OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 11, Iss. 6 — Jun. 1, 1972
  • pp: 1389–1398

Approximate Analyses of the Refractive Attenuation of Laser Beam Intensities by Turbulent Absorbing Media

M. R. Wohlers  »View Author Affiliations

Applied Optics, Vol. 11, Issue 6, pp. 1389-1398 (1972)

View Full Text Article

Enhanced HTML    Acrobat PDF (1344 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Consideration is given to certain physical phenomena that can attenuate the intensity of a laser beam by refractively spreading or scattering the beam as it propagates. The total attenuation caused by these effects can be well above the usual geometric spreading and absorption losses. Two specific phenomena are analyzed: the nonlinear thermal blooming of the beam (thermal lens effect) and the spreading caused by random variations of the index of refraction of the medium in which the beam is propagating (turbulence effects). The intent of the investigation is to obtain reasonably simple analytic expressions that can be used to estimate or set bounds on the extent of the attenuation. Such expressions are obtained for both the transient and the steady-state effects of thermal blooming when the medium is moving relative to the laser beam, and various estimates are also obtained for the turbulence-induced attenuation of the peak intensity of a beam. For comparison, estimates are also given of the effective attenuation of the beam when it is viewed by a fixed observer, if there are random variations in its direction of propagation.

© 1972 Optical Society of America

Original Manuscript: September 9, 1971
Published: June 1, 1972

M. R. Wohlers, "Approximate Analyses of the Refractive Attenuation of Laser Beam Intensities by Turbulent Absorbing Media," Appl. Opt. 11, 1389-1398 (1972)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Landau, E. Lifshitz, Fluid Mechanics (Pergamon, London, 1959).
  2. J. Wallace, M. Camac, J. Opt. Soc. Am. 60, 12, 1587 (1970). [CrossRef]
  3. A. Wood, M. Camac, E. Gerry, Appl. Opt. 10, 8, 1877 (1971). [CrossRef]
  4. J. Gordon et al., J. Appl. Phys. 36, 1, 3 (1965). [CrossRef]
  5. P. Kelley, Phys. Rev. Lett. 15, 1105 (1965); F. Gebhardt, D. Smith, Appl. Phys. Lett. 14, 52 (1969); IEEE Trans. Quant. Electron. QE-7, 63 (1971). [CrossRef]
  6. E. Jahnke, F. Emde, Tables of Functions (Dover, New York, 1945).
  7. H. Kleinman, P. Kelley, MIT Lincoln Lab, Optics Research Summary (1970).
  8. The review paper by R. Lawrence, J. Strohbehn, Proc. IEEE 58, 1523 (1970), contains an excellent bibliography on the subject. [CrossRef]
  9. R. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

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.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited