{"id":1991,"date":"2021-08-28T20:36:00","date_gmt":"2021-08-28T12:36:00","guid":{"rendered":"https:\/\/blog.francis67.cc\/?p=1991"},"modified":"2021-08-29T11:03:44","modified_gmt":"2021-08-29T03:03:44","slug":"%e5%85%89%e7%9a%84%e5%81%8f%e6%8c%af","status":"publish","type":"post","link":"https:\/\/blog.francis67.cc\/?p=1991","title":{"rendered":"\u5149\u7684\u504f\u632f"},"content":{"rendered":"\n<p>\u504f\u632f\u662f\u6a2a\u6ce2\u7684\u4e00\u79cd\u6027\u8d28\uff0c\u7535\u78c1\u6ce2\u7684\u504f\u632f\u6001\u901a\u5e38\u662f\u6307\u7535\u573a\u77e2\u91cf\u7684\u65b9\u5411\u3002<\/p>\n\n\n\n<p>\u5b9e\u9645\u751f\u6d3b\u4e2d\u7684\u5149\u6e90\uff0c\u5927\u591a\u662f\u975e\u76f8\u5e72\u5149\uff0c\u4ed6\u4eec\u53e0\u52a0\u540e\u6210\u4e3a<strong><em>\u975e\u504f\u632f\u5149<\/em><\/strong>\u6216<strong><em>\u968f\u673a\u504f\u632f\u5149<\/em><\/strong>\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u6211\u4eec\u53ea\u8ba8\u8bba\u7b80\u5355\u7684\u6a21\u578b\uff0c\u5373\u5355\u8272\u5e73\u9762\u6ce2\u3002<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E5%81%8F%E6%8C%AF%E7%9A%84%E8%A1%A8%E7%A4%BA\" >\u504f\u632f\u7684\u8868\u793a<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E7%BA%BF%E5%81%8F%E6%8C%AF%E5%85%89\" >\u7ebf\u504f\u632f\u5149<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E5%9C%86%E5%81%8F%E6%8C%AF%E5%85%89\" >\u5706\u504f\u632f\u5149<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E6%A4%AD%E5%9C%86%E5%81%8F%E6%8C%AF%E5%85%89\" >\u692d\u5706\u504f\u632f\u5149<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E7%90%BC%E6%96%AF%E7%9F%A9%E9%98%B5\" >\u743c\u65af\u77e9\u9635<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E5%81%8F%E6%8C%AF%E5%99%A8\" >\u504f\u632f\u5668<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E7%9B%B8%E4%BD%8D%E5%BB%B6%E8%BF%9F%E5%99%A8\" >\u76f8\u4f4d\u5ef6\u8fdf\u5668<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E5%9B%9B%E5%88%86%E4%B9%8B%E4%B8%80%E6%B3%A2%E7%89%87\" >\u56db\u5206\u4e4b\u4e00\u6ce2\u7247<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80%E6%B3%A2%E7%89%87\" >\u4e8c\u5206\u4e4b\u4e00\u6ce2\u7247<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E6%97%8B%E8%BD%AC\" >\u65cb\u8f6c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%8F%82%E6%95%B0\" >\u65af\u6258\u514b\u65af\u53c2\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/blog.francis67.cc\/?p=1991\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%81%8F%E6%8C%AF%E7%9A%84%E8%A1%A8%E7%A4%BA\"><\/span>\u504f\u632f\u7684\u8868\u793a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5047\u8bbe\u7535\u78c1\u6ce2\u6cbfz\u65b9\u5411\u4f20\u64ad\uff0c\u5b83\u7684\u6570\u5b66\u8868\u8fbe\u5f0f\u53ef\u4ee5\u5199\u4f5c<\/p>\n\n\n\n<p>$$  \\vec{\\mathbf{E}}= E_{x}\\vec{\\mathbf{x}} +E_{y}\\vec{\\mathbf{y}} $$<\/p>\n\n\n\n<p>\u590d\u6570\u57df\u8868\u793a\u4e3a<\/p>\n\n\n\n<p>$$ \\widetilde{\\mathbf{E}}= \\widetilde{E_{x}}\\vec{\\mathbf{x}} +\\widetilde{E_{y}}\\vec{\\mathbf{y}} $$<\/p>\n\n\n\n<p>\u5176\u4e2d<\/p>\n\n\n\n<p>$$ \\widetilde{E_{x}} = E_{0x}e^{i(kz-\\omega t+\\varphi _{x})} $$<\/p>\n\n\n\n<p> $$ \\widetilde{E_{y}} = E_{0y}e^{i(kz-\\omega t+\\varphi _{y})} $$ <\/p>\n\n\n\n<p>\u6240\u4ee5\u7535\u573a\u5728\u590d\u6570\u57df\u7684\u8868\u793a\u53ef\u4ee5\u5199\u4e3a<\/p>\n\n\n\n<p>$$ \\widetilde{\\mathbf{E}} = \\left [ E_{0x}e^{i\\varphi _{x}} \\vec{\\mathbf{x}}  + E_{0y}e^{i\\varphi _{y}} \\vec{\\mathbf{y}}  \\right ]e^{i(kz-\\omega t)} = \\widetilde{ \\mathbf {E_{0}}} e^{i(kz-\\omega t)}   $$<\/p>\n\n\n\n<p>\u56e0\u4e3a\u504f\u632f\u6001\u5b8c\u5168\u7531\u7535\u573a\u5206\u91cf\u7684<strong><em>\u76f8\u5bf9\u5f3a\u5ea6\u548c\u76f8\u4f4d<\/em><\/strong>\u51b3\u5b9a\uff0c\u6839\u636e \\(  \\widetilde{ \\mathbf {E_{0}}}  \\)\u5c31\u53ef\u4ee5\u5b8c\u5168\u786e\u5b9a\u5149\u7684\u504f\u632f\u6001\uff0c\u5176\u77e9\u9635\u5f62\u5f0f\u79f0\u4e3a<strong><em>\u743c\u65af\u77e2\u91cf\uff08Jones vector\uff09<\/em><\/strong><\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} = \\begin{bmatrix}\nE_{0x}e^{i\\varphi_{x}} \\\\ E_{0y}e^{i\\varphi _{y}}\n\\end{bmatrix}\n\\end{equation}\n\n\n\n<p>\u743c\u65af\u77e2\u91cf\u65e0\u6cd5\u8868\u793a <strong><em>\u975e\u504f\u632f\u5149<\/em><\/strong>\u6216<strong><em>\u968f\u673a\u504f\u632f\u5149<\/em><\/strong> <\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%BA%BF%E5%81%8F%E6%8C%AF%E5%85%89\"><\/span>\u7ebf\u504f\u632f\u5149<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u4efb\u610f\\( \\alpha\\)\u7684\u7ebf\u504f\u5149\uff0c\u76f8\u5bf9\u76f8\u4f4d\u5dee\u4e3a<strong><em>0<\/em><\/strong>\u6216<strong><em>\u03c0<\/em><\/strong>\uff0c\u53ef\u4ee5\u8ba9\\( \\varphi_{x} =\\varphi_{y} = 0\\)<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} = \\begin{bmatrix}\nAcos\\left ( \\alpha \\right ) \\\\ Asin\\left ( \\alpha \\right )\n\\end{bmatrix}\n\\end{equation}\n\n\n\n<p>\u4e3a\u4e86\u4f7f \\( \\widetilde{ \\mathbf {E_{0}}} \\) \u5f52\u4e00\u5316\uff0c\u6b64\u5904 A = 1<\/p>\n\n\n\n<p>\u5047\u8bbe \\( \\varphi_{x} = 0 \\)\uff0c\\( \\varphi_{y} = \\varepsilon \\) \uff0c\u5b9a\u4e49\u76f8\u4f4d\u5dee \\(  \\Delta \\varphi = \\varphi_{y} &#8211; \\varphi_{x} =  \\varepsilon  \\)<\/p>\n\n\n\n<p>\u5f53\u76f8\u4f4d\u5dee\u4e3a\\( +\\pi \/2 \\)\u65f6\uff0c\u4e3a<strong><em>\u5de6\u65cb\u5149\uff08left-circularly polarized\uff0cLCP\uff09<\/em><\/strong>\uff0c\u7535\u573a\u77e2\u91cf\u7684\u7bad\u5934\u9006\u65f6\u9488\u65cb\u8f6c<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} = \\begin{bmatrix}\nAcos\\left ( \\alpha \\right ) \\\\ Asin\\left ( \\alpha \\right ) \n\\end{bmatrix}\n=\\begin{bmatrix}\nA \\\\ A e^{i\\pi \/2} \n\\end{bmatrix} \n=A\\begin{bmatrix}\n1 \\\\ i \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u6b64\u5904\\( A =\\frac{1}{\\sqrt{2}} \\)<\/p>\n\n\n\n<p> \u5f53\u76f8\u4f4d\u5dee\u4e3a\\( -\\pi \/2 \\)\u65f6\uff0c\u4e3a<strong><em>\u53f3\u65cb\u5149\uff08right-circularly polarized\uff0cRCP\uff09 <\/em><\/strong>\uff0c\u7535\u573a\u77e2\u91cf\u7684\u7bad\u5934\u987a\u65f6\u9488\u65cb\u8f6c <\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} \n= \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n1 \\\\ -i \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9C%86%E5%81%8F%E6%8C%AF%E5%85%89\"><\/span>\u5706\u504f\u632f\u5149<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u66f4\u52a0\u4e00\u822c\u7684\u5f62\u5f0f<\/p>\n\n\n\n<p>\u987a\u65f6\u9488<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} \n=  \\begin{bmatrix}\nA \\\\iB \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u9006\u65f6\u9488<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} \n=  \\begin{bmatrix}\nA \\\\-iB \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%A4%AD%E5%9C%86%E5%81%8F%E6%8C%AF%E5%85%89\"><\/span>\u692d\u5706\u504f\u632f\u5149<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u987a\u65f6\u9488<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} \n=  \\begin{bmatrix}\nA \\\\ B+iC \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u9006\u65f6\u9488<\/p>\n\n\n\n\\begin{equation}\n\\widetilde{ \\mathbf {E_{0}}} \n=  \\begin{bmatrix}\nA \\\\ B-iC \n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u66f4\u52a0\u4e00\u822c\u7684\u5f62\u5f0f\u7684\u63cf\u8ff0\uff0c\u692d\u5706\u65b9\u7a0b<\/p>\n\n\n\n\\begin{equation}\n\\frac{ \\widetilde{ E_{x}}^{2}} {E_{0x}^{2}} + \\frac{ \\widetilde{ E_{y}}^{2}} {E_{0y}^{2}} &#8211; \\frac{ 2\\widetilde{ E_{x}}\\widetilde{ E_{y}}} {E_{0x}E_{0y}} cos\\varepsilon  = sin^{2}\\varepsilon \n\\end{equation}\n\n\n\n<p>\u692d\u5706\u7684\u53c2\u6570\u53ef\u7531\u65b9\u5411\u89d2\uff08orientation angle\uff09\\( \\psi\\left ( 0 \\leq \\psi \\leq \\pi \\right ) \\)\u548c\u692d\u5706\u5ea6\u89d2\u8868\u793a\uff08ellipticity angle\uff09 \\( \\chi \\left ( -\\pi\/4 \\leq \\chi \\leq \\pi\/4 \\right ) \\)<\/p>\n\n\n\n<p>\u5f15\u5165\u8f85\u52a9\u89d2\uff08auxiliary angle\uff09<\/p>\n\n\n\n<p>$$ tan\\alpha = \\frac{E_{0y}}{E_{0x}}, 0 \\leq \\alpha \\leq \\pi\/2 $$<\/p>\n\n\n\n<p>\u6240\u4ee5<\/p>\n\n\n\n\\begin{equation}\ntan2\\psi = \\left ( tan2\\alpha \\right )cos\\varepsilon  \\\\\nsin2\\chi = \\left ( sin2\\alpha \\right )sin\\varepsilon \n\\end{equation}\n\n\n\n<p>\u5f15\u5165\u5e9e\u52a0\u83b1\u7403\uff08Poincare sphere\uff09<\/p>\n\n\n\n\\begin{equation}\n\\begin{aligned}\nx &#038;= cos(2\\chi)cos(2\\psi ) ,  0 \\leq \\psi \\leq \\pi \\\\\ny &#038;= cos(2\\chi)sin(2\\psi)  , -\\pi\/4 \\leq \\chi \\leq \\pi\/4 \\\\\nz &#038;= sin2\\chi \\\\\n1 &#038;= x^{2}+y^{2}+z^{2}\n\\end{aligned}\n\\end{equation}\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%90%BC%E6%96%AF%E7%9F%A9%E9%98%B5\"><\/span>\u743c\u65af\u77e9\u9635<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5149\u5b66\u5143\u4ef6\u53ef\u4ee5\u6539\u53d8\u900f\u5c04\u5149\u7684\u504f\u632f\u6001\uff0c\u7528\u743c\u65af\u77e9\u9635\u8868\u793a\u5149\u5b66\u5143\u4ef6\u5bf9\u900f\u5c04\u5149\u504f\u632f\u6001\u7684\u6539\u53d8\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%81%8F%E6%8C%AF%E5%99%A8\"><\/span>\u504f\u632f\u5668<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u53ea\u900f\u8fc7\u67d0\u4e00\u7ebf\u504f\u632f\u6001\u7684\u5149\uff0c\u4e0b\u9762\u7684\u77e9\u9635\u8868\u793a\uff0c\u53ea\u900f\u8fc7\\(\\vec{x}\\)\u65b9\u5411\u7684\u5206\u91cf<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} = \\begin{bmatrix}\n1 &#038; 0 \\\\  \n0 &#038; 0 \n\\end{bmatrix}\n\\end{equation}\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%9B%B8%E4%BD%8D%E5%BB%B6%E8%BF%9F%E5%99%A8\"><\/span>\u76f8\u4f4d\u5ef6\u8fdf\u5668<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u4f7f\u7535\u573a\u5206\u91cf\u7684\u76f8\u4f4d\u5206\u522b\u5ef6\u8fdf\\( \\varepsilon _{x}\\) \u548c  \\( \\varepsilon _{y}\\) <\/p>\n\n\n\n\\begin{equation}\nE_{0x}e^{i\\varphi_{x}} \\rightarrow E_{0x}e^{i(\\varphi_{x}+\\varepsilon _{x})}\n\\\\\nE_{0y}e^{i\\varphi _{y}}  \\rightarrow E_{0y}e^{i(\\varphi_{y}+\\varepsilon _{y})}\n\\end{equation}\n\n\n\n<p>\u5199\u6210\u77e9\u9635\u5f62\u5f0f<\/p>\n\n\n\n\\begin{equation}\n\\begin{bmatrix}\ne^{i\\varepsilon_{x}} &amp; 0\n\\\\\n0 &amp; e^{i\\varepsilon_{y}}\n\\end{bmatrix} \n\\begin{bmatrix}\nE_{0x}e^{i\\varphi_{x}}\n\\\\\n E_{0y}e^{i\\varphi_{y}}\n\\end{bmatrix} \n=\n\\begin{bmatrix}\nE_{0x}e^{i(\\varphi_{x}+\\varepsilon_{x})}\n\\\\\nE_{0y}e^{i(\\varphi_{y}+\\varepsilon_{y})}\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u6240\u4ee5\u666e\u9002\u7684\u76f8\u4f4d\u5ef6\u8fdf\u5668\u7684\u743c\u65af\u77e9\u9635\u4e3a<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} = \\begin{bmatrix}\ne^{i\\varepsilon_{x}} &amp; 0\n\\\\\n0 &amp; e^{i\\varepsilon_{y}}\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9B%9B%E5%88%86%E4%B9%8B%E4%B8%80%E6%B3%A2%E7%89%87\"><\/span>\u56db\u5206\u4e4b\u4e00\u6ce2\u7247<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>quarter-wave plate (QWP)  \u6ee1\u8db3\\( \\left | \\varepsilon_{x} &#8211; \\varepsilon_{y} \\right | = \\pi\/2 \\)<\/p>\n\n\n\n<p>\u6162\u8f74\u5782\u76f4\u65f6 \\( \\varepsilon_{x} &#8211; \\varepsilon_{y} = -\\pi\/2 \\)<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} =  \\begin{bmatrix}\ne^{-i\\pi\/4} &amp; 0\n\\\\\n0 &amp; e^{i\\pi\/4}\n\\end{bmatrix} \n= \ne^{-i\\pi\/4}\\begin{bmatrix}\n1 &amp; 0\n\\\\\n0 &amp; i\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u6162\u8f74\u6c34\u5e73\u65f6\\( \\varepsilon_{x} &#8211; \\varepsilon_{y} = \\pi\/2\\)<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} =  \\begin{bmatrix}\ne^{i\\pi\/4} &amp; 0\n\\\\\n0 &amp; e^{-i\\pi\/4}\n\\end{bmatrix} \n= \ne^{i\\pi\/4}\\begin{bmatrix}\n1 &amp; 0\n\\\\\n0 &amp; -i\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80%E6%B3%A2%E7%89%87\"><\/span>\u4e8c\u5206\u4e4b\u4e00\u6ce2\u7247<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>half-wave plate (HWP)  \u6ee1\u8db3\\( \\left | \\varepsilon_{x} &#8211; \\varepsilon_{y} \\right | = \\pi \\) <\/p>\n\n\n\n<p>\u540c\u7406<\/p>\n\n\n\n<p>\u6162\u8f74\u5782\u76f4\u65f6 \\( \\varepsilon_{x} &#8211; \\varepsilon_{y} = -\\pi \\)<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} =  \\begin{bmatrix}\ne^{-i\\pi\/2} &amp; 0\n\\\\\n0 &amp; e^{i\\pi\/2}\n\\end{bmatrix} \n= \ne^{-i\\pi\/2}\\begin{bmatrix}\n1 &amp; 0\n\\\\\n0 &amp; -1\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u6162\u8f74\u6c34\u5e73\u65f6\\( \\varepsilon_{x} &#8211; \\varepsilon_{y} = \\pi \\)<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{M} =  \\begin{bmatrix}\ne^{i\\pi\/2} &#038; 0\n\\\\\n0 &#038; e^{-i\\pi\/2}\n\\end{bmatrix} \n= \ne^{i\\pi\/2}\\begin{bmatrix}\n1 &#038; 0\n\\\\\n0 &#038; -1\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%97%8B%E8%BD%AC\"><\/span>\u65cb\u8f6c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u5c06\u67d0\u4e00\u89d2\u5ea6 \\(\\theta\\) \u7684\u7ebf\u504f\u632f\u5149\u65cb\u8f6c \\( \\beta \\) \u89d2\u5ea6<\/p>\n\n\n\n<p>\\( \\theta \\rightarrow \\left ( \\theta+ \\beta \\right ) \\)<\/p>\n\n\n\n\\begin{equation}\n\\mathbf{R}(\\beta) = \\begin{bmatrix}\ncos\\beta &amp; -sin\\beta\n\\\\\nsin\\beta &amp; cos\\beta\n\\end{bmatrix} \n\\end{equation}\n\n\n\n<p>\u65cb\u8f6c\u77e9\u9635\u7684\u6027\u8d28\\(  \\mathbf{R}\\mathbf{R}^{-1} = \\mathbf{R}\\mathbf{R}^{T} = \\mathbf{I} = \\mathbf{R}(\\beta)\\mathbf{R}(-\\beta)  \\)<\/p>\n\n\n\n<p>\u82e5\u5c06\u5149\u5b66\u5143\u4ef6\u65cb\u8f6c  \\( \\beta \\)  \u89d2\u5ea6<\/p>\n\n\n\n<p>$$ \\mathbf{M}(\\beta) = \\mathbf{R}(\\beta) \\mathbf{M} \\mathbf{R}(-\\beta) $$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%8F%82%E6%95%B0\"><\/span>\u65af\u6258\u514b\u65af\u53c2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>$$ S_{0}^{2} = S_{1}^{2} +S_{2}^{2} +S_{3}^{2} $$<\/p>\n\n\n\n\\begin{equation}\nS = \\begin{pmatrix}\nS_{0}\\\\ \nS_{1}\\\\ \nS_{2}\\\\ \nS_{3}\n\\end{pmatrix}\n= \\begin{pmatrix}\nE_{0x}^{2} + E_{0y}^{2}\\\\ \nE_{0x}^{2} &#8211; E_{0y}^{2}\\\\ \n2E_{0x}E_{0y}cos\\varepsilon \\\\ \n2E_{0x}E_{0y}sin\\varepsilon \n\\end{pmatrix}\n\\end{equation}\n\n\n\n<p>\u5176\u4e2d\\(  \\varphi_{y} &#8211; \\varphi_{x} =  \\varepsilon  \\)<\/p>\n\n\n\n<p>\u8003\u8651\u5230\u4e00\u822c\u692d\u5706\u504f\u632f\u7684\u60c5\u51b5\uff0c \u5b9e\u7528\u692d\u5706\u53c2\u6570\uff0c\u4e5f\u53ef\u4ee5\u5199\u4e3a<\/p>\n\n\n\n\\begin{equation}\nS = \\begin{pmatrix}\nS_{0}\\\\ \nS_{1}\\\\ \nS_{2}\\\\ \nS_{3}\n\\end{pmatrix}\n= S_{0}\\begin{pmatrix}\n1\\\\ \ncos(2\\chi)cos(2\\psi )\\\\ \ncos(2\\chi)sin(2\\psi )\\\\ \nsin(2\\chi )\n\\end{pmatrix}\n\\end{equation}\n\n\n\n<p>\u65af\u6258\u514b\u65af\u5206\u91cf\u53ef\u4ee5\u8868\u793a\u504f\u632f\u5149\uff0c\u4e5f\u53ef\u4ee5\u8868\u793a\u90e8\u5206\u504f\u632f\u5149\u6216\u968f\u673a\u504f\u632f\u5149<\/p>\n\n\n\n<p>\u5b9a\u4e49\u504f\u632f\u5ea6<strong><em>P<\/em><\/strong>\uff08degree of polarization \uff0cDOP\uff09<\/p>\n\n\n\n\\begin{equation}\nS = \\begin{pmatrix}\nS_{0}\\\\ \nS_{1}\\\\ \nS_{2}\\\\ \nS_{3}\n\\end{pmatrix}\n= \\left ( 1- \\mathbf{\\mathit{P}} \\right )\n\\begin{pmatrix}\nS_{0}\\\\ \n0\\\\ \n0\\\\ \n0\n\\end{pmatrix}\n+ \\mathbf{\\mathit{P}} \\begin{pmatrix}\nS_{0}\\\\ \nS_{1}\\\\ \nS_{2}\\\\ \nS_{3}\n\\end{pmatrix}, 0 \\leq \\mathbf{\\mathit{P}} \\leq 1\n\\end{equation}\n\n\n\n<p>\u504f\u632f\u5ea6<strong><em>P<\/em><\/strong>\u53ef\u7531\u4e0b\u5217\u516c\u5f0f\u8ba1\u7b97<\/p>\n\n\n\n<p>$$ \\mathbf{\\mathit{P}} = \\frac{I_{pol}}{I_{tot}} = \\frac{\\sqrt{S_{1}^{2}+S_{2}^{2}+S_{3}^{2}}}{S_{0}} $$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol class=\"wp-block-list\"><li>Pedrotti, F. L., Pedrotti, L. M. &amp; Pedrotti, L. S. <em>Introduction to optics<\/em>. (Pearson\/Prentice Hall, 2007).<\/li><li>Collett, E. <em>Field guide to polarization<\/em>. (SPIE Press, 2005).<\/li><li><a href=\"https:\/\/spie.org\/publications\/fg05_p57-61_jones_matrix_calculus\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/spie.org\/publications\/fg05_p57-61_jones_matrix_calculus<\/a> <\/li><li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Jones_calculus\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/en.wikipedia.org\/wiki\/Jones_calculus<\/a><\/li><li><a href=\"http:\/\/electron9.phys.utk.edu\/optics421\/modules\/m7\/Jones.htm\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/electron9.phys.utk.edu\/optics421\/modules\/m7\/Jones.htm<\/a><\/li><\/ol>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u504f\u632f\u662f\u6a2a\u6ce2\u7684\u4e00\u79cd\u6027\u8d28\uff0c\u7535\u78c1\u6ce2\u7684\u504f\u632f\u6001\u901a\u5e38\u662f\u6307\u7535\u573a\u77e2\u91cf\u7684\u65b9\u5411\u3002 \u5b9e\u9645\u751f\u6d3b\u4e2d\u7684\u5149\u6e90\uff0c\u5927\u591a\u662f\u975e\u76f8\u5e72\u5149\uff0c\u4ed6\u4eec\u53e0\u52a0\u540e\u6210\u4e3a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[345,346,349,348,347],"class_list":["post-1991","post","type-post","status-publish","format-standard","hentry","category-notes","tag-345","tag-346","tag-349","tag-348","tag-347"],"_links":{"self":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1991","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1991"}],"version-history":[{"count":79,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1991\/revisions"}],"predecessor-version":[{"id":2079,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1991\/revisions\/2079"}],"wp:attachment":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1991"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1991"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1991"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}