{"title":"Poincaré sphere and Stokes parameters of orbital angular momentum wave based on Euler's formula.","authors":"Zhiwei Sun","doi":"10.1364/OL.562261","DOIUrl":null,"url":null,"abstract":"<p><p>The orbital angular momentum (OAM) Poincaré sphere has been developed using the mathematical relationship between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes. However, it did not exhibit correspondence to spin angular momentum (SAM), the other angular momentum (AM) form. Here, based on Euler's formula, a definition method for general OAM waves is presented, in which the OAM wave is superposed by two orthogonal trigonometric-function waves. As SAM waves exhibit an ellipse in a direction-space, OAM waves exhibit an ellipse in a function-space. Based on this finding, the OAM Poincaré sphere is constructed through polar-spherical coordinate transformation. Finally, a physical monitoring method to monitor OAM Stokes parameters is presented and verified by Rayleigh-Sommerfeld's (RS) diffraction theory computation. This study can be used in AM theoretical research, OAM generation and manipulation, and OAM multiplexing and information encoding.</p>","PeriodicalId":19540,"journal":{"name":"Optics letters","volume":"50 13","pages":"4382-4385"},"PeriodicalIF":3.3000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optics letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1364/OL.562261","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
The orbital angular momentum (OAM) Poincaré sphere has been developed using the mathematical relationship between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes. However, it did not exhibit correspondence to spin angular momentum (SAM), the other angular momentum (AM) form. Here, based on Euler's formula, a definition method for general OAM waves is presented, in which the OAM wave is superposed by two orthogonal trigonometric-function waves. As SAM waves exhibit an ellipse in a direction-space, OAM waves exhibit an ellipse in a function-space. Based on this finding, the OAM Poincaré sphere is constructed through polar-spherical coordinate transformation. Finally, a physical monitoring method to monitor OAM Stokes parameters is presented and verified by Rayleigh-Sommerfeld's (RS) diffraction theory computation. This study can be used in AM theoretical research, OAM generation and manipulation, and OAM multiplexing and information encoding.
期刊介绍：
The Optical Society (OSA) publishes high-quality, peer-reviewed articles in its portfolio of journals, which serve the full breadth of the optics and photonics community.
Optics Letters offers rapid dissemination of new results in all areas of optics with short, original, peer-reviewed communications. Optics Letters covers the latest research in optical science, including optical measurements, optical components and devices, atmospheric optics, biomedical optics, Fourier optics, integrated optics, optical processing, optoelectronics, lasers, nonlinear optics, optical storage and holography, optical coherence, polarization, quantum electronics, ultrafast optical phenomena, photonic crystals, and fiber optics. Criteria used in determining acceptability of contributions include newsworthiness to a substantial part of the optics community and the effect of rapid publication on the research of others. This journal, published twice each month, is where readers look for the latest discoveries in optics.
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