Log-amplitude and phase-correlation and structure functions of higher-order annular laser beams in a turbulent atmosphere are derived. A higher-order annular beam source is defined as the superposition of two different higher-order Hermite-Gaussian beams. A special case of such an excitation is the annular Gaussian beam in which two beams operate at fundamental modes of different Gaussian beam sizes, yielding a doughnut-shaped (annular) beam when the second beam is subtracted from the first beam. Our formulation utilizes Rytov approximation, which makes it applicable in the weak-turbulence regime, especially for log-amplitude fluctuations. Limiting cases of our formulations correctly match with known higher-order-mode solutions that in turn reduce to the Gaussian-beam-wave (TEM_00-mode) results. Our results can be applied to determine the scintillation index and the phase fluctuations in free-space optics links under higher-order annular laser beam excitation. Except for the numerical evaluation of a specific example covering an annular Gaussian beam, the results in general are left in integral form and need to be numerically evaluated in detail to obtain quantitative results.
© 2005 Optical Society of America
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
Yahya Baykal, "Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium," J. Opt. Soc. Am. A 22, 672-679 (2005)