OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 12, Iss. 4 — Apr. 1, 1973
  • pp: 710–718

Optics of Thermal Lensing in Solids

Bernard Bendow and Peter D. Gianino  »View Author Affiliations

Applied Optics, Vol. 12, Issue 4, pp. 710-718 (1973)

View Full Text Article

Enhanced HTML    Acrobat PDF (813 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The vector Kirchhoff approach to thermal lensing in solids is investigated. The relation of the thermal rise in the sample to the optics of lensing is elucidated. Various analytical results and series representations for the transmitted intensity are derived for the case of Gaussian beams incident on circular samples, in various special limits. An expression for the time-dependent shift in the diffraction focus is obtained. Numerical computations illustrating lensing effects both at small times and in the steady state are presented. Effects of stress-induced birefringence, including the oscillation of the maximum intensity and diffraction focus as a function of time, are illustrated. Similar effects are also shown to occur when the incident power or sample thickness is varied, for solids characterized by large stress-induced contributions.

© 1973 Optical Society of America

Original Manuscript: August 17, 1972
Published: April 1, 1973

Bernard Bendow and Peter D. Gianino, "Optics of Thermal Lensing in Solids," Appl. Opt. 12, 710-718 (1973)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. See, for example, J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, J. Appl. Phys. 36, 3 (1965). [CrossRef]
  2. A. Hordvik, in Conference on High Power Infrared Laser Window Materials, C. S. Sahagian, C. A. Pitha, Eds. (AFCRL-71-0592, 1971), p. 389.
  3. M. Sparks, J. Appl. Phys. 42, 5029 (1971); F. A. Horrigan, T. F. Deutsch, Raytheon Research Division Reports on Contract DAAH01-70-C-1251 (1970, unpublished); J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972); P. D. Gianino, J. R. Jasperse, AFCRL-72-0202(1972). [CrossRef]
  4. J. Marburger, M. Flannery, in Conference on High Power Infrared Laser Window Materials, C. S. Sahagian, C. A. Pitha, Eds. (AFCRL-71-0592, 1971), p. 11; D. A. Holmes, J. E. Korka, P. V. Avizonis, Appl. Opt. 11, 565 (1972). [CrossRef] [PubMed]
  5. B. Bendow, J. R. Jasperse, P. D. Gianino, Optics Commun. 5, 98 (1972). [CrossRef]
  6. B. Bendow, P. D. Gianino, Bull. Am. Phys. Soc. 17, 672 (1972) and AFCRL-72-0322 (1972).
  7. M. Born, E. Wolf, Principles of Optics (Macmillan Co., New York, 1964), Chap. 5.
  8. See, for example, J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Chap. 9.
  9. J. P. Campbell, L. G. DeShazer, J. Opt. Soc. Am. 59, 1427 (1969). [CrossRef]
  10. B. Bendow, P. D. Gianino, AFCRL-72-0322 (1972).
  11. F. W. Quelle, Appl. Opt. 5, 633 (1966). [CrossRef] [PubMed]
  12. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), 2d ed., Chap. 1; N. Y. Ölcer, Brit. J. Appl. Phys. 18, 89 (1967). [CrossRef]
  13. M. Abramowitz, I. Stegun, Eds. Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964).
  14. G. O. Olaofe, J. Opt. Soc. Am. 60, 1654 (1970). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited