{"id":12008,"date":"2025-03-19T07:18:05","date_gmt":"2025-03-18T22:18:05","guid":{"rendered":"https:\/\/www11.ieice.org\/cs\/ap\/wp\/?page_id=12008"},"modified":"2025-12-05T18:26:02","modified_gmt":"2025-12-05T09:26:02","slug":"reflection_and_transmission","status":"publish","type":"page","link":"https:\/\/www.ieice.org\/cs\/ap\/misc\/denpan-db\/prop_model_db\/model_list\/reflection_and_transmission\/","title":{"rendered":"\u53cd\u5c04\u30fb\u900f\u904e\u7279\u6027"},"content":{"rendered":"
<\/div>

<\/path><\/svg><\/i> \"Loading\"<\/p>

<\/div>(since 2025\/12\/5)<\/p>\n\n\n\n

\u30e2\u30c7\u30eb\u306e\u6982\u8981<\/h3>\n\n\n\n

\u3000\u4f1d\u642c\u7d4c\u8def\u5185\u306b\u5b58\u5728\u3059\u308b\u969c\u5bb3\u7269\u306b\u96fb\u6ce2\u304c\u5165\u5c04\u3059\u308b\u3068\u3001\u305d\u306e\u5883\u754c\u3067\u53cd\u5c04\u30fb\u900f\u904e\u304c\u8d77\u3053\u308b\u3002\u6211\u3005\u306e\u751f\u6d3b\u3057\u3066\u3044\u308b\u7a7a\u9593\u306f\u69d8\u3005\u306a\u6750\u8cea\u3084\u5f62\u72b6\u3092\u6301\u3063\u305f\u5a92\u8cea\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u304c\u3001\u4e00\u822c\u7684\u306a\u5efa\u7bc9\u6750\u6599\u306f\u4e00\u5c64\u307e\u305f\u306f\u591a\u5c64\u306e\u8a98\u96fb\u4f53\u304b\u3064\u975e\u78c1\u6027\u4f53\u3067\u8fd1\u4f3c\u3067\u304d\u308b\u5834\u5408\u304c\u591a\u3044\u3002\u3053\u306e\u3068\u304d\u3001\u5404\u5c64\u306e\u8a98\u96fb\u4f53\u306e\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308c\u3070\u53cd\u5c04\u30fb\u900f\u904e\u7279\u6027\u3092\u7406\u8ad6\u7684\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u306e\u305f\u3081\u3001\u5e7e\u4f55\u5149\u5b66\u7684\u306b\u4f1d\u642c\u640d\u5931\u3092\u6c42\u3081\u308b\u8a08\u7b97\u624b\u6cd5\u3068\u6574\u5408\u6027\u304c\u9ad8\u304f\u3001\u30ec\u30a4\u30c8\u30ec\u30fc\u30b9\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3078\u306e\u5b9f\u88c5\u304c\u5bb9\u6613\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3000\u3053\u3053\u3067\u306f\u3001\u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3084ITU-R\u52e7\u544aP.2040\u306e\u57fa\u672c\u7684\u306a\u53cd\u5c04\u30fb\u900f\u904e\u7279\u6027\u306e\u7406\u8ad6\u5f0f\u3092\u7d39\u4ecb\u3059\u308b[1][2]\u3002\u3053\u306e\u7406\u8ad6\u5f0f\u306f\u96fb\u6ce2\u3092\u5e73\u9762\u6ce2\u3001\u5883\u754c\u3092\u7121\u9650\u306b\u5e83\u304c\u308b\u5e73\u9762\u3068\u3057\u3066\u8fd1\u4f3c\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u5b9f\u74b0\u5883\u3078\u9069\u7528\u3059\u308b\u5834\u5408\u306f\u3001\u30a2\u30f3\u30c6\u30ca\u3068\u5883\u754c\u3068\u306e\u8ddd\u96e2\u3001\u6ce2\u9577\u3068\u5883\u754c\u9762\u306e\u5927\u304d\u3055\u306e\u95a2\u4fc2\u306a\u3069\u304b\u3089\u9069\u5207\u306b\u4f7f\u308f\u308c\u308b\u5fc5\u8981\u304c\u3042\u308b\u70b9\u306b\u6ce8\u610f\u3059\u308b\u3002ITU-R\u52e7\u544aP.2040\u3067\u306f\u3001\u3044\u304f\u3064\u304b\u5b9f\u7528\u7684\u306a\u8a08\u7b97\u65b9\u6cd5\u3082\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b[2]\u3002\u6587\u732e[3]\u3067\u306f\u3001\u30ec\u30a4\u30c8\u30ec\u30fc\u30b7\u30f3\u30b0\u6cd5\u306b\u304a\u3051\u308b\u53cd\u5c04\u30fb\u900f\u904e\u7279\u6027\u306e\u8a08\u7b97\u65b9\u6cd5\u304c\u6570\u5f0f\u5316\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3053\u3061\u3089\u3082\u305c\u3072\u3054\u89a7\u3044\u305f\u3060\u304d\u305f\u3044\u3002<\/p>\n\n\n

