Mohammed S. Qusailah, Abdu A. Alkelly, Wafa’a A. Al-Bahry
{"title":"洛伦兹-高斯涡旋光束在梯度指数介质中的传播特性","authors":"Mohammed S. Qusailah, Abdu A. Alkelly, Wafa’a A. Al-Bahry","doi":"10.1155/2023/3772408","DOIUrl":null,"url":null,"abstract":"Based on the Huygens–Fresnel integral and ABCD matrix, the propagation equation for the Lorentz–Gauss vortex beam (LGVB) in a gradient-index medium (GRIN) is rederived. The evolution of the intensity and phase distributions of an LGVB through a GRIN medium are numerically calculated as a function of the gradient-index parameter with changes in the incident beam parameters. The results showed that the propagation path and intensity distributions changed periodically with increasing propagation distance. In contrast, phase distributions change at multiples of <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.04 12.7178\" width=\"13.04pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,7.684,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"12.9951838 -9.28833 7.724 12.7178\" width=\"7.724pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,13.045,0)\"></path></g></svg></span> or <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 19.28 12.7178\" width=\"19.28pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.24,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.924,0)\"><use xlink:href=\"#g113-48\"></use></g></svg><span></span><span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"19.2351838 -9.28833 7.747 12.7178\" width=\"7.747pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,19.285,0)\"><use xlink:href=\"#g113-224\"></use></g></svg>,</span></span> depending on whether the <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 12.9526 8.68572\" width=\"12.9526pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> values are odd or even, respectively. At the same time, the parameters of the gradient index determine the periodic values of the Lorentz–Gauss vortex beams during propagation, and as <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 7.68094 12.7178\" width=\"7.68094pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-224\"></use></g></svg> increased, the period of evolution decreased. The Lorentz–Gauss vortex beam propagating through the gradient index will develop from a square beam to a Gaussian vortex beam more quickly with an increase of <span><svg height=\"11.4899pt\" style=\"vertical-align:-5.52899pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 30.338 11.4899\" width=\"30.338pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,8.931,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,13.363,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,22.707,0)\"></path></g></svg><span></span><span><svg height=\"11.4899pt\" style=\"vertical-align:-5.52899pt\" version=\"1.1\" viewbox=\"33.9201838 -5.96091 19.434 11.4899\" width=\"19.434pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,33.97,0)\"><use xlink:href=\"#g113-120\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,42.9,3.132)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,47.332,3.132)\"></path></g></svg>.</span></span> In addition, the topological charge affects the size of the dark spot at the center of the beam and the size of the beam, causing the phase distributions to change periodically in the medium. This study is beneficial for laser optics and optical communications.","PeriodicalId":55995,"journal":{"name":"International Journal of Optics","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Propagation Properties of a Lorentz–Gauss Vortex Beam in a Gradient-Index Medium\",\"authors\":\"Mohammed S. Qusailah, Abdu A. Alkelly, Wafa’a A. Al-Bahry\",\"doi\":\"10.1155/2023/3772408\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Based on the Huygens–Fresnel integral and ABCD matrix, the propagation equation for the Lorentz–Gauss vortex beam (LGVB) in a gradient-index medium (GRIN) is rederived. The evolution of the intensity and phase distributions of an LGVB through a GRIN medium are numerically calculated as a function of the gradient-index parameter with changes in the incident beam parameters. The results showed that the propagation path and intensity distributions changed periodically with increasing propagation distance. In contrast, phase distributions change at multiples of <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 13.04 12.7178\\\" width=\\\"13.04pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,7.684,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"12.9951838 -9.28833 7.724 12.7178\\\" width=\\\"7.724pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,13.045,0)\\\"></path></g></svg></span> or <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 19.28 12.7178\\\" width=\\\"19.28pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,6.24,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.924,0)\\\"><use xlink:href=\\\"#g113-48\\\"></use></g></svg><span></span><span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"19.2351838 -9.28833 7.747 12.7178\\\" width=\\\"7.747pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,19.285,0)\\\"><use xlink:href=\\\"#g113-224\\\"></use></g></svg>,</span></span> depending on whether the <svg height=\\\"8.68572pt\\\" style=\\\"vertical-align:-0.0498209pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 12.9526 8.68572\\\" width=\\\"12.9526pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g></svg> values are odd or even, respectively. At the same time, the parameters of the gradient index determine the periodic values of the Lorentz–Gauss vortex beams during propagation, and as <svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 7.68094 12.7178\\\" width=\\\"7.68094pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-224\\\"></use></g></svg> increased, the period of evolution decreased. The Lorentz–Gauss vortex beam propagating through the gradient index will develop from a square beam to a Gaussian vortex beam more quickly with an increase of <span><svg height=\\\"11.4899pt\\\" style=\\\"vertical-align:-5.52899pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 30.338 11.4899\\\" width=\\\"30.338pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.931,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,13.363,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,22.707,0)\\\"></path></g></svg><span></span><span><svg height=\\\"11.4899pt\\\" style=\\\"vertical-align:-5.52899pt\\\" version=\\\"1.1\\\" viewbox=\\\"33.9201838 -5.96091 19.434 11.4899\\\" width=\\\"19.434pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,33.97,0)\\\"><use xlink:href=\\\"#g113-120\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,42.9,3.132)\\\"><use xlink:href=\\\"#g50-49\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,47.332,3.132)\\\"></path></g></svg>.</span></span> In addition, the topological charge affects the size of the dark spot at the center of the beam and the size of the beam, causing the phase distributions to change periodically in the medium. This study is beneficial for laser optics and optical communications.\",\"PeriodicalId\":55995,\"journal\":{\"name\":\"International Journal of Optics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Optics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1155/2023/3772408\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Optics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2023/3772408","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
The Propagation Properties of a Lorentz–Gauss Vortex Beam in a Gradient-Index Medium
Based on the Huygens–Fresnel integral and ABCD matrix, the propagation equation for the Lorentz–Gauss vortex beam (LGVB) in a gradient-index medium (GRIN) is rederived. The evolution of the intensity and phase distributions of an LGVB through a GRIN medium are numerically calculated as a function of the gradient-index parameter with changes in the incident beam parameters. The results showed that the propagation path and intensity distributions changed periodically with increasing propagation distance. In contrast, phase distributions change at multiples of or , depending on whether the values are odd or even, respectively. At the same time, the parameters of the gradient index determine the periodic values of the Lorentz–Gauss vortex beams during propagation, and as increased, the period of evolution decreased. The Lorentz–Gauss vortex beam propagating through the gradient index will develop from a square beam to a Gaussian vortex beam more quickly with an increase of . In addition, the topological charge affects the size of the dark spot at the center of the beam and the size of the beam, causing the phase distributions to change periodically in the medium. This study is beneficial for laser optics and optical communications.
期刊介绍:
International Journal of Optics publishes papers on the nature of light, its properties and behaviours, and its interaction with matter. The journal considers both fundamental and highly applied studies, especially those that promise technological solutions for the next generation of systems and devices. As well as original research, International Journal of Optics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.