## 1 Introduction  
The study of laser beams propagation through the atmosphere has received wide attention due to its important applications in high-speed/high-capacity free-space optical communications and remote sensing. In these systems, the laser beams experience random refractive index fluctuations induced by atmospheric turbulence. This turbulence gives rise to extra beam broadening, beam wander and scintillation, which limits the performance of these systems. Therefore, the knowledge of the atmospheric turbulence and its interaction with light beams are of great importance. Over the past decades, the theory of light beams propagation in isotropic turbulence has been well developed [1]. However, many experimental results showed that anisotropic turbulence can exist in a wide range of altitudes from the earth's surface [2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. As early as 1970, [PERSON] and co-workers experimentally found the evidence of anisotropic turbulence near the ground [2]. They measured relative beam wander of two or more parallel narrow beams through a 130 m horizontal path about one meter above the ground and found that the variance of the refractive index fluctuations in the vertical and horizontal direction is different. [PERSON] et al. presented the experimental evidence of the ubiquitous presence of very strong temperature gradients in the vertical direction, compared to those in the horizontal direction, within very thin layers/sheets in the atmosphere up to 25 km from the ground [3]. [PERSON] et al. investigated the spatial structure of temperature and density in the middle atmosphere through the observations of star scintillations and found strong anisotropy of temperature gradient in the horizontal and vertical direction for heights 12-45 km from the ground [4]. The anisotropy of turbulence in the stratosphere was investigated by [PERSON] and co-workers. They found the existence of anisotropic refractive index fluctuations from balloon-borne observations of stellar scintillation [5]. The generation of anisotropic turbulence in the laboratory and the approach for designing phase screens for anisotropic turbulence were reported in [12; 13]. Meanwhile, theoretical models for structure functions or power spectrum densities obeying Kolmogorov or non-Kolmogorov statistics were proposed to describe the anisotropic refractive index fluctuations of the turbulence [5; 6; 14; 15]. Recently, there has been a growing interest in research of the behavior of optical fields in the presence of anisotropic turbulence. Based on the Rytov method, theoretical models for the log-amplitude correlation function, the angle of arrival fluctuation as well as the modulation transfer function of a plane wave and a spherical wave passing through the anisotropic Kolmogorov or non-Kolmogorov atmosphere, have been established [16; 17; 18; 19; 20; 21; 22]. Furthermore, the statistical properties, such as long-term beam spread, scintillation index and beam wander of a Gaussian beam in weak and moderate-to-strong anisotropic turbulence, were investigated by [PERSON] et al. [23; 24; 25] and [PERSON] et al. [26], respectively. On the other hand, another technique, known as the extended Huygens-Fresnel (eHF) principle, has also been applied to study the behavior of laser beams in anisotropic turbulence [27; 28; 29; 30]. The advantage of the eHF method is that it can be used to treat the propagation characteristics for a wide range of optical fields, including partially coherent fields (see [31; 32] and reference therein). The validity of this method extends from weak to strong turbulence. However, in these studies using the eHF method, it is assumed that the statistics of the turbulence in the transverse plane orthogonal to the beam propagation axis is isotropic. Thus, the turbulent anisotropy acts only as the modifier to the strength of turbulence. When a light beam propagates along a horizontal path near the ground, the turbulence affects the beam differently in two transverse directions, perpendicular to propagation axis.