{"id":1266,"date":"2019-11-15T15:26:05","date_gmt":"2019-11-15T15:26:05","guid":{"rendered":"https:\/\/www.hajim.wdev.rochester.edu\/optics\/alonso\/?page_id=1266"},"modified":"2020-01-06T17:59:14","modified_gmt":"2020-01-06T17:59:14","slug":"uncertainty-relations-and-their-applications-in-optics","status":"publish","type":"page","link":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/publications\/uncertainty-relations-and-their-applications-in-optics\/","title":{"rendered":"Uncertainty relations and their applications in optics"},"content":{"rendered":"\n<h4 class=\"wp-block-heading\">This work includes the definition of measures of spread for periodic distributions (e.g., over a circle or a sphere), the uncertainty relations these measures satisfy, and applications to nonparaxial fields and short pulses.<\/h4>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Uncertainty relations for periodic distributions (Fourier series and discrete Fourier transforms)<\/strong><\/h2>\n\n\n\n<p>Journal articles<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"http:\/\/dx.doi.org\/10.1016\/j.sigpro.2004.08.005\">M.A. Alonso and M.J. Bastiaans, &#8220;Mapping-based width measures and uncertainty relations for periodic functions,&#8221; Signal Proc.&nbsp;<strong>84<\/strong>, 2425-2435 (2004).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1088\/0305-4470\/36\/25\/309\">G.W. Forbes, M.A. Alonso, and A.E. Siegman, &#8220;Uncertainty relations and minimum uncertainty states for the discrete Fourier transform and the Fourier series,&#8221; J. Phys. A: Math. Gen.&nbsp;<strong>36<\/strong>, 7027-7047 (2003).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1119\/1.1383599\">G.W. Forbes and M.A. Alonso, &#8220;Consistent analogues of the Fourier uncertainty relation,&#8221; Am. J. Phys.&nbsp;<strong>69<\/strong>, 1091-1095 (2001).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1119\/1.1317562\">G.W. Forbes and M.A. Alonso, &#8220;Measures of spread for periodic distributions and the associated uncertainty relations,&#8221; Am. J. Phys.&nbsp;<strong>69<\/strong>, 340-347 (2001).<\/a><\/li><\/ul>\n\n\n\n<p>Conference proceedings<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"http:\/\/www-optica.inaoep.mx\/ICSSUR\/00%20-%20Squeezed%20States%20and%20Uncertainty%20Relations.pdf\">M.A. Alonso and G.W. Forbes, &#8220;Periodic minimum uncertainty states,&#8221; Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations, H. Moya-Cessa et al., Eds. (Rinton, Princeton, 2003), pp. 1-6.<\/a><\/li><li><a href=\"http:\/\/www.sps.ele.tue.nl\/members\/m.j.bastiaans\/pdfs\/perfunc.pdf\">M.A. Alonso and M.J. Bastiaans, &#8220;Mapping-based width measures and uncertainty relations for periodic functions,&#8221; Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology, 2003. ISSPIT (2003), pp. 625-628.<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Uncertainty relations for wave fields and pulses<\/strong><\/h2>\n\n\n\n<p>Journal articles<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"http:\/\/iopscience.iop.org\/1367-2630\/16\/12\/123023\/\">M.A. Alonso, T. Set\u00e4l\u00e4, and A.T. Friberg, &#8220;Minimum uncertainty solutions for partially coherent fields and quantum mixed states,&#8221; N. J. Phys.&nbsp;<strong>16<\/strong>, 123023 (2014).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.2971\/jeos.2011.11035\">M.A. Alonso, T. Set\u00e4l\u00e4, and A.T. Friberg, &#8220;Optimal pulses for arbitrary dispersive media,&#8221; J. Eur. Opt. Soc. R.P.&nbsp;<strong>6<\/strong>, 11035 (2011).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1088\/2040-8978\/13\/6\/064016\">M.A. Alonso, &#8220;The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,&#8221; J. Opt.&nbsp;<strong>13<\/strong>, 064016 (2011).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1088\/1464-4258\/10\/3\/033001\">C.J.R. Sheppard, M.A. Alonso, and N.J. Moore, &#8220;Localization measures for high-aperture wavefields based on moments of the pupil,&#8221; J. Opt. A&nbsp;<strong>10<\/strong>, 033001 (2008).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.24.003115\">N.J. Moore, M.A. Alonso, and C.J.R. Sheppard, &#8220;Monochromatic electromagnetic fields with maximum focal energy density,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>24<\/strong>, 3115-3122 (2007).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.24.002057\">N.J. Moore, M.A. Alonso, and C.J.R. Sheppard, &#8220;Monochromatic scalar fields with maximum focal irradiance,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>24<\/strong>, 2057-2064 (2007).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.23.000933\">M.A. Alonso, R. Borghi, and M. Santarsiero, &#8220;Joint spatial-directional features for fields focused at a complex point,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>23<\/strong>, 933-939 (2006).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.23.000701\">M.A. Alonso, R. Borghi, and M. Santarsiero, &#8220;Nonparaxial fields with maximum joint spatial-directional localization. II. Vectorial case,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>23<\/strong>, 701-712 (2006).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.23.000691\">M.A. Alonso, R. Borghi, and M. Santarsiero, &#8220;Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>23<\/strong>, 691-700 (2006).<\/a><\/li><li><a href=\"http:\/\/dx.doi.org\/10.1364\/JOSAA.17.002391\">M.A. Alonso and G.W. Forbes, &#8220;Uncertainty products for nonparaxial fields,&#8221; J. Opt. Soc. Am. A&nbsp;<strong>17<\/strong>, 2391-2402 (2000).<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>This work includes the definition of measures of spread for periodic distributions (e.g., over a circle or a sphere), the uncertainty relations these measures satisfy, and applications to nonparaxial fields and short pulses. Uncertainty relations for periodic distributions (Fourier series and discrete Fourier transforms) Journal articles M.A. Alonso and M.J. Bastiaans, &#8220;Mapping-based width measures and &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/publications\/uncertainty-relations-and-their-applications-in-optics\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Uncertainty relations and their applications in optics&#8221;<\/span><\/a><\/p>\n","protected":false},"author":0,"featured_media":2556,"parent":936,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1266","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/pages\/1266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/types\/page"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/comments?post=1266"}],"version-history":[{"count":2,"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/pages\/1266\/revisions"}],"predecessor-version":[{"id":2706,"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/pages\/1266\/revisions\/2706"}],"up":[{"embeddable":true,"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/pages\/936"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/media\/2556"}],"wp:attachment":[{"href":"https:\/\/www.hajim.rochester.edu\/optics\/alonso\/wp-json\/wp\/v2\/media?parent=1266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}