Soc. Am. A 29(5), 711–721 (2012).
1. Introduction
Propagation of optical pulses through atmospheric turbulence has attracted much attention over
many years by reason of its importance in practical applications, e.g., high-speed free-space
optical (FSO) communications, lidar, ranging, etc. Atmospheric turbulence causes such pulse
distortions as temporal broadening and time-of-arrival fluctuations; a deep understanding of
them is useful in analyzing and designing engineering systems involving optical pulse prop-
agation in the earth’s atmosphere. Over the past decades, numerous researchers have studied
various aspects in the problem of pulse propagation through atmospheric turbulence [1–10].
However, the existing works with respect to these topics generally build themselves on an as-
sumption that refractive-index fluctuations in the atmosphere are statistically homogeneous and
isotropic.
Anisotropy of atmospheric turbulence has been observed by many experimental measure-
ments [11–14]. This behavior is often attributed to the phenomenon that turbulent irregularities
in some portions of the atmosphere are elongated along the earth’s surface [15–17]. For in-
stance, the scale of large turbulent irregularities along the horizontal direction in the upper
troposphere and stratosphere may be much greater than that along the vertical one [16,17].
Consequently, the widely made assumption of isotropic turbulence in the treatments of optical-
wave propagation through the atmosphere does not always hold true in practical situations.
Up to now, considerable efforts have been made to elucidate the effects of anisotropic atmo-
spheric turbulence on optical wave propagation. Consortini et al. [18] studied the impact that
anisotropic atmospheric turbulence has on the mutual dancing of two parallel propagated nar-
row laser beams. Manning [15] theoretically examined the mutual coherence function (MCF)
for a monochromatic plane wave propagating in anisotropic atmospheric turbulence, and found
that the horizontal MCF differs from the vertical one. Gurvich and BelenKii [19] analyzed the
degradation of star image caused by stratospheric turbulence, which is usually anisotropic. Kon
[20] developed a qualitative theory to analyze the amplitude and phase fluctuations of waves
propagating in anisotropic atmospheric turbulence, and later these issues have been quantita-
tively dealt with by others [21,22]. The spreading and scintillation index of a beam wave trav-
elling in anisotropic atmospheric turbulence have also been formulated recently [23,24]. These
works reveal that anisotropy may play an important role in analysis of optical wave propaga-
tion through atmospheric turbulence. However, there have, to our knowledge, been no reports
concerning the problem that how the aforementioned temporal pulse broadening behaves when
the assumption of isotropic turbulence is no longer valid. Thus, a detailed investigation into it
is imperative.
The purpose of this paper is to understand the effects of anisotropy on the temporal broad-
ening of optical pulses propagating along a horizontal path in the earth’s turbulent atmosphere.
First, by employing the extended Huygens-Fresnel principle, we formulate the two-frequency
MCF for beam waves travelling horizontally in anisotropic atmospheric turbulence. Then, with
the help of this formulation, the expression for the mean square temporal width of Gaussian-
beam-wave pulses is developed based on the temporal moment method. Finally, numerical
calculations are carried out, and according to the results obtained, we address the question as
to how anisotropy of turbulence affects the temporal broadening behavior of optical pulses.
2. Theoretical formulations
As in [16,17,20,24], we assume that anisotropic turbulent irregularities, in the mean, can be
visualized as an oblate spheroid generated by ellipse rotation around the minor axis. In the
Received 21 Oct 2014; revised 7 Dec 2014; accepted 7 Jan 2015; published 17 Feb 2015
23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.004814 | OPTICS EXPRESS 4816