{"id":209243,"date":"2024-03-21T14:06:51","date_gmt":"2024-03-21T14:06:51","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/%e7%be%a4%e9%80%9f%e5%ba%a6%e5%88%86%e6%95%a3%ef%bc%88gvd%ef%bc%89%e3%81%ae%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/"},"modified":"2024-05-17T15:09:28","modified_gmt":"2024-05-17T15:09:28","slug":"%e7%be%a4%e9%80%9f%e5%ba%a6%e5%88%86%e6%95%a3%ef%bc%88gvd%ef%bc%89%e3%81%ae%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/ja\/%e7%be%a4%e9%80%9f%e5%ba%a6%e5%88%86%e6%95%a3%ef%bc%88gvd%ef%bc%89%e3%81%ae%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306e\u5f0f | \u6982\u8981\u3068\u8a08\u7b97\u65b9\u6cd5"},"content":{"rendered":"<p class=\"sidekick\">\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306f\u3001\u5149\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u30d1\u30eb\u30b9\u306e\u6642\u9593\u7684\u5e83\u304c\u308a\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u91cd\u8981\u306a\u73fe\u8c61\u3067\u3001\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u3082\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<h2>\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306e\u5f0f | \u6982\u8981\u3068\u8a08\u7b97\u65b9\u6cd5<\/h2>\n<p>\u7fa4\u901f\u5ea6\u5206\u6563\uff08Group Velocity Dispersion, GVD\uff09\u306f\u3001\u5149\u3084\u6ce2\u52d5\u306e\u4f1d\u642c\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u6982\u5ff5\u306e\u4e00\u3064\u3067\u3059\u3002\u7279\u306b\u5149\u30d5\u30a1\u30a4\u30d0\u30fc\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u3001\u6ce2\u306e\u30d1\u30eb\u30b9\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7fa4\u901f\u5ea6\u5206\u6563\u306e\u57fa\u672c\u6982\u5ff5\u3068\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<h2>\u7fa4\u901f\u5ea6\u5206\u6563\u306e\u6982\u8981<\/h2>\n<p>\u7fa4\u901f\u5ea6\u5206\u6563\u3068\u306f\u3001\u7570\u306a\u308b\u5468\u6ce2\u6570\u6210\u5206\u304c\u7570\u306a\u308b\u901f\u5ea6\u3067\u4f1d\u642c\u3059\u308b\u305f\u3081\u306b\u3001\u30d1\u30eb\u30b9\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u5e83\u304c\u308b\u73fe\u8c61\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u901a\u4fe1\u4fe1\u53f7\u304c\u6b6a\u3093\u3060\u308a\u3001\u30ec\u30fc\u30b6\u30fc\u30d1\u30eb\u30b9\u304c\u9577\u304f\u306a\u3063\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7fa4\u901f\u5ea6\u5206\u6563\u306f\u3001\u7279\u306b\u9ad8\u7cbe\u5ea6\u304c\u6c42\u3081\u3089\u308c\u308b\u5149\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u907f\u3051\u3089\u308c\u306a\u3044\u8ab2\u984c\u3067\u3059\u3002<\/p>\n<h2>\u7fa4\u901f\u5ea6\u3068\u5206\u6563\u95a2\u4fc2<\/h2>\n<p>\u7fa4\u901f\u5ea6 \\(v_g\\) \u306f\u3001\u4f4d\u76f8\u901f\u5ea6 \\(v_p\\) \u3068\u7570\u306a\u308b\u6982\u5ff5\u3067\u3001\u6ce2\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3084\u60c5\u5831\u304c\u4f1d\u642c\u3059\u308b\u901f\u5ea6\u3092\u8868\u3057\u307e\u3059\u3002\u4f4d\u76f8\u901f\u5ea6\u306f\u3001\u6ce2\u306e\u4f4d\u76f8\u304c\u4f1d\u642c\u3059\u308b\u901f\u5ea6\u3067\u3059\u3002\u3053\u306e2\u3064\u306e\u901f\u5ea6\u306f\u4e00\u822c\u7684\u306b\u5468\u6ce2\u6570\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u4f4d\u76f8\u901f\u5ea6 \\(v_p\\) \u3068\u632f\u52d5\u6570 \\( \\omega \\) \u306b\u306f\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p>\\[ k = \\frac{\\omega}{v_p} \\]<\/p>\n<p>\u3053\u3053\u3067\u3001\\( k \\) \u306f\u6ce2\u6570 (\u6ce2\u306e\u7a7a\u9593\u5468\u6ce2\u6570) \u3067\u3059\u3002\u305d\u3057\u3066\u3001\u7fa4\u901f\u5ea6\u306f\u6b21\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p>\\[<br \/>\nv_g = \\frac{d\\omega}{dk}<br \/>\n\\]<\/p>\n<p>\u3057\u304b\u3057\u3001\u5206\u6563\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u7fa4\u901f\u5ea6\u3082\u5468\u6ce2\u6570\u306b\u4f9d\u5b58\u3057\u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u5316\u3057\u307e\u3059\uff1a<\/p>\n<p>\\[<br \/>\nv_g(\\omega) = \\frac{d\\omega}{dk}<br \/>\n\\]<\/p>\n<p>\u3053\u3053\u3067\u3001\u5206\u6563\u4fc2\u6570 \\(D\\) \u3092\u4f7f\u3063\u3066\u3001\u7fa4\u901f\u5ea6\u5206\u6563 \\( \\beta_2 \\) \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff1a<\/p>\n<p>\\[<br \/>\n\\beta_2 = \\frac{d^2 k}{d\\omega^2}<br \/>\n\\]<\/p>\n<h2>\u7fa4\u901f\u5ea6\u5206\u6563\u306e\u8a08\u7b97\u65b9\u6cd5<\/h2>\n<p>\u7fa4\u901f\u5ea6\u5206\u6563\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u307e\u305a\u5206\u6563\u95a2\u4fc2\u5f0f\uff08 \\(\\omega\\) \u3068 \\(k\\) \u306e\u95a2\u4fc2\uff09\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5206\u6563\u95a2\u4fc2\u5f0f\u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u5fc5\u8981\u306a\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u3066 \\(\\beta_2\\) \u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\u5149\u30d5\u30a1\u30a4\u30d0\u30fc\u306b\u304a\u3051\u308b\u5177\u4f53\u4f8b\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5149\u30d5\u30a1\u30a4\u30d0\u30fc\u306e\u5206\u6563\u95a2\u4fc2\u5f0f\u306f\u901a\u5e38\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p>\\[<br \/>\n\\beta(\\omega) = \\beta_0 + \\beta_1(\\omega &#8211; \\omega_0) + \\frac{1}{2} \\beta_2 (\\omega &#8211; \\omega_0)^2 + \\ldots<br \/>\n\\]<\/p>\n<p>\u3053\u3053\u3067\u3001\\(\\beta_0\\)\u3001\\(\\beta_1\\)\u3001\\(\\beta_2\\)\u306f\u305d\u308c\u305e\u308c0\u6b21\u30011\u6b21\u30012\u6b21\u306e\u5206\u6563\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001\\(\\omega_0\\)\u306f\u4e2d\u5fc3\u5468\u6ce2\u6570\u3067\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u7fa4\u901f\u5ea6\u5206\u6563\u306f\u3053\u306e2\u6b21\u9805 \\(\\beta_2\\) \u306b\u95a2\u9023\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2>\u6570\u5024\u4f8b<\/h2>\n<p>\u5177\u4f53\u7684\u306a\u6570\u5024\u4f8b\u3068\u3057\u3066\u3001\u8a2d\u8a08\u3055\u308c\u305f\u5149\u30d5\u30a1\u30a4\u30d0\u30fc\u306b\u304a\u3044\u3066\u3001\u7279\u5b9a\u306e\u6ce2\u9577\u3067\u306e\\(\\beta_2\\)\u304c\\(-20 \\, \\text{ps}^2\/\\text{km}\\)\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u30d5\u30a1\u30a4\u30d0\u30fc\u306b\u5149\u30d1\u30eb\u30b9\u3092\u901a\u3059\u3068\u3001\u30d1\u30eb\u30b9\u306e\u5e83\u304c\u308a\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p>\\[<br \/>\nt_{\\text{dispersion}} = \\beta_2 L (\\Delta\\omega)^2<br \/>\n\\]<\/p>\n<p>\u3053\u3053\u3067\u3001 \\(L\\) \u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u306e\u9577\u3055\u3001\\(\\Delta\\omega\\) \u306f\u5468\u6ce2\u6570\u5e2f\u57df\u5e45\u3067\u3059\u3002\u4eee\u306b\u3001\u30d5\u30a1\u30a4\u30d0\u30fc\u306e\u9577\u3055\u304c100km\u3067\u3001\u5468\u6ce2\u6570\u5e2f\u57df\u5e45\u304c1THz\uff08\\(1 \\times 10^{12} \\, \\text{Hz}\\)\uff09\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30d1\u30eb\u30b9\u306e\u6642\u9593\u5e83\u304c\u308a\u306f\uff1a<\/p>\n<p>\\[<br \/>\nt_{\\text{dispersion}} = (-20 \\times 10^{-12} \\,\\text{s}^2\/\\text{km}) \\times 100 \\,\\text{km} \\times (1 \\times 10^{12} \\,\\text{Hz})^2<br \/>\n\\]<\/p>\n<p>\\[<br \/>\nt_{\\text{dispersion}} = -2000 \\times 10^{-12} \\,\\text{s} = -2 \\,\\text{ps}<br \/>\n\\]<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5149\u30d5\u30a1\u30a4\u30d0\u30fc\u5185\u3067\u306e\u30d1\u30eb\u30b9\u306e\u5e83\u304c\u308a\u306f2\u30d4\u30b3\u79d2\u3068\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u73fe\u5b9f\u306e\u8a2d\u8a08\u3067\u306f\u8ca0\u306e\u5024\u304c\u5e83\u304c\u308a\u306e\u6e2c\u5b9a\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001\u7d76\u5bfe\u5024\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306f\u3001\u5149\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3042\u308a\u3001\u6ce2\u306e\u30d1\u30eb\u30b9\u306e\u4f1d\u642c\u306b\u5927\u304d\u306a\u5f71\u97ff\u3092\u4e0e\u3048\u307e\u3059\u3002\u57fa\u672c\u7684\u306a\u6570\u5f0f\u3084\u8a08\u7b97\u65b9\u6cd5\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u52b9\u679c\u7684\u306a\u30b7\u30b9\u30c6\u30e0\u8a2d\u8a08\u3084\u6700\u9069\u5316\u304c\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002\u7fa4\u901f\u5ea6\u5206\u6563\u306e\u8a73\u7d30\u306a\u7406\u89e3\u306f\u3001\u6280\u8853\u306e\u9032\u6b69\u3068\u5171\u306b\u307e\u3059\u307e\u3059\u91cd\u8981\u3068\u306a\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306f\u3001\u5149\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u30d1\u30eb\u30b9\u306e\u6642\u9593\u7684\u5e83\u304c\u308a\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u91cd\u8981\u306a\u73fe\u8c61\u3067\u3001\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u3082\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[96],"tags":[97],"class_list":["post-209243","post","type-post","status-publish","format-standard","hentry","category-96","tag-97","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306e\u5f0f | \u6982\u8981\u3068\u8a08\u7b97\u65b9\u6cd5<\/title>\n<meta name=\"description\" content=\"\u7fa4\u901f\u5ea6\u5206\u6563\uff08GVD\uff09\u306f\u3001\u5149\u901a\u4fe1\u3084\u30ec\u30fc\u30b6\u30fc\u6280\u8853\u306b\u304a\u3044\u3066\u30d1\u30eb\u30b9\u306e\u6642\u9593\u7684\u5e83\u304c\u308a\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u91cd\u8981\u306a\u73fe\u8c61\u3067\u3001\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u3082\u89e3\u8aac\u3057\u307e\u3059\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.electricity-magnetism.org\/ja\/%e7%be%a4%e9%80%9f%e5%ba%a6%e5%88%86%e6%95%a3%ef%bc%88gvd%ef%bc%89%e3%81%ae%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/\" \/>\n<meta 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