Abstract

Karr [ J. Opt. Soc. Am. A 6, 1038 ( 1989)] recently derived an eigenvalue equation for the temporal growth rate of the thermal blooming compensation instability, using a Green’s-function matrix formulation. A rigorous and concise derivation of all the Green’s-function matrix elements is presented here for the case of arbitrary axial variation of the wind velocity and thermal blooming strength. Starting with the perturbation growth equation of the high-power beam in an arbitrary Galilean reference frame, the high-power and beacon-propagation equations are solved by the scalar Green’s-function method. Although Green’s function of the high-power beam equation has a closed form only in special cases, the general solution is useful as a rigorous basis for the Wentzel–Kramers–Brillouin approximation and for other approximations. Finally, the matrix closed-loop compensation equation is assembled from the Green’s functions of the high-power beam, low-power beacon, and compensation subsystems.

© 1989 Optical Society of America

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