Long distance propagation of wave beams in paraxial regime

Guillaume Bal, Anjali Nair
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Abstract

This paper concerns the propagation of high frequency wave-beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are approximately described by a complex Gaussian field whose scintillation index is unity. This provides a model of the speckle formation observed in many practical settings. The main step of the derivation consists in showing that closed-form moment equations in the It\^o-Schr\"odinger regime are still approximately satisfied in the paraxial regime. The rest of the proof is then an extension of results derived in [Bal, G. and Nair, A., arXiv:2402.17107.]
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波束在准轴向的长距离传播
本文涉及高频波束在高扰动大气中的传播。利用波传播的准轴模型,我们证明了在长距离弱耦合状态下,波场近似由闪烁指数为一的复高斯场来描述。推导的主要步骤包括证明 It\^o-Schr\"odinger 体系中的闭式矩方程在准轴向体系中仍然近似满足。证明的其余部分是对 [Bal, G. and Nair, A., arXiv:2402.17107.] 中得出的结果的扩展。
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