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In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{{{\\boldsymbol{p}}}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>p<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{{{\\boldsymbol{l}}}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>l<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian (STHG) wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{{{\\boldsymbol{p}}}}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>p<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{{{\\boldsymbol{l}}}}}}.$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>l<\/mml:mi>\n                  <mml:mo>.<\/mml:mo>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.<\/jats:p>","DOI":"10.1038\/s41467-024-49819-4","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T06:02:22Z","timestamp":1719468142000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":72,"title":["Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers"],"prefix":"10.1038","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-9523-0389","authenticated-orcid":false,"given":"Xin","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4730-7742","authenticated-orcid":false,"given":"Qian","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nianjia","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andy","family":"Chong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3440-7709","authenticated-orcid":false,"given":"Yangjian","family":"Cai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8745-4213","authenticated-orcid":false,"given":"Qiwen","family":"Zhan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"49819_CR1","doi-asserted-by":"publisher","first-page":"8185","DOI":"10.1103\/PhysRevA.45.8185","volume":"45","author":"L Allen","year":"1992","unstructured":"Allen, L., Beijersbergen, M. 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