Scalar Green's-function derivation of the thermal blooming compensation instability equations

Journal Article · Fri Dec 01 04:00:00 EST 1989 · Journal of the Optical Society of America A: Optics and Image Science; (USA)

DOI:https://doi.org/10.1364/JOSAA.6.001859· OSTI ID:7070781

Morris, J R ^[1]

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1. Lawrence Livermore National Laboratory, Livermore, California 94550 (US)

Karr (J. Opt. Soc. Am. A {bold 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.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7070781
• Journal Information: Journal of the Optical Society of America A: Optics and Image Science; (USA), Journal Name: Journal of the Optical Society of America A: Optics and Image Science; (USA) Vol. 6:12; ISSN 0740-3232; ISSN JOAOD
• Country of Publication: United States
• Language: English

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426002* -- Engineering-- Lasers & Masers-- (1990-)
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