{"title":"波束在准轴向的长距离传播","authors":"Guillaume Bal, Anjali Nair","doi":"arxiv-2409.09514","DOIUrl":null,"url":null,"abstract":"This paper concerns the propagation of high frequency wave-beams in highly\nturbulent atmospheres. Using a paraxial model of wave propagation, we show in\nthe long-distance weak-coupling regime that the wavefields are approximately\ndescribed by a complex Gaussian field whose scintillation index is unity. This\nprovides a model of the speckle formation observed in many practical settings.\nThe main step of the derivation consists in showing that closed-form moment\nequations in the It\\^o-Schr\\\"odinger regime are still approximately satisfied\nin the paraxial regime. The rest of the proof is then an extension of results\nderived in [Bal, G. and Nair, A., arXiv:2402.17107.]","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"97 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Long distance propagation of wave beams in paraxial regime\",\"authors\":\"Guillaume Bal, Anjali Nair\",\"doi\":\"arxiv-2409.09514\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper concerns the propagation of high frequency wave-beams in highly\\nturbulent atmospheres. Using a paraxial model of wave propagation, we show in\\nthe long-distance weak-coupling regime that the wavefields are approximately\\ndescribed by a complex Gaussian field whose scintillation index is unity. This\\nprovides a model of the speckle formation observed in many practical settings.\\nThe main step of the derivation consists in showing that closed-form moment\\nequations in the It\\\\^o-Schr\\\\\\\"odinger regime are still approximately satisfied\\nin the paraxial regime. The rest of the proof is then an extension of results\\nderived in [Bal, G. and Nair, A., arXiv:2402.17107.]\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"97 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09514\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09514","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
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。
Long distance propagation of wave beams in paraxial regime
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.]