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Temporal-frequency spectrum of an optical wave propagating under saturation conditions

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Abstract

An expression is derived for the log-amplitude temporal-frequency spectrum of a plane wave propagating in a turbulent medium, which is valid under strong-scintillation conditions. From consideration of the Kolmogorov spectrum, for σT2 ≲ 1 ( σT2 is the log-amplitude variance obtained from perturbation theory) the results of the analysis agree with those of Tatarskii and others. For σT2 ≳ 1, the frequency spectrum shifts to higher frequencies and the peak in the spectrum occurs at νpeakν0(σT)6/5, where ν0 is the peak frequency obtained for σT2 ≲ 1 (i.e., from perturbation theory). Additionally, the spectrum broadens and the maximum value of the spectrum decreases with increasing values of σT2. The normalized log-amplitude temporal-frequency spectrum is a universal function of ν/ν0 only for σT2 ≲ 1 whereas, for σT2 ≳ 1, the normalized spectrum is a function of both ν0 and σT2. The present results are in good qualitative agreement with recent atmospheric experiments. Finally, the need for increased electronic bandwidth for experimental measurements in the saturation regime is indicated and the implications of the analysis regarding the temporal-frequency spectrum of beam waves is discussed.

© 1974 Optical Society of America

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