Two-frequency mutual coherence function for Gaussian-beam pulses propagating along a horizontal path in weak anisotropic atmospheric turbulence

Abstract

A theoretical formulation of the spherical-wave two-frequency mutual coherence function (MCF) for a propagation path characterized by a complex ABCD matrix with anisotropic atmospheric turbulence existing somewhere is developed. A specialization of this formulation leads to an expression for the two-frequency MCF of an equivalent pulsed Gaussian beam propagating in weak anisotropic atmospheric turbulence along a horizontal line-of-sight path; relevant closed-form analytical solutions under both near- and far-field conditions are obtained. The small- and large-scale solutions for both the plane- and spherical-wave spatial-coherence radii in either horizontal or vertical direction are derived. Analysis shows that the formula for the on-axis two-frequency MCF of a pulsed Gaussian beam under the weak-turbulence condition in both the near- and far-field regions is distinguished from that applicable in the strong-turbulence limit only by whether the turbulence-induced beam broadening can be thought of as negligible. Under both the near- and far-field conditions, the turbulence-induced increment of the mean-square temporal-pulse half-width is proportional to the effective anisotropy factor of turbulence. The MCF becomes statistically anisotropic due to the anisotropy of turbulence. For the spatial coherence radius of either a plane or spherical wave propagating along a horizontal line-of-sight path in anisotropic atmospheric turbulence, the corresponding small-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient depending only on the effective anisotropy factor of turbulence. The corresponding large-scale solution is proportional to that for the plane-wave spatial-coherence radius in the isotropic-turbulence case with a proportionality coefficient that depends on both the effective anisotropy factor and spectral index of turbulence.

Characterizing Turbulence-Induced Decay of Mutual Unbiasedness of Complementary Bases Relevant to Propagated Photonic Spatial-Mode States

“…However, there are experimental observations demonstrating the existence of statistical anisotropy of the turbulence in some portions of the atmosphere (see, e.g., [16], [17]). It has been shown that the anisotropy of the turbulence has an important impact on optical-wave propagation [18], [19]. In fact, the wave field of the spatial-mode states in the Hadamard basis may feature a non-circularly-symmetric pattern, viz., may exhibit obvious direction-dependence (see, e.g., Fig.…”

“…This may arouse one's curiosity about whether anisotropy of turbulence plays a role in decaying the mutual unbiasedness of complementary bases relevant to propagated photonic spatial-mode states. To deal with this issue, below we choose a turbulence spectrum taking the following form [18]…”

“…where K = (κ x , κ y , κ z ) is the vector wave number, A(α) = (α−1)cos(απ /2)/(4π 2 ), (•) represents the gamma function, ζ e denotes the effective anisotropy factor, α is the spectral index, 3 < α < 4, andC 2 n is the generalized refractive-index structure constant in units of m 3−α . We point out that the above spectrum is obtained from (20) in [18] by assuming an inner scale l 0 of zero and an outer scale L 0 of infinity for the turbulence whose anisotropy exists in planes perpendicular to the z-axis, i.e., the propagation axis. The turbulence spectrum with l 0 →0 and L 0 → ∞ is proper for many cases and used widely in the literature [3], [10], [11].…”

“…In arriving at the second step of (12), it is assumed that ϕ(r, L) is a Gaussian random process. For atmospheric turbulence statistically modeled by (8), it follows that [18]…”

An efficient recognition method for turbulence intensity via random matrix theory

“…Obviously, atmosphere is one of the important factors that cause the distortion of optical signals. It will lead to the phenomena such as irradiance scintillation, beam drift, beam expansion and arrival angle fluctuation [2]. If the strong turbulence cannot be detected, the spot information of light field is too difficult to be calculated.…”