\n
\"\"
\u56f31\u3000\u5883\u754c\u9762\u306e\u53cd\u5c04\u30fb\u900f\u904e<\/figcaption><\/figure><\/div>\n\n\n

\u6570\u5f0f<\/h3>\n\n\n\n

\u53cd\u5c04\u4fc2\u6570\u30fb\u900f\u904e\u4fc2\u6570<\/strong><\/h5>\n\n\n\n

\u3000\u56f31\u306e\u3088\u3046\u306b\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\u306e\u7570\u306a\u308b2\u3064\u306e\u5a92\u8cea1\u30012\u306e\u5883\u754c\u9762\u306b\u5165\u5c04\u3059\u308b\u5e73\u9762\u6ce2\u3092\u8003\u3048\u308b\u3002\u3053\u3053\u3067\u306fITU-R\u52e7\u544aP.2040\u306b\u306a\u3089\u3044\u3001\u5a92\u8cea1\u30012\u306f\u3068\u3082\u306b\u975e\u78c1\u6027\u4f53\u3068\u3057\u3001\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\u3092\u305d\u308c\u305e\u308c\\( \\eta_1 \\)\u3001\\( \\eta_2 \\)\u3068\u8868\u3059\u3002\u5a92\u8cea1\u304b\u3089\u5165\u5c04\u89d2\\( \\theta_i \\)\u3067\u5a92\u8cea2\u306b\u5165\u5c04\u3057\u305f\u96fb\u6ce2\u306e\u4e00\u90e8\u306f\u53cd\u5c04\u89d2\\( \\theta_r \\)\u3067\u53cd\u5c04\u3057\u3001\u6b8b\u308a\u306f\u900f\u904e\u89d2\uff08\u5c48\u6298\u89d2\uff09\\( \\theta_t \\)\u3067\u5a92\u8cea2\u3078\u900f\u904e\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u53cd\u5c04\u306e\u6cd5\u5247\u304a\u3088\u3073\u30b9\u30cd\u30eb\u306e\u6cd5\u5247\u3088\u308a\u3001\u5165\u5c04\u89d2\\( \\theta_i \\)\u3001\u53cd\u5c04\u89d2\\( \\theta_r \\)\u3001\u900f\u904e\u89d2\\( \\theta_t \\)\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(
\\theta_i = \\theta_r
\\tag{1}
\\)<\/p>\n\n\n\n

\\(
\\sqrt{ \\eta_1 } \\sin \\theta_i = \\sqrt{ \\eta_2 } \\sin \\theta_t
\\tag{2}
\\)<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001\u5f0f(2)\u3088\u308a\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n

\\(
{\\displaystyle
\\frac{ \\sin \\theta_i }{ \\sin \\theta_t } = \\frac{ \\sqrt{ \\eta_2 } }{ \\sqrt{ \\eta_1 } } = \\frac{ n_2 }{ n_1 } = n
}
\\tag{3}
\\)<\/p>\n\n\n\n

