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 attenution of the beam when it is viewed by a fixed observer, if there are random variations in its direction of propagation.
M. R. Wohlers, "Approximate Analyses of the Refractive Attenuation of Laser Beam Intensities by Turbulent Absorbing Media," Appl. Opt. 11, 1389-1398 (1972)