## Atmospheric Turbulence Induced Laser Beam Spread

Applied Optics, Vol. 10, Issue 12, pp. 2771-2773 (1971)

http://dx.doi.org/10.1364/AO.10.002771

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No abstract available.

**History**

Original Manuscript: August 9, 1971

Published: December 1, 1971

**Citation**

H. T. Yura, "Atmospheric Turbulence Induced Laser Beam Spread," Appl. Opt. **10**, 2771-2773 (1971)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-10-12-2771

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### References

- R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971). [CrossRef] [PubMed]
- R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971). [CrossRef]
- C. E. Coulman, Solar Phys. 7, 122 (1969). [CrossRef]
- For example, ρo can be obtained by varying the slit separation in a Young’s interferometer and noting the separation where the fringe visibility is down by 1/e (as compared to its value for small slit separations).
- The spot size is defined here as twice the distance from the z axis where the mean irradiance distribution is down by 1/e.
- The mathematical expression used here to represent this aperture disturbance is given byUA(r)=Uo exp[-r2(wo-2+ikf-1)/2].
- We note that the detailed computer calculations of Lutomirski on the propagation of a truncated Gaussian wavefront in a turbulent atmosphere8 show that the results for the nontruncated Gaussian are valid when the truncation diameter exceeds 2wo. Conversely, when 2wo exceeds the truncation diameter, the results obtained in Ref. 1 for a plane wave in a circular aperture are applicable.
- R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).
- Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82). [CrossRef]
- S. Valley, ed., Handbook of Geophysics (Macmillan, New York, 1960), pp. 13–1, 13–2.
- R. S. Lawrence, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970). [CrossRef]

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