\\( n_1 \\)\u3001\\( n_2 \\)\u306f\u305d\u308c\u305e\u308c\u771f\u7a7a\u306e\u5c48\u6298\u7387\\( n_0 \\)=1\u3092\u57fa\u6e96\u3068\u3057\u305f\u5a92\u8cea1\u30012\u306e\u7d76\u5bfe\u5c48\u6298\u7387\u3001\\( n \\)\u306f\u5a92\u8cea1\u304b\u3089\u5a92\u8cea2\u3078\u306e\u76f8\u5bfe\u5c48\u6298\u7387\u3067\u3042\u308b\u3002
\u3000\u96fb\u6ce2\u306f\u3001\u96fb\u754c\u3068\u78c1\u754c\u304c\u4e92\u3044\u306b\u5782\u76f4\u306b\u632f\u52d5\u3057\u306a\u304c\u3089\u7a7a\u9593\u3092\u4f1d\u642c\u3057\u3066\u3044\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u504f\u6ce2\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u53cd\u5c04\u30fb\u900f\u904e\u306b\u304a\u3051\u308b\u504f\u6ce2\u306e\u65b9\u5411\u306f\u3001\u96fb\u754c\uff08\u307e\u305f\u306f\u78c1\u754c\uff09\u306e\u5411\u304d\u3068\u5165\u5c04\u9762\u3068\u306e\u95a2\u4fc2\u306b\u3088\u3063\u3066\u6c7a\u307e\u308b\u3002\u5165\u5c04\u9762\u3068\u306f\u3001\u5883\u754c\u9762\u306e\u6cd5\u7dda\u3068\u96fb\u6ce2\u306e\u9032\u884c\u65b9\u5411\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5e73\u9762\u3067\u3042\u308b\u3002\u56f32\u306b2\u7a2e\u985e\u306e\u76f4\u7dda\u504f\u6ce2\uff08TE\u6ce2\u3001TM\u6ce2\uff09\u306e\u53cd\u5c04\u30fb\u900f\u904e\u306e\u69d8\u5b50\u3092\u793a\u3059\u3002TE\uff08Transverse Electric\uff09\u6ce2\u306f\u3001\u96fb\u754c\u6210\u5206\u304c\u5165\u5c04\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\u3067\u3042\u308b\u3002\u3053\u306e\u305f\u3081\u3001\u76f4\u4ea4\u504f\u6ce2\u3068\u3082\u547c\u3070\u308c\u308b\u3002\u307e\u305f\u3001\u5927\u5730\u3092\u5883\u754c\u9762\u3068\u307f\u306a\u3057\u305f\u3068\u304d\u3001TE\u6ce2\u306f\u6c34\u5e73\u504f\u6ce2\uff08Horizontal polarization\uff09\u3068\u547c\u3070\u308c\u3001\u7121\u7dda\u901a\u4fe1\u306b\u304a\u3044\u3066\u306f\u3053\u306e\u8a00\u8449\u304c\u3088\u304f\u4f7f\u308f\u308c\u308b\u3002\u96fb\u6ce2\u306e\u53cd\u5c04\u30fb\u900f\u904e\u7279\u6027\u306e\u6307\u6a19\u3068\u3057\u3066\u53cd\u5c04\u4fc2\u6570\u30fb\u900f\u904e\u4fc2\u6570\u304c\u7528\u3044\u3089\u308c\u308b\u3002\u53cd\u5c04\u4fc2\u6570\u30fb\u900f\u904e\u4fc2\u6570\u306f\u7a7a\u9593\u3092\u4f1d\u642c\u3057\u305f\u969b\u306e\u4f1d\u642c\u640d\u5931\u3092\u542b\u307e\u305a\u3001\u305d\u308c\u305e\u308c\u3001\u5883\u754c\u9762\u306b\u304a\u3051\u308b\u5165\u5c04\u6ce2\u306e\u96fb\u754c\\( E_i \\)\u3068\u53cd\u5c04\u6ce2\u306e\u96fb\u754c\\( E_r \\)\u306e\u6bd4\u3001\u5883\u754c\u9762\u306b\u304a\u3051\u308b\u5165\u5c04\u6ce2\u306e\u96fb\u754c\\( E_i \\)\u3068\u900f\u904e\u6ce2\u306e\u96fb\u754c\\( E_t \\)\u306e\u6bd4\u3067\u8868\u3055\u308c\u308b\u3002TE\u6ce2\u306b\u304a\u3051\u308b\u53cd\u5c04\u4fc2\u6570\\( R_{\\rm TE} \\)\u304a\u3088\u3073\u900f\u904e\u4fc2\u6570\\( T_{\\rm TE} \\)\u306f\u6b21\u5f0f\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(
R_{\\rm TE} = {\\displaystyle \\frac{ E_r }{ E_i } } = \\left\\{
\\begin{array}{ll}
{\\displaystyle \\frac{ \\sqrt{ \\eta_1 } \\cos \\theta_1 \\ – \\sqrt{ \\eta_2 } \\cos \\theta_2 }{ \\sqrt{ \\eta_1 } \\cos \\theta_1 + \\sqrt{ \\eta_2 } \\cos \\theta_2 } }
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 < 1 } \\\\
1
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 \\geq 1 }
\\end{array}
\\right.
\\tag{4}
\\)<\/p>\n\n\n\n

\\(
T_{\\rm TE} = {\\displaystyle \\frac{ E_t }{ E_i } } = \\left\\{
\\begin{array}{ll}
{\\displaystyle \\frac{ 2 \\sqrt{ \\eta_1 } \\cos \\theta_1 }{ \\sqrt{ \\eta_1 } \\cos \\theta_1 + \\sqrt{ \\eta_2 } \\cos \\theta_2 } }
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 < 1 } \\\\
0
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 \\geq 1 }   
\\end{array}
\\right.
\\tag{5}
\\)<\/p>\n\n\n\n

\u4e00\u65b9\u3001TM\uff08Transverse Magnetic\uff09\u6ce2\u306f\u3001\u78c1\u754c\u6210\u5206\u304c\u5165\u5c04\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\u3067\u3042\u308b\u3002\u3059\u306a\u308f\u3061\u96fb\u754c\u6210\u5206\u304c\u5165\u5c04\u9762\u306b\u5bfe\u3057\u3066\u5e73\u884c\u3067\u3042\u308b\u305f\u3081\u3001\u5e73\u884c\u504f\u6ce2\u3068\u3082\u547c\u3070\u308c\u308b\u3002\u5927\u5730\u3092\u5883\u754c\u9762\u3068\u307f\u306a\u3057\u305f\u3068\u304d\u3001TM\u6ce2\u306f\u5782\u76f4\u504f\u6ce2\uff08Vertical polarization\uff09\u3068\u547c\u3070\u308c\u308b\u3002TM\u6ce2\u306b\u304a\u3051\u308b\u53cd\u5c04\u4fc2\u6570\\( R_{\\rm TM} \\) <\/sub>\u3001\u900f\u904e\u4fc2\u6570\\( T_{\\rm TM} \\)\u306f\u6b21\u5f0f\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(
R_{\\rm TM} = {\\displaystyle \\frac{ E_r }{ E_i } } = \\left\\{
\\begin{array}{ll}
{\\displaystyle \\frac{ \\sqrt{ \\eta_2 } \\cos \\theta_1 \\ – \\sqrt{ \\eta_1 } \\cos \\theta_2 }{ \\sqrt{ \\eta_2 } \\cos \\theta_1 + \\sqrt{ \\eta_1 } \\cos \\theta_2 } }
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 < 1 } \\\\
1
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 \\geq 1 }
\\end{array}
\\right.
\\tag{6}
\\)<\/p>\n\n\n\n

