{"title":"M6形式化——将激光束质量因子M2推广到三维域","authors":"A. Brodsky, N. Kaplan","doi":"10.1515/aot-2020-0007","DOIUrl":null,"url":null,"abstract":"Abstract Here we define a theoretical basis for the generalization of the beam quality factor M2 to three-dimensional (3D) space, which we call M6 formalism. The formalism is established through the use of examples of multifocal and Axicon optical systems to illustrate discrete and continuous axial beam shaping, respectively. For the continuous case, we expand the definition of the Rayleigh range to incorporate a quality factor having both axial and transverse components Madd2$M_{{\\rm{add}}}^2$ and M2. Using geometrical ray tracing simulations, a proportion factor C is found to empirically describe the axial quality factor Mz2$M_z^2$ of an optical setup including an Axicon and a paraxial focusing lens with a Gaussian single mode input beam. Using our M6 formalism depth of focus (DOF) ranges are calculated for higher M2 beams, and are shown to be in good agreement with the simulated DOF range, demonstrating the usefulness of the M6 formalism for the design of real optical systems.","PeriodicalId":46010,"journal":{"name":"Advanced Optical Technologies","volume":"9 1","pages":"167 - 173"},"PeriodicalIF":2.3000,"publicationDate":"2020-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/aot-2020-0007","citationCount":"1","resultStr":"{\"title\":\"M6 formalism – generalization of the laser beam quality factor M2 to the 3D domain\",\"authors\":\"A. Brodsky, N. Kaplan\",\"doi\":\"10.1515/aot-2020-0007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Here we define a theoretical basis for the generalization of the beam quality factor M2 to three-dimensional (3D) space, which we call M6 formalism. The formalism is established through the use of examples of multifocal and Axicon optical systems to illustrate discrete and continuous axial beam shaping, respectively. For the continuous case, we expand the definition of the Rayleigh range to incorporate a quality factor having both axial and transverse components Madd2$M_{{\\\\rm{add}}}^2$ and M2. Using geometrical ray tracing simulations, a proportion factor C is found to empirically describe the axial quality factor Mz2$M_z^2$ of an optical setup including an Axicon and a paraxial focusing lens with a Gaussian single mode input beam. Using our M6 formalism depth of focus (DOF) ranges are calculated for higher M2 beams, and are shown to be in good agreement with the simulated DOF range, demonstrating the usefulness of the M6 formalism for the design of real optical systems.\",\"PeriodicalId\":46010,\"journal\":{\"name\":\"Advanced Optical Technologies\",\"volume\":\"9 1\",\"pages\":\"167 - 173\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2020-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/aot-2020-0007\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced Optical Technologies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/aot-2020-0007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Optical Technologies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/aot-2020-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"OPTICS","Score":null,"Total":0}
M6 formalism – generalization of the laser beam quality factor M2 to the 3D domain
Abstract Here we define a theoretical basis for the generalization of the beam quality factor M2 to three-dimensional (3D) space, which we call M6 formalism. The formalism is established through the use of examples of multifocal and Axicon optical systems to illustrate discrete and continuous axial beam shaping, respectively. For the continuous case, we expand the definition of the Rayleigh range to incorporate a quality factor having both axial and transverse components Madd2$M_{{\rm{add}}}^2$ and M2. Using geometrical ray tracing simulations, a proportion factor C is found to empirically describe the axial quality factor Mz2$M_z^2$ of an optical setup including an Axicon and a paraxial focusing lens with a Gaussian single mode input beam. Using our M6 formalism depth of focus (DOF) ranges are calculated for higher M2 beams, and are shown to be in good agreement with the simulated DOF range, demonstrating the usefulness of the M6 formalism for the design of real optical systems.
期刊介绍:
Advanced Optical Technologies is a strictly peer-reviewed scientific journal. The major aim of Advanced Optical Technologies is to publish recent progress in the fields of optical design, optical engineering, and optical manufacturing. Advanced Optical Technologies has a main focus on applied research and addresses scientists as well as experts in industrial research and development. Advanced Optical Technologies partners with the European Optical Society (EOS). All its 4.500+ members have free online access to the journal through their EOS member account. Topics: Optical design, Lithography, Opto-mechanical engineering, Illumination and lighting technology, Precision fabrication, Image sensor devices, Optical materials (polymer based, inorganic, crystalline/amorphous), Optical instruments in life science (biology, medicine, laboratories), Optical metrology, Optics in aerospace/defense, Simulation, interdisciplinary, Optics for astronomy, Standards, Consumer optics, Optical coatings.