{"id":215,"date":"2018-01-05T06:02:05","date_gmt":"2018-01-05T06:02:05","guid":{"rendered":"http:\/\/www.shalomeo.com\/blog\/?p=215"},"modified":"2018-01-05T06:02:05","modified_gmt":"2018-01-05T06:02:05","slug":"crystal-optical-research","status":"publish","type":"post","link":"https:\/\/www.shalomeo.com\/blog\/crystal-optical-research\/215.html","title":{"rendered":"Crystal Optical Research"},"content":{"rendered":"

<\/h2>\n

The<\/span> study<\/span> of the<\/span> propagation<\/span> of light,<\/span> and<\/span> associated<\/span> phenomena,<\/span> in crystalline<\/span> solids.<\/span> For<\/span> a simple<\/span> cubic<\/span> crystal<\/span> the<\/span> atomic<\/span>arrangement<\/span> is such<\/span> that<\/span> in each<\/span> direction<\/span> through<\/span> the<\/span> crystal<\/span> the<\/span> crystal<\/span> presents<\/span> the<\/span> same<\/span> optical<\/span> appearance.<\/span> The<\/span> atoms<\/span>in anisotropic<\/span> crystals<\/span><\/strong> are<\/span> closer<\/span> together<\/span> in some<\/span> planes<\/span> through<\/span> the<\/span> material<\/span> than<\/span> in others.<\/span> In anisotropic<\/span> crystals<\/span> the<\/span>optical<\/span> characteristics<\/span> are<\/span> different<\/span> in different<\/span> directions.<\/span> In classical<\/span> physics<\/span> the<\/span> progress<\/span> of an electromagnetic<\/span> wave<\/span>through<\/span> a material<\/span> involves<\/span> the<\/span> periodic<\/span> displacement<\/span> of electrons.<\/span> In anisotropic<\/span> substances<\/span> the<\/span> forces<\/span> resisting<\/span> these<\/span>displacements<\/span> depend<\/span> on the<\/span> displacement<\/span> direction.<\/span> Thus<\/span> the<\/span> velocity<\/span> of a light<\/span> wave<\/span> is different<\/span> in different<\/span> directions<\/span> and<\/span>for<\/span> different<\/span> states<\/span> of polarization.<\/span> The<\/span> absorption<\/span> of the<\/span> wave<\/span> may<\/span> also<\/span> be different<\/span> in different<\/span> directions.<\/span> See<\/span><\/i> Dichroism, Trichroism<\/p>\n

In an isotropic<\/span> medium<\/span> the<\/span> light<\/span> from<\/span> a point<\/span> source<\/span> spreads<\/span> out<\/span> in a spherical<\/span> shell.<\/span> The<\/span> light<\/span> from<\/span> a point<\/span> source<\/span> embedded<\/span>in an anisotropic<\/span> crystal<\/span> spreads<\/span> out<\/span> in two<\/span> wave<\/span> surfaces,<\/span> one<\/span> of which<\/span> travels<\/span> at a faster<\/span> rate<\/span> than<\/span> the<\/span> other.<\/span> The<\/span>polarization<\/span> of the<\/span> light<\/span> varies<\/span> from<\/span> point<\/span> to point<\/span> over<\/span> each<\/span> wave<\/span> surface,<\/span> and<\/span> in any<\/span> particular<\/span> direction<\/span> from<\/span> the<\/span> source<\/span> the<\/span>polarization<\/span> of the<\/span> two<\/span> surfaces<\/span> is opposite.<\/span> The<\/span> characteristics<\/span> of these<\/span> surfaces<\/span> can<\/span> be determined<\/span> experimentally<\/span> bymaking<\/span> measurements<\/span> on a given<\/span> crystal.<\/span><\/p>\n

In the<\/span> most<\/span> general<\/span> case<\/span> of a transparent<\/span> anisotropic<\/span> medium,<\/span> the<\/span> dielectric<\/span> constant<\/span> is different<\/span> along<\/span> each<\/span> of three<\/span>orthogonal<\/span> axes.<\/span> This<\/span> means<\/span> that<\/span> when<\/span> the<\/span> light<\/span> vector<\/span> is oriented<\/span> along<\/span> each<\/span> direction,<\/span> the<\/span> velocity<\/span> of light<\/span> is different.<\/span> One<\/span>method<\/span> for<\/span> calculating<\/span> the<\/span> behavior<\/span> of a transparent<\/span> anisotropic<\/span> material<\/span> is through<\/span> the<\/span> use<\/span> of the<\/span> index<\/span> ellipsoid,<\/span> also<\/span> called<\/span>the<\/span> reciprocal<\/span> ellipsoid,<\/span> optical<\/span> indicatrix,<\/span> or ellipsoid<\/span> of wave<\/span> normals.<\/span> This<\/span> is the<\/span> surface<\/span> obtained<\/span> by plotting<\/span> the<\/span> value<\/span> ofthe<\/span> refractive<\/span> index<\/span> in each<\/span> principal<\/span> direction<\/span> for<\/span> a linearly<\/span> polarized<\/span> light<\/span> vector<\/span> lying<\/span> in that<\/span> direction<\/span> (see<\/span> illustration).<\/span> The<\/span>different<\/span> indices<\/span> of refraction,<\/span> or wave<\/span> velocities<\/span> associated<\/span> with<\/span> a given<\/span> propagation<\/span> direction,<\/span> are<\/span> then<\/span> given<\/span> by sections<\/span>through<\/span> the<\/span> origin<\/span> of the<\/span> coordinates<\/span> in which<\/span> the<\/span> index<\/span> ellipsoid<\/span> is drawn.<\/span> These<\/span> sections<\/span> are<\/span> ellipses,<\/span> and<\/span> the<\/span> major<\/span> and<\/span>minor<\/span> axes<\/span> of the<\/span> ellipse<\/span> represent<\/span> the<\/span> fast<\/span> and<\/span> slow<\/span> axes<\/span> for<\/span> light<\/span> proceeding<\/span> along<\/span> the<\/span> normal<\/span> to the<\/span> plane<\/span> of the<\/span> ellipse.<\/span>The<\/span> length<\/span> of the<\/span> axes<\/span> represents<\/span> the<\/span> refractive<\/span> indices<\/span> for<\/span> the<\/span> fast<\/span> and<\/span> slow<\/span> wave,<\/span> respectively.<\/span> The<\/span> most<\/span> asymmetric<\/span> type<\/span>of ellipsoid<\/span> has<\/span> three<\/span> unequal<\/span> axes.<\/span> It is a general<\/span> rule<\/span> in crystallography<\/span> that<\/span> no property<\/span> of a crystal<\/span> will<\/span> have<\/span> less<\/span>symmetry<\/span> than<\/span> the<\/span> class<\/span> in which<\/span> the<\/span> crystal<\/span> belongs.<\/span><\/p>\n

Optics,Wafers and Crystals<\/p>\n","protected":false},"excerpt":{"rendered":"

The study of the propagation of light, and associa …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/posts\/215"}],"collection":[{"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/comments?post=215"}],"version-history":[{"count":0,"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/posts\/215\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/media?parent=215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/categories?post=215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shalomeo.com\/blog\/wp-json\/wp\/v2\/tags?post=215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}