\\(
T_{\\rm TM} = {\\displaystyle \\frac{ E_t }{ E_i } } = \\left\\{
\\begin{array}{ll}
{\\displaystyle \\frac{ 2 \\sqrt{ \\eta_1 } \\cos \\theta_1 }{ \\sqrt{ \\eta_2 } \\cos \\theta_1 + \\sqrt{ \\eta_1 } \\cos \\theta_2 } }
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 < 1 } \\\\
0
& {\\displaystyle \\sqrt{ \\left| \\frac{ \\eta_1 }{ \\eta_2 } \\right| } \\sin \\theta_1 \\geq 1 }   
\\end{array}
\\right.
\\tag{7}
\\)<\/p>\n\n\n\n

\u3053\u308c\u3089\u306e\u5f0f\u306f\u30d5\u30ec\u30cd\u30eb\u306e\u5f0f\u3068\u547c\u3070\u308c\u308b\u3002
\u3000TM\u30e2\u30fc\u30c9\u306b\u304a\u3044\u3066\u5165\u5c04\u89d2\u304c\u7279\u5b9a\u306e\u89d2\u5ea6\u306b\u306a\u308b\u3068\u3001\u53cd\u5c04\u6ce2\u306e\u632f\u5e45\u304c\u30bc\u30ed\u306b\u306a\u308b\u3002\u3053\u306e\u89d2\u5ea6\u3092\u30d6\u30ea\u30e5\u30fc\u30b9\u30bf\u30fc\u89d2\uff08Brewster angle\uff09\u3068\u3044\u3046\u3002\u30d6\u30ea\u30e5\u30fc\u30b9\u30bf\u30fc\u89d2\\( \\theta_{\\rm B} \\)\u306f2\u3064\u306e\u5a92\u8cea\u306e\u5c48\u6298\u7387\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u3001\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\u3068\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n

\\(
{\\displaystyle
\\tan \\theta_{\\rm B} = \\sqrt{ \\frac{ \\eta_2 }{ \\eta_1 } }
}
\\tag{8}
\\)<\/p>\n\n\n\n

\u3000\u8a98\u96fb\u7387\u306e\u5927\u304d\u3044\u5a92\u8cea\u304b\u3089\u8a98\u96fb\u7387\u306e\u5c0f\u3055\u3044\u5a92\u8cea\u306b\u96fb\u6ce2\u304c\u5165\u5c04\u3059\u308b\u3068\u304d\u3001\u5165\u5c04\u89d2\u304c\u3042\u308b\u89d2\u5ea6\u3092\u8d85\u3048\u308b\u3068\u3001\u96fb\u6ce2\u306f\u3059\u3079\u3066\u53cd\u5c04\u3055\u308c\u900f\u904e\u3057\u306a\u304f\u306a\u308b\u3002\u3053\u306e\u73fe\u8c61\u3092\u5168\u53cd\u5c04\u3068\u547c\u3073\u3001\u3053\u306e\u3068\u304d\u306e\u89d2\u5ea6\u3092\u81e8\u754c\u89d2\uff08Critical angle\uff09\u3068\u547c\u3076\u3002\u56f31\u306b\u304a\u3044\u3066\\( \\eta_1 \\)\\( > \\)\\( \\eta_2 \\)\u306e\u3068\u304d\u3001\u81e8\u754c\u89d2\\( \\theta_{\\rm C} \\)\u3068\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\u3068\u306e\u9593\u306b\u306f\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n

\\(
{\\displaystyle
\\sin \\theta_{\\rm C} = \\sqrt{ \\frac{ \\eta_2 }{ \\eta_1 } }
}
\\tag{9}
\\)<\/p>\n\n\n\n

<\/div>\n\n\n
\n
\"\"
\u56f32\u3000\u76f4\u7dda\u504f\u6ce2\u306b\u304a\u3051\u308b\u5883\u754c\u9762\u306e\u53cd\u5c04\u30fb\u900f\u904e<\/figcaption><\/figure><\/div>\n\n\n
\u81ea\u7531\u7a7a\u9593\u5185\u306e\u5358\u5c64\u5e73\u677f\u306e\u53cd\u5c04\u4fc2\u6570\u30fb\u900f\u904e\u4fc2\u6570<\/strong><\/h5>\n\n\n\n

