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The stability of a phase-compensated laser beam propagating in a turbulent absorbing fluid is considered. Small-scale transverse optical perturbations caused by turbulence and noise grow in thermal blooming by two instabilities: the uncompensated stimulated thermal Rayleigh scattering instability and the closed-loop instability. Linearized perturbation theory is used to calculate the electric field spectrum as a Taylor series in time and as a superposition of stable and unstable modes. The method is applicable to fluids with arbitrary parameter variations along the path. Compensated perturbations grow exponentially, and uncompensated ones grow quasi-exponentially. The instability growth rates and the turbulence and noise excitation strengths are derived for a simple fluid with homogeneous parameters. The linearized theory of perturbation growth is in good agreement with numerical simulations of full nonlinear thermal blooming. If the growth rate exceeds the damping rate from other phenomena, then the perturbations grow until they are limited by nonlinear saturation, at which point the beam is significantly degraded. At saturation the laser beam spontaneously breaks into small-scale transverse structures such as filaments or ribbons. The strongest damping mechanism in the open air is typically wind shear, which sets a threshold blooming rate and a threshold absorbed irradiance. Below threshold the perturbations grow linearly; above threshold they grow quasi-exponentially. Other atmospheric damping phenomena, such as diffusion and turbulent mixing, have a smaller effect.
© 1990 Optical Society of America
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