Correlation between turbulence-impacted optical signals collected via a pair of adjacent spatial-mode receivers

Optical spatial-mode reception has a physical nature quite different from that of the traditional optical power-in-the-bucket (PIB) reception. The former belongs to coherent reception scheme while the latter pertains to incoherent reception scheme. Under weak-turbulence conditions, the statistical correlation between turbulence-impacted optical signals collected by a pair of adjacent spatial-mode receivers is mathematically formulated in terms of a new theoretical framework that takes into account the distinctive nature of the spatial-mode reception. The aperture Fresnel number, coherence Fresnel number, separation Fresnel number and mode Fresnel number are identified as fundamental determinative parameters in evaluation of the correlation coefficient. With the help of the obtained formulations, two analytical asymptotic formulae for the correlation coefficient are further derived under the conditions that the aperture Fresnel number is much smaller than the coherence Fresnel number and separation Fresnel number, respectively. Despite the use of asymptotic approximations in the theoretical derivation, it is found that the two asymptotic formulae indeed have utility in many situations of practical interest to us. Furthermore, Monte-Carlo-simulation-based calculations are carried out to examine the accuracy of employing the two asymptotic formulae to approximate the correlation coefficient. It is shown that the ranges of applicability of these two asymptotic formulae are mainly determined by the coherence Fresnel number and the ratio of the separation Fresnel number to the aperture Fresnel number, basically irrespective of the mode Fresnel number.