\u3000\u56f33\u306e\u3088\u3046\u306b\u3001\u6ce2\u6e90\u304b\u3089\u5341\u5206\u306b\u9060\u65b9\u306b\u3042\u308b\u81ea\u7531\u7a7a\u9593\u5185\u306e\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\\( \\eta \\)\u304b\u3064\u539a\u3055\\( d \\)\u306e\u5358\u5c64\u5e73\u677f\u306b\u5165\u5c04\u3059\u308b\u5e73\u9762\u6ce2\u306f\u3001\u5358\u5c64\u5e73\u677f\u3078\u306e\u5165\u5c04\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04\u3060\u3051\u3067\u306a\u304f\u3001\u5c64\u306e\u5185\u90e8\u306b\u304a\u3051\u308b\u53cd\u5c04\u3001\u3059\u306a\u308f\u3061\u591a\u91cd\u53cd\u5c04\u306e\u5f71\u97ff\u304c\u8868\u308c\u308b\u3002\u81ea\u7531\u7a7a\u9593\u3067\u306f\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\\( \\eta_0 \\)=1\u304a\u3088\u3073\u539a\u3055\\( d_0 \\)=0\u3068\u5b9a\u7fa9\u3055\u308c\u308b\u305f\u3081\u3001\u81ea\u7531\u7a7a\u9593\u5185\u306e\u5358\u5c64\u5e73\u677f\u306b\u304a\u3051\u308b\u53cd\u5c04\u4fc2\u6570\\( R \\)\u304a\u3088\u3073\u900f\u904e\u4fc2\u6570\\( T \\)\u306f\u6b21\u5f0f\u3068\u306a\u308b\u3002\u306a\u304a\u3001\u3053\u3053\u3067\u306e\u53cd\u5c04\u4fc2\u6570\\( R \\)\u306f\u5883\u754c\u97621\u306b\u304a\u3051\u308b\u5165\u5c04\u6ce2\u306e\u96fb\u754c\\( E_i \\)\u3068\u53cd\u5c04\u6ce2\u306e\u96fb\u754c\\( E_r \\)\u306e\u6bd4\u3001\u900f\u904e\u4fc2\u6570\\( T \\)\u306f\u5883\u754c\u97621\u306b\u304a\u3051\u308b\u5165\u5c04\u6ce2\u306e\u96fb\u754c\\( E_i \\)\u3068\u5883\u754c\u97622\u306b\u304a\u3051\u308b\u900f\u904e\u6ce2\u306e\u96fb\u754c\\( E_t \\)\u306e\u6bd4\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\\(
{\\displaystyle
R = \\frac{ E_r }{ E_i } = \\frac{ r \\{ 1 – \\exp ( -j2q ) \\} }{ 1 – r^2 \\exp ( -j2q ) }
}
\\tag{10}
\\)<\/p>\n\n\n\n

\\(
{\\displaystyle
T = \\frac{ E_t }{ E_i } = \\frac{ ( 1 – r^2 ) \\exp ( -jq ) } { 1 – r^2 \\exp ( -j2q ) }
}
\\tag{11}
\\)<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001\\( r \\)\u306f\u8a08\u7b97\u3059\u308b\u53cd\u5c04\u4fc2\u6570\\( R \\)\u304a\u3088\u3073\u900f\u904e\u4fc2\u6570\\( T \\)\u306e\u504f\u6ce2\uff08TE\u6ce2\u3001TM\u6ce2\uff09\u306b\u5fdc\u3058\u3066\u6b21\u5f0f\u3088\u308a\u9078\u629e\u3059\u308b\u3002<\/p>\n\n\n\n

\\(
r = \\left\\{
\\begin{array}{ll}
{\\displaystyle \\frac{ \\cos \\theta_0 \\ – \\sqrt{ \\eta \\ – \\sin^2 \\theta_0 } }{ \\cos \\theta_0 + \\sqrt{ \\eta \\ – \\sin^2 \\theta_0 } } }
& {\\rm TE} \\\\
{\\displaystyle \\frac{ \\eta \\cos \\theta_0 \\ – \\sqrt{ \\eta \\ – \\sin^2 \\theta_0 } }{ \\eta \\cos \\theta_0 + \\sqrt{ \\eta \\ – \\sin^2 \\theta_0 } } }
& {\\rm TM}
\\end{array}
\\right.
\\tag{12}
\\)<\/p>\n\n\n\n

<\/div>\n\n\n\n

\\(
{\\displaystyle
q = \\frac{ 2 \\pi d }{ \\lambda } \\sqrt{ \\eta \\ \u2013 \\sin^2 \\theta_0 }
}
\\tag{13}
\\)<\/p>\n\n\n\n

<\/div>\n\n\n
\n
\"\"
\u56f33\u3000\u81ea\u7531\u7a7a\u9593\u5185\u306e\u5358\u5c64\u5e73\u677f\u306e\u53cd\u5c04\u30fb\u900f\u904e<\/figcaption><\/figure><\/div>\n\n\n

