{"id":438533,"date":"2017-08-08T02:00:00","date_gmt":"2017-08-07T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=1f864a48bb60bffc1eba0f88bf8edfa4"},"modified":"2017-08-08T02:00:00","modified_gmt":"2017-08-07T23:00:00","slug":"geometric-mechanics-of-ray-optics-as-particle-dynamics-refraction-index-with-cylindrical-symmetry","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=438533","title":{"rendered":"Geometric mechanics of ray optics as particle dynamics: refraction index with cylindrical symmetry"},"content":{"rendered":"<p>Starting from the Fermat principle of geometrical optics, we analyse the ray dynamics in a graded<br \/>\nrefractive index system device with cylindrical symmetry and a refractive index that decreases<br \/>\nparabolically with the radial coordinate. By applying Hamiltonian dynamics to the study of the ray<br \/>\npath we obtain the strict equivalence of this optical system with the dynamics of a particle with an<br \/>\nequivalent mass moving in a potential function that may exhibit a well, depending on the value of<br \/>\nsome associated parameters. We analyse the features of this potential function as well as the energy<br \/>\nvalues and the symmetries of the system and see that both the azimuthal and axial components of the<br \/>\noptical conjugate momentum are two constants of motion. The phase space relation for the momentum<br \/>\nradial component is obtained analytically, and then we can obtain the components of the momentum<br \/>\nvector at any point, given the value of the radial coordinate, and from this we have the direction<br \/>\n&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Starting from the Fermat principle of geometrical optics, we analyse the ray dynamics in a graded<br \/>\nrefractive index system device with cylindrical symmetry and a refractive index that decreases<br \/>\nparabolically with the radial coordinate. By applying Ham&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-438533","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/438533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=438533"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/438533\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=438533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=438533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=438533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}