P. Lörtschner, J. Steffen, G Herziger, Dynamic stable resonators: a design procedure, Opt. Quantum Electron. 7, 505, 1975CrossRefGoogle Scholar
  11. 4.51
    P.H. Sarkies, A stable YAG resonator yielding a beam of very low divergence and high output energy, Opt. Commun. 31, 189, 1979CrossRefGoogle Scholar
  12. 4.52
    R. Iffländer, H.P. Kortz, H. Weber, Beam divergence and refractive power of directly coated solid-state lasers, Opt. Comm 29, 223, 1979CrossRefGoogle Scholar
  13. 4.53
    H.P. Kortz, R. Iffländer, H. Weber, Stability and beam divergence of multimode lasers with internal variable lenses, Appl. zOpt. 20, 4124, 1981CrossRefGoogle Scholar
  14. 4.54
    A. J. Berry, D.C. Hanna, C.G. Swayers, High power single frequency operation of a Q-switched TEM00 mode Nd:YAG laser, Opt. Commun. 40, 54, 1981CrossRefGoogle Scholar
  15. 4.55
    D.C. Hanna, C.G. Swayers, M.A. Yuratich, Telescopic resonators for large volume TEM00 mode operation, Opt. Quantum Electron. 13, 493, 1981CrossRefGoogle Scholar
  16. 4.56
    V. Magni, Resonators for solid state lasers with large-volume fundamental mode and high alignment stability, Appl. Opt. 25, 2039, 1986CrossRefGoogle Scholar
  17. 4.57
    S. DeSilvestri, P. Laporta, V. Magni, Misalignment sensitivity of solid-state laser resonators with thermal lensing, Opt. Commun. 59, 43, 1986CrossRefGoogle Scholar
  18. 4.58
    R. Iffländer, H. Weber, Focusing of multimode laser beams with variable beam parameters, Optica Acta 33, 1083, 1086CrossRefGoogle Scholar
  19. 4.59
    H. Weber, Iffländer, P. Seiler, High power Nd-lasers for industrial applications, Proceedings of the Society of Photo-Optical Instrumentation Engineers vol. 650, 92, 1986Google Scholar
  20. 4.60
    J.S. Uppal, J.C. Monga, F.D. Bhawalkar, Analysis of an unstable confocal ring laser with a thermally induced active medium, Appl. Opt. 25, 1389, 1986CrossRefGoogle Scholar
  21. 4.61
    V. Magni, Multi-element stable resonators containing a variable lens, J. Opt. Soc. Am. A 4, 1962, 1987CrossRefGoogle Scholar
  22. 4.62
    D. Metcal, P. de Giovanni, J. Zachorowski, M. Leduc, Laser resonators containing self-focusing elements, Appl. Opt. 26, 4508, 1987CrossRefGoogle Scholar
  23. 4.63
    N. Hodgson, H. Weber, High power solid state lasers with unstable resonators, Opt. Quantum Electron. 22(39), 39, 1990CrossRefGoogle Scholar
  24. 4.64
    V. Magni, S. deSilvestri, L-J. Qian, O. Svelto, Rod-imaging supergaussian unstable resonator for high power solid state lasers, Opt. Commun. 94, 87, 1992CrossRefGoogle Scholar
  25. 4.65
    N. Hodgson, C. Rahlff, H. Weber, Dependence of the refractive power of Nd:YAG on the intracavity-intensity, Opt. & Laser Techn. 25(3), 179, 1993CrossRefGoogle Scholar
  26. 4.66
    N. Hodgson, G. Bostanjoglo, The near-concentric unstable resonator (NCUR) — an improved resonator design for high power solid state lasers, Opt. Commun. 99, 75, 1993CrossRefGoogle Scholar
  27. 4.67
    N. Hodgson, H. Weber, Influence of spherical aberration of the active medium on the performance of Nd: YAG lasers, IEEE J. Quantum Electron. 29, 2497, 1993CrossRefGoogle Scholar
  28. 4.68
    N. Hodgson, D.J. Golding, D. Eisel, Efficient high power operation at 1.44um of Nd-doped crystals, Proceedings of the Society of Photo-Optical Instrumentation Engineers vol. 2206, High power gas and solid state lasers, 426, 1994Google Scholar
  29. 4.69
    R. Martinez-Herrero, P.M. Mejias, N. Hodgson, H. Weber, Beam-quality changes generated by thermally-induced spherical aberration in laser cavities, IEEE J. Quantum Electron. 31, 2173, 1995CrossRefGoogle Scholar
  30. 4.70
    K. Yasui, Efficient and stable operation of a high-brightness cw 500-W Nd:YAG rod laser, Appl. Opt. 35(15), 2566, 1996CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 1997

Authors and Affiliations

  • Norman Hodgson
    • 1
  • Horst Weber
    • 2
  1. 1.Humphrey InstrumentsCarl Zeiss Inc.San LeandroUSA
  2. 2.Optisches InstitutTechnische Universität BerlinBerlinGermany

Personalised recommendations