\u30d1\u30e9\u30e1\u30fc\u30bf<\/h3>\n\n\n\n
\n
\n
\u8a18\u53f7<\/td>\u30d1\u30e9\u30e1\u30fc\u30bf\u8aac\u660e[\u5358\u4f4d]<\/td><\/tr>
\\( \\lambda \\)<\/td>\u6ce2\u9577 [m]<\/td><\/tr>
\\( \\theta_0 \\)<\/td>\u5165\u5c04\u89d2 [deg.]<\/td><\/tr>
\\( \\eta \\)<\/td>\u5a92\u8cea\u306e\u8907\u7d20\u6bd4\u8a98\u96fb\u7387<\/td><\/tr>
\\( d \\)<\/td>\u5a92\u8cea\u306e\u539a\u3055 [m]<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n

\u8a08\u7b97\u4f8b<\/h3>\n\n\n\n

\u3000\u56f33\u306b\u304a\u3044\u3066\u3001\u6ce2\u6e90\u304b\u3089\u5341\u5206\u306b\u9060\u65b9\u306b\u3042\u308b\u81ea\u7531\u7a7a\u9593\u5185\u306e\u539a\u3055\\( d \\)=10cm\u306e\u30b3\u30f3\u30af\u30ea\u30fc\u30c8\uff08\u8907\u7d20\u6bd4\u8a98\u96fb\u7387\\( \\eta \\)=5.24\u2212\\( j \\)0.71\uff09\u306b\u5468\u6ce2\u65702GHz\u306e\u6b63\u5f26\u6ce2\u304c\u5165\u5c04\u3057\u305f\u3068\u304d\u3001\u5f0f(10)\u304a\u3088\u3073(11)\u3067\u6c42\u3081\u3089\u308c\u308b\u53cd\u5c04\u4fc2\u6570\u304a\u3088\u3073\u900f\u904e\u4fc2\u6570\u306e\u632f\u5e45\\( |R| \\)\u304a\u3088\u3073\\( |T| \\)\u3092\u4e00\u4f8b\u3068\u3057\u3066\u793a\u3059\u3002\u305f\u3060\u3057\u3001\u5149\u901f\u306f2.99792458\u00d7108 <\/sup>m\/s\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\n
\n
\"\"
\u56f34\u3000\u539a\u305510cm\u306e\u30b3\u30f3\u30af\u30ea\u30fc\u30c8\u5e73\u677f\u306e\u53cd\u5c04\u4fc2\u6570\uff202GHz<\/figcaption><\/figure><\/div><\/div>\n\n\n\n
\n
\"\"
\u56f35\u3000\u539a\u305510cm\u306e\u30b3\u30f3\u30af\u30ea\u30fc\u30c8\u5e73\u677f\u306e\u900f\u904e\u4fc2\u6570\uff202GHz<\/figcaption><\/figure><\/div><\/div>\n<\/div>\n\n\n\n

\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b<\/h3>\n\n\n\n

ITU-R\u52e7\u544aP.2040\u306e\u5358\u5c64\u307e\u305f\u306f\u591a\u5c64\u5e73\u677f\u306e\u53cd\u5c04\u4fc2\u6570\u304a\u3088\u3073\u900f\u904e\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308bMATLAB\u30b3\u30fc\u30c9\u3092\u63d0\u4f9b\u3059\u308b\u3002 \u95a2\u6570\u201cfunc_extract_coefficients_v3\u201d\u3067\u306f\u3001ITU-R\u52e7\u544aP.2040-3\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u6750\u8cea\u3054\u3068\u306e\u96fb\u6c17\u5b9a\u6570\u306b\u95a2\u3059\u308b\u4fc2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

