Most system analyses of CW high-power lasers propagating in the atmosphere assume a simple additive linear relation of the impact of thermal blooming and optical turbulence in the atmosphere to the propagated laser beam spreading. In other words, both effects are treated as if they would follow Gaussian statistics in an RMS sense.
While the statistics of optical propagation in a turbulent atmosphere can be modeled as Gaussian to first order, thermal blooming is a deterministic nonlinear optical phenomenon. To the best of our knowledge, there is no reason for adding linearly the beam spreading due to these two optical effects. In fact, assuming no interplay in the presence of a strong nonlinear optical interaction is
counter-intuitive. As a result, we have performed extensive numerical Monte-Carlo optical wave-propagation simulations, >50,000 realizations, in the presence of thermal-blooming and
atmospheric turbulence to varying degrees. During the propagation, the amplitude and the phase of a high power laser
field are coupled by the interplay of diffraction, refractive turbulence and thermal blooming. In some cases, we have
observed in our numerical experiments a strong coupling between turbulence and nonlinear thermal blooming.