Partially coherent off-axis Gaussian beam scintillations

Abstract

The scintillation index at the receiver origin is formulated for a partially coherent off-axis Gaussian beam in atmospheric turbulence by employing the extended Huygens–Fresnel principle. Our formula correctly reduces to the existing coherent and partially coherent Gaussian beam scintillation indices in the limiting cases. For off-axis Gaussian beams with imaginary, real and complex displacement parameters, the scintillation index reduces when the incidence becomes more incoherent. When the source size of the off-axis Gaussian beam increases, the scintillations increase for partially coherent sources and decrease for incoherent sources, the tendency being observed for imaginary, real and complex displacement parameters. For the fully coherent off-axis Gaussian beams, increase in the source size first causes an increase in the scintillations, eventually reaching saturation at large source sizes, the increase is not monotonic and may exhibit a peak around the Fresnel zone sized off-axis Gaussian sources. For all degrees of partial coherence, off-axis beams possessing imaginary displacement parameters exhibit larger scintillations when the displacement parameter increases for large sized incidences, however, for small sized incidences, scintillations stay at the same level when the imaginary displacement parameter increases, the fixed scintillation value being lower for more incoherent sources. For off-axis Gaussian sources possessing real displacement parameters, this behavior is reciprocal with respect to the source size, i.e. for all degrees of partial coherence, off-axis beams possessing real displacement parameters exhibit larger scintillations when the displacement parameter increases for small sized incidences, and for large sized incidences, scintillations stay at the same level when the real displacement parameter increases, the fixed scintillation value again being lower for more incoherent sources. For all degrees of partial coherence, off-axis Gaussian beams possessing imaginary displacement parameters exhibit larger scintillations than the off-axis Gaussian beams possessing real displacement parameters when the absolute value of displacement parameter increases for large sized incidences.