%% init\n\n% =================================================================================================== %\n% Input parameters\n%  freq_GHz     : frequency [GHz] ( SCALAR )\n%  idx_material : material index of each layer referenced in ITU-R Rec. P.2040-3 ( 1xN VECTOR )\n%  width_meter  : material width of each layer [m] ( 1xN VECTOR )\n% --------------------------------------------------------------------------------------------------- %\n% Material index\n%  1: air (0.001-100 GHz)\n%  2: Concrete (1-100 GHz)\n%  3: Brick (1-40 GHz)\n%  4: Plasterboard (1-100 GHz)\n%  5: Wood (0.001-100 GHz)\n%  6: Glass (0.1-100 GHz)\n%  7: Glass (220-450 GHz)\n%  8: Ceiling board (1-100 GHz)\n%  9: Ceiling board (220-450 GHz)\n% 10: Chipboard (1-100 GHz)\n% 11: Plywood (1-40 GHz)\n% 12: Marble (1-60 GHz)\n% 13: Floorboard (50-100 GHz)\n% 14: Metal (1-100 GHz)\n% 15: Very dry ground (1-10 GHz)\n% 16: Medium dry ground (1-10 GHz)\n% 17: Wet ground (1-10 GHz)\n% =================================================================================================== %\n\nfreq_GHz = 2;\nidx_material = 2; width_meter = 100e-3;\n% idx_material = [ 6 , 1 , 6 ]; width_meter = [ 6e-3 , 10e-3 , 6e-3 ];\n\ntheta_ref_deg = ( 0 : 0.1 : 90 )'; % Incident angle\n\n\n%% Material coefficients\n\n[ coef_material , coef_air ] = func_extract_coefficients_v3( idx_material );\n\n\n%% Electrical constants\n\n[ ~ , eta_air ] = func_electrical_constants( freq_GHz , coef_air ); % air\n[ ~ , eta_material ] = func_electrical_constants( freq_GHz , coef_material ); % material\n\n\n%% Reflection\/Transmission coefficients\n\n% --- Parameters of each layer ---\neta_n = [ eta_air , eta_material.' , eta_air ];\nd_n_meter = [ 0 , width_meter , 0 ];\nc = 2.99792458e8;\nwavelength = c \/ ( freq_GHz * 1e9 );\ngamma_n = 2 * pi \/ wavelength * sqrt( eta_n - sind( theta_ref_deg ).^2 );\ntheta_n_deg = asind( sind( theta_ref_deg ) .\/ sqrt( eta_n ) );\n\n% --- Fresnel reflection coefficient ---\nr_TE_n = ( sqrt( eta_n( 1 : end-1 ) ) .* cosd( theta_n_deg( : , 1 : end-1 ) ) - sqrt( eta_n( 2 : end ) ) .* cosd( theta_n_deg( : , 2 : end ) ) ) ...\n.\/ ( sqrt( eta_n( 1 : end-1 ) ) .* cosd( theta_n_deg( : , 1 : end-1 ) ) + sqrt( eta_n( 2 : end ) ) .* cosd( theta_n_deg( : , 2 : end ) ) );\nr_TM_n = ( sqrt( eta_n( 1 : end-1 ) ) .* cosd( theta_n_deg( : , 2 : end ) ) - sqrt( eta_n( 2 : end ) ) .* cosd( theta_n_deg( : , 1 : end-1 ) ) ) ...\n.\/ ( sqrt( eta_n( 1 : end-1 ) ) .* cosd( theta_n_deg( : , 2 : end ) ) + sqrt( eta_n( 2 : end ) ) .* cosd( theta_n_deg( : , 1 : end-1 ) ) );\n\n% --- Reflection coefficient for each layer ---\nNum_layer = length( eta_n );\nR_TE_n = zeros( length( theta_ref_deg ) , Num_layer );\nR_TM_n = zeros( length( theta_ref_deg ) , Num_layer );\n\nfor i_layer = ( Num_layer - 1 ) : -1 : 1\n\nR_TE_n( : , i_layer ) = ( r_TE_n( : , i_layer ) + R_TE_n( : , i_layer + 1 ) .* exp( -2j * gamma_n( : , i_layer + 1 ) .* d_n_meter( i_layer + 1 ) ) ) ...\n.\/ ( 1 + r_TE_n( : , i_layer ) .* R_TE_n( : , i_layer + 1 ) .* exp( -2j * gamma_n( : , i_layer + 1 ) .* d_n_meter( i_layer + 1 ) ) );\n\nR_TM_n( : , i_layer ) = ( r_TM_n( : , i_layer ) + R_TM_n( : , i_layer + 1 ) .* exp( -2j * gamma_n( : , i_layer + 1 ) .* d_n_meter( i_layer + 1 ) ) ) ...\n.\/ ( 1 + r_TM_n( : , i_layer ) .* R_TM_n( : , i_layer + 1 ) .* exp( -2j * gamma_n( : , i_layer + 1 ) .* d_n_meter( i_layer + 1 ) ) );\n\nend\n\nR_TE = R_TE_n( : , 1 );\nR_TM = R_TM_n( : , 1 );\n\nT_TE = prod( ( exp( -1j * gamma_n( : , 1 : end-1 ) .* d_n_meter( : , 1 : end-1 ) ) .* ( 1 + r_TE_n ) ) ...\n.\/ ( 1 + r_TE_n .* R_TE_n( : , 2 : end ) .* exp( -2j * gamma_n( : , 2 : end ) .* d_n_meter( 2 : end ) ) ) , 2 );\nT_TM = prod( ( exp( -1j * gamma_n( : , 1 : end-1 ) .* d_n_meter( : , 1 : end-1 ) ) .* ( 1 + r_TM_n ) ) ...\n.\/ ( 1 + r_TM_n .* R_TM_n( : , 2 : end ) .* exp( -2j * gamma_n( : , 2 : end ) .* d_n_meter( 2 : end ) ) ) , 2 );\n\n\n%% functions\n\nfunction [ coef , coef0 ] = func_extract_coefficients_v3( Index )\n% ----------------------------------------------------------------- %\n% Material properties described in TABLE 3 in Rec. ITU-R P.2040-3\n% ----------------------------------------------------------------- %\ncoef_mtrl = [\n1 0 0 0 % 1: air (0.001-100 GHz)\n5.24 0 0.0462 0.7822 % 2: Concrete (1-100 GHz)\n3.91 0 0.0238 0.16 % 3: Brick (1-40 GHz)\n2.73 0 0.0085 0.9395 % 4: Plasterboard (1-100 GHz)\n1.99 0 0.0047 1.0718 % 5: Wood (0.001-100 GHz)\n6.31 0 0.0036 1.3394 % 6: Glass (0.1-100 GHz)\n5.79 0 0.0004 1.658 % 7: Glass (220-450 GHz)\n1.48 0 0.0011 1.075 % 8: Ceiling board (1-100 GHz)\n1.52 0 0.0029 1.029 % 9: Ceiling board (220-450 GHz)\n2.58 0 0.0217 0.78 % 10: Chipboard (1-100 GHz)\n2.71 0 0.33 0 % 11: Plywood (1-40 GHz)\n7.074 0 0.0055 0.9262 % 12: Marble (1-60 GHz)\n3.66 0 0.0044 1.3515 % 13: Floorboard (50-100 GHz)\n1 0 10e7 0 % 14: Metal (1-100 GHz)\n3 0 0.00015 2.52 % 15: Very dry ground (1-10 GHz only)\n15 -0.1 0.035 1.63 % 16: Medium dry ground (1-10 GHz only)\n30 -0.4 0.15 1.3 % 17: Wet ground (1-10 GHz only)\n];\n\ncoef0 = coef_mtrl( 1 , : ); % air\ncoef = coef_mtrl( Index , : ); % material\n\nend\n\n\nfunction [ conductivity , permittivity ] = func_electrical_constants( freq_GHz , coef_material )\n% ----------------------------------------------------------------- %\n% Formulae in Sec. 2.1 & 3 in Rec. ITU-R P.2040-3\n% ----------------------------------------------------------------- %\n\na = coef_material( : , 1 );\nb = coef_material( : , 2 );\nc = coef_material( : , 3 );\nd = coef_material( : , 4 );\n\nconductivity = c .* ( freq_GHz ).^d; % eq.(28)\n\neta_prime = a .* ( freq_GHz ).^b; % eq.(29)\neta_prime2 = 17.98 * conductivity .\/ freq_GHz; % eq.(59)\npermittivity = eta_prime - 1j * eta_prime2; % eq.(10)\n\nend<\/code><\/pre><\/div>\n\n\n\n
\u53c2\u7167<\/h2>\n\n\n\n[1] \u7d30\u77e2\u826f\u96c4\uff08\u76e3\u4fee\uff09, \u201d\u4f1d\u642c\u306e\u6cd5\u5247,\u201d \u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af, ch.2, pp.11–18, \u30ea\u30a2\u30e9\u30a4\u30ba\u793e, 1999.<\/p>\n\n\n\n[2] Recommendation ITU-R P.2040-3, \u201cEffects of building materials and structures on radiowave propagation above about 100 MHz,\u2019\u2019 Aug. 2023.<\/p>\n\n\n\n[3] \u4eca\u4e95\u54f2\u6717, \u201d\u30ec\u30a4\u30c8\u30ec\u30fc\u30b7\u30f3\u30b0\u6cd5\u306e\u57fa\u790e,\u201d \u96fb\u6ce2\u4f1d\u642c\u89e3\u6790\u306e\u305f\u3081\u306e\u30ec\u30a4\u30c8\u30ec\u30fc\u30b7\u30f3\u30b0\u6cd5, ch.3, pp.42–88, \u30b3\u30ed\u30ca\u793e, \u6771\u4eac, 2016.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u30e2\u30c7\u30eb\u306e\u6982\u8981 \u3000\u4f1d\u642c\u7d4c\u8def\u5185\u306b\u5b58\u5728\u3059\u308b\u969c\u5bb3\u7269\u306b\u96fb\u6ce2\u304c\u5165\u5c04\u3059\u308b\u3068\u3001\u305d\u306e\u5883\u754c\u3067\u53cd\u5c04\u30fb\u900f\u904e\u304c\u8d77\u3053\u308b\u3002\u6211\u3005\u306e\u751f\u6d3b\u3057\u3066\u3044\u308b\u7a7a\u9593\u306f\u69d8\u3005\u306a\u6750\u8cea\u3084\u5f62\u72b6\u3092\u6301\u3063\u305f\u5a92\u8cea\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u304c\u3001\u4e00\u822c\u7684\u306a\u5efa\u7bc9\u6750\u6599\u306f\u4e00\u5c64\u307e\u305f\u306f\u591a\u5c64\u306e\u8a98\u96fb\u4f53\u304b\u3064\u975e\u78c1\u6027\u4f53\u3067\u8fd1 […]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":12073,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-12008","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/12008","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/comments?post=12008"}],"version-history":[{"count":101,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/12008\/revisions"}],"predecessor-version":[{"id":14852,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/12008\/revisions\/14852"}],"up":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/12073"}],"wp:attachment":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/media?parent=12008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}