{"id":284833,"date":"2017-04-12T08:30:29","date_gmt":"2017-04-12T04:30:29","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=284833"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=284833","title":{"rendered":"\u0410\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u041c\u0430\u043a\u0441\u0432\u0435\u043b\u043b\u0430: \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u043c\u043e\u0434\u044b \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0430 (\u043b\u044e\u0431\u0438\u0442\u0435\u043b\u044f\u043c \u00ab\u043c\u0430\u0442\u0430\u043d\u0430\u00bb)"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/files\/fbc\/d5e\/b09\/fbcd5eb09cc74856ad8f598719959831.png\"\/><br \/>  \u041a\u0430\u043a-\u0442\u043e \u043c\u043d\u0435 \u043f\u043e\u043d\u0430\u0434\u043e\u0431\u0438\u043b\u0430\u0441\u044c &quot;<b>\u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043c\u043e\u0434\u0430 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0430<\/b>&quot;. \u041d\u043e \u044f \u043d\u0438\u0433\u0434\u0435 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b <b>\u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043c\u0430\u0433\u043d\u0438\u0442\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f<\/b>. \u041d\u0443 \u0438 \u00ab\u0441\u0434\u0435\u043b\u0430\u043b \u0441\u0430\u043c\u00bb, \u0440\u0430\u0437 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b, \u0438 <b>\u043e\u0444\u043e\u0440\u043c\u0438\u043b \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0442\u0443\u0442, \u0432 \u0441\u0442\u0430\u0442\u044c\u0435<\/b>. \u0422\u0430\u043a \u0447\u0442\u043e, \u0441\u043a\u043e\u0440\u0435\u0435 \u0432\u0441\u0435\u0433\u043e, \u043d\u0438\u0433\u0434\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0432\u044b \u0442\u0430\u043a\u043e\u0433\u043e \u043d\u0435 \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u0435 \u2014 \u0443\u043d\u0438\u043a\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0430\u044f \u0432\u0435\u0449\u044c! \u0412 \u043a\u043d\u0438\u0436\u043a\u0430\u0445 \u044d\u0442\u043e \u043d\u0435 \u043f\u0438\u0448\u0443\u0442, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d\u043e \u0434\u043b\u0438\u043d\u043d\u043e\u0435 \u2014 \u043e\u0431\u044b\u0447\u043d\u043e \u043f\u0438\u0448\u0443\u0442 \u0441\u0430\u043c\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0435, \u0430 \u043f\u0440\u043e \u043e\u0431\u0449\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u044e\u0442 \u0432\u0441\u043a\u043e\u043b\u044c\u0437\u044c. \u041d\u0443 \u0432\u043e\u0442 \u043e\u043d, \u043e\u0431\u0449\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439, \u043f\u043e\u0434 \u043a\u0430\u0442\u043e\u043c.<br \/>  <a name=\"habracut\"><\/a><\/p>\n<h1>\u041f\u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0438<\/h1>\n<p>  <img decoding=\"async\" src=\"https:\/\/habrastorage.org\/files\/285\/c92\/256\/285c922566f84774bda9a2b8e56d7a8e.png\"\/><br \/>  \u0420\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u041c\u0430\u043a\u0441\u0432\u0435\u043b\u043b\u0430 \u0441 \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u043c\u0438:<br \/>   \u2014 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u043e \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0441\u0435\u0440\u0434\u0446\u0435\u0432\u0438\u043d\u044b \u0440\u0430\u0434\u0438\u0443\u0441\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ac1\/7c5\/491\/ac17c549119a8b8b949d7612ef39b71d.svg\" alt=\"$a$\" data-tex=\"inline\"\/><\/math> \u0441 \u0434\u0438\u044d\u043b\u0435\u043a\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u043e\u0441\u0442\u044c\u044e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/546\/2dd\/992\/5462dd99246419b600bfddd89d060f96.svg\" alt=\"$\\varepsilon_1$\" data-tex=\"inline\"\/><\/math> \u0438 \u043e\u0431\u043e\u043b\u043e\u0447\u043a\u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0432\u043d\u0435\u0448\u043d\u0435\u0433\u043e \u0440\u0430\u0434\u0438\u0443\u0441\u0430 \u0441 \u0434\u0438\u044d\u043b\u0435\u043a\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u043e\u0441\u0442\u044c\u044e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/11d\/cea\/024\/11dcea0241793318d113a919a71faf0f.svg\" alt=\"$\\varepsilon_2$\" data-tex=\"inline\"\/><\/math>,<br \/>   \u2014 \u043f\u043e\u043b\u0435 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u043d\u043e \u043f\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>, \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u0432\u0441\u0435\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u043f\u043e\u043b\u044f \u0435\u0434\u0438\u043d\u0430: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b3b\/a34\/750\/b3ba34750c977801ab284655b95d3e30.svg\" alt=\"$k_z$\" data-tex=\"inline\"\/><\/math>,<br \/>   \u2014 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f \u043d\u0430 \u043e\u0441\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b4a\/45f\/4e9\/b4a45f4e932e1387725106759a0c8914.svg\" alt=\"$O_z$\" data-tex=\"inline\"\/><\/math> \u2014 \u0431\u0435\u0437 \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0435\u0439,<br \/>   \u2014 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/965\/d48\/1b2\/965d481b2fcddfb67656705dfdbeb054.svg\" alt=\"$r \\rightarrow\\infty$\" data-tex=\"inline\"\/><\/math> \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c\u044b \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u043c,<br \/>   \u2014 \u0442\u0430\u043d\u0433\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f \u043d\u0430 \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u0438 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/04a\/19d\/223\/04a19d223277d42ef0c6bb517085e6e7.svg\" alt=\"$r=a$\" data-tex=\"inline\"\/><\/math> \u2014 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/7da\/30f\/985\/7da30f985104e51704706b00778d1357.svg\" alt=\"$E_{z,1}\\bigg|_{r=a}=E_{z,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/7f9\/130\/32e\/7f913032e72f06cad91d428d411a7164.svg\" alt=\"$E_{\\varphi,1}\\bigg|_{r=a}=E_{\\varphi,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/e0a\/194\/091\/e0a194091b8dad5d8728eaf99fb9213e.svg\" alt=\"$H_{z,1}\\bigg|_{r=a}=H_{z,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a63\/84a\/234\/a6384a234b28b3144151952be98e98b8.svg\" alt=\"$H_{\\varphi,1}\\bigg|_{r=a}=H_{\\varphi,2}\\bigg|_{r=a}$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>1. \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u041c\u0430\u043a\u0441\u0432\u0435\u043b\u043b\u0430, \u0432\u044b\u0437\u0432\u0430\u043d\u043d\u043e\u0435 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u043d\u043e\u0441\u0442\u044c\u044e \u043f\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math><\/h1>\n<p>  \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u0432 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u041c\u0430\u043a\u0441\u0432\u0435\u043b\u043b\u0430 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043f\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/4c2\/fd1\/b3a\/4c2fd1b3a93de71b2f6e3ec656bae77b.svg\" alt=\"$\\textbf{E}(x,y,z,t) = \\left( \\begin{array}{c} e_x(x,y)\\\\ e_y(x,y)\\\\ e_z(x,y) \\end{array} \\right) \\exp\\left\\lbrace ik_zz - i\\omega t \\right\\rbrace, \\quad \\textbf{B}(x,y,z,t) = \\left( \\begin{array}{c} b_x(x,y)\\\\ b_y(x,y)\\\\ b_z(x,y) \\end{array} \\right) \\exp\\left\\lbrace ik_zz - i\\omega t \\right\\rbrace,$\" data-tex=\"display\"\/><\/math><\/p>\n<p>   \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>-\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/e2f\/5d2\/d00\/e2f5d2d002f597ff630fa367d63b6973.svg\" alt=\"$\\Delta_{\\bot}e_z + \\gamma^2e_z=0,\\,\\Delta_{\\bot}b_z + \\gamma^2b_z=0,\\,\\text{\u0433\u0434\u0435 }\\Delta_{\\bot}=\\frac{\\partial^2}{\\partial x^2}+\\frac{\\partial^2}{\\partial y^2},\\quad \\gamma^2 = \\varepsilon\\mu\\frac{\\omega^2}{c^2}-k^2_z.$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u044b\u0440\u0430\u0436\u0430\u044e\u0442\u0441\u044f \u0447\u0435\u0440\u0435\u0437 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>-\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e \u0437\u0430\u043a\u043e\u043d\u0443:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/5bd\/551\/cd0\/5bd551cd0c47cabd918841c620ce8df0.svg\" alt=\"$\\textbf{b}_{\\bot} = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\operatorname{grad}_{\\bot}b_z + \\varepsilon\\mu\\frac{\\omega}{c}\\left[ \\hat{\\textbf{z}}\\times\\operatorname{grad}_{\\bot}e_z\\right] \\right\\rbrace, \\, \\textbf{e}_{\\bot} = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\operatorname{grad}_{\\bot}e_z - \\frac{\\omega}{c}\\left[ \\hat{\\textbf{z}}\\times\\operatorname{grad}_{\\bot}b_z\\right] \\right\\rbrace,$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u0433\u0434\u0435 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/456\/3b7\/515\/4563b7515fed70d0b19538fa060e9c8a.svg\" alt=\"$\\hat{\\textbf{z}}$\" data-tex=\"inline\"\/><\/math> \u2014 \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0434\u043e\u043b\u044c \u043e\u0441\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b4a\/45f\/4e9\/b4a45f4e932e1387725106759a0c8914.svg\" alt=\"$O_z$\" data-tex=\"inline\"\/><\/math>, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3d5\/d09\/4d2\/3d5d094d220e29849adcabc144bade19.svg\" alt=\"$\\operatorname{grad}_{\\bot} = \\hat{\\textbf{x}} \\partial_x+\\hat{\\textbf{y}}\\partial_y$\" data-tex=\"inline\"\/><\/math>, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8c4\/6f0\/692\/8c46f069255114b09a01745e7d92c181.svg\" alt=\"$\\textbf{e}_{\\bot} = \\hat{\\textbf{x}}e_x + \\hat{\\textbf{y}} e_y,\\,\\textbf{b}_{\\bot} = \\hat{\\textbf{x}}b_x +\\hat{\\textbf{y}}b_y$\" data-tex=\"inline\"\/><\/math>.<\/p>\n<h1>2. \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>-\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432 \u043f\u043e\u043b\u044f\u0440\u043d\u044b\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0445<\/h1>\n<p>  \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/468\/5c9\/069\/4685c906953725958227b0317261b556.svg\" alt=\"$e_z,\\,b_z$\" data-tex=\"inline\"\/><\/math> \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d \u0432\u0438\u0434, \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u043f\u0435\u0440\u0435\u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0438\u0441\u043a\u043e\u043c\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/36a\/677\/94d\/36a67794d87775806486ca2be8a70f39.svg\" alt=\"$\\Delta_{\\bot}\\psi + \\gamma^2\\psi=0.$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u0412 \u043f\u043e\u043b\u044f\u0440\u043d\u044b\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/214\/ff2\/7d1\/214ff27d1371afcf90b156a133529999.svg\" alt=\"$r^2\\frac{\\partial^2}{\\partial r^2}\\psi + r\\frac{\\partial}{\\partial r}\\psi + \\frac{\\partial^2 }{\\partial \\varphi^2}\\psi + r^2\\left( \\frac{\\varepsilon\\mu}{c^2}\\omega^2 - k_z^2 \\right) \\psi = 0.$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>3. \u0420\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438<\/h1>\n<p>  \u041f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u043e\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/21b\/896\/243\/21b896243fe5b059f831c8b753fb6f34.svg\" alt=\"$\\psi(r,\\varphi) = u(r)v(\\varphi)$\" data-tex=\"inline\"\/><\/math> \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0440\u0430\u0437\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/f34\/caa\/2c5\/f34caa2c5bead43cd6477de054f68616.svg\" alt=\"$\\frac{1}{u(r)}r^2\\frac{\\partial^2}{\\partial r^2}u(r) + \\frac{1}{u(r)}r\\frac{\\partial}{\\partial r}u(r) + r^2\\left( \\frac{\\varepsilon\\mu}{c^2}\\omega^2 - k_z^2 \\right) = - \\frac{1}{v(\\varphi)}\\frac{\\partial^2 }{\\partial \\varphi^2}v(\\varphi).$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u0432 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/152\/8de\/5b4\/1528de5b495ea7fc923b47a280115aeb.svg\" alt=\"$\\nu^2$\" data-tex=\"inline\"\/><\/math> \u0432\u044b\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430: <\/p>\n<p><math>$$display$$- \\frac{1}{v(\\varphi)}\\frac{\\partial^2 }{\\partial \\varphi^2}v(\\varphi) = \\nu^2,$$display$$<\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b2a\/43d\/15f\/b2a43d15f80590181570c540ae144ff6.svg\" alt=\"$\\frac{1}{u(r)}r^2\\frac{\\partial^2}{\\partial r^2}u(r) + \\frac{1}{u(r)}r\\frac{\\partial}{\\partial r}u(r) + r^2\\left( \\frac{\\varepsilon\\mu}{c^2}\\omega^2 - k_z^2 \\right) = \\nu^2.$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>4. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/h1>\n<p>  \u041f\u0435\u0440\u0432\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/689\/5f4\/5f9\/6895f45f9655493d2b9a518435cead6b.svg\" alt=\"$v = \u0421_1\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace$\" data-tex=\"inline\"\/><\/math>. <\/p>\n<p>  \u0418\u0437 \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u043e\u0433\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044f <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/57d\/aec\/390\/57daec390e78bcbc6b30e70a7ba112cc.svg\" alt=\"$v(\\varphi)=v(\\varphi+2\\pi)$\" data-tex=\"inline\"\/><\/math>, \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8c0\/9be\/c86\/8c09bec86e984194d3f2f86b29281852.svg\" alt=\"$\\nu$\" data-tex=\"inline\"\/><\/math> \u2014 \u0446\u0435\u043b\u043e\u0435: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b04\/530\/a2b\/b04530a2b2e77185a96ee14ec4a749a7.svg\" alt=\"$\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace=\\exp\\left\\lbrace i\\nu (\\varphi+2\\pi) \\right\\rbrace\\rightarrow 1=\\exp\\left\\lbrace i\\nu2\\pi \\right\\rbrace = \\cos(2\\pi\\nu)+ i\\sin(2\\pi\\nu) \\Rightarrow$\" data-tex=\"inline\"\/><\/math> <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/aca\/c09\/ee6\/acac09ee66569e3fdf52263fc90f9dca.svg\" alt=\"$\\Rightarrow\\cos(2\\pi\\nu)=1, \\sin(2\\pi\\nu)=0 \\Rightarrow \\nu =\\ldots -2,-1,0,1,2\\ldots$\" data-tex=\"inline\"\/><\/math><\/p>\n<h1>5. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/h1>\n<p>  \u0412\u0442\u043e\u0440\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043b\u0438\u0431\u043e \u043a \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0411\u0435\u0441\u0441\u0435\u043b\u044f, \u043b\u0438\u0431\u043e \u043a \u043c\u043e\u0434\u0438\u0444\u0438\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0411\u0435\u0441\u0441\u0435\u043b\u044f:<br \/>  1. \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0411\u0435\u0441\u0441\u0435\u043b\u044f: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a16\/9dd\/cd4\/a169ddcd46a52620f70f25554af54c38.svg\" alt=\"$\\rho_1^2\\frac{d^2u}{d\\rho_1^2} + \\rho_1\\frac{du}{d\\rho_1} + (\\rho_1^2 - \\nu^2)u = 0,\\text{ \u043f\u0440\u0438 }\\rho_1 = r \\sqrt{ \\frac{\\varepsilon_1\\mu}{c^2}\\omega^2 - k_z^2 },$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  2. \u041c\u043e\u0434\u0438\u0444\u0438\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0411\u0435\u0441\u0441\u0435\u043b\u044f: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/42e\/648\/c22\/42e648c227ce99469cc9528d6ed09a98.svg\" alt=\"$\\rho_2^2\\frac{d^2u}{d\\rho_2^2} + \\rho_2\\frac{du}{d\\rho_2} - (\\rho_2^2 + \\nu^2)u = 0,\\text{ \u043f\u0440\u0438 }\\rho_2 = r \\sqrt{ k_z^2 - \\frac{\\varepsilon_2\\mu}{c^2}\\omega^2 }.$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8_%D0%91%D0%B5%D1%81%D1%81%D0%B5%D0%BB%D1%8F\">\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0411\u0435\u0441\u0441\u0435\u043b\u044f<\/a> \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0411\u0435\u0441\u0441\u0435\u043b\u044f <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/701\/8a7\/05d\/7018a705d35a6afb9be21b61b976f071.svg\" alt=\"$J_{\\nu}(\\rho_1)$\" data-tex=\"inline\"\/><\/math> \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041d\u0435\u0439\u043c\u0430\u043d\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3c8\/a16\/f0b\/3c8a16f0b79e48d5bcc2a1416f740f61.svg\" alt=\"$Y_{\\nu}(\\rho_1)$\" data-tex=\"inline\"\/><\/math>. <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9C%D0%BE%D0%B4%D0%B8%D1%84%D0%B8%D1%86%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%BD%D1%8B%D0%B5_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8_%D0%91%D0%B5%D1%81%D1%81%D0%B5%D0%BB%D1%8F\">\u041c\u043e\u0434\u0438\u0444\u0438\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0411\u0435\u0441\u0441\u0435\u043b\u044f<\/a> \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0418\u043d\u0444\u0435\u043b\u044c\u0434\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/587\/e63\/9f7\/587e639f71e6b6397eb0707482272f57.svg\" alt=\"$I_{\\nu}(\\rho_2)$\" data-tex=\"inline\"\/><\/math> \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u041c\u0430\u043a\u0434\u043e\u043d\u0430\u043b\u044c\u0434\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/788\/a03\/050\/788a03050d0968a505f283be990f69bb.svg\" alt=\"$K_{\\nu}(\\rho_2)$\" data-tex=\"inline\"\/><\/math>.<\/p>\n<p>  \u0412 \u0441\u0438\u043b\u0443 \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u044b\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u0439: \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/abc\/13b\/be7\/abc13bbe7182948a78af958d3a9c9120.svg\" alt=\"$r=0$\" data-tex=\"inline\"\/><\/math> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u0435\u0437 \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0435\u0439, \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/5c5\/596\/345\/5c55963452b1e89571fef57d580f4092.svg\" alt=\"$r=\\infty$\" data-tex=\"inline\"\/><\/math> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c\u0430 \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u043c, \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/04a\/19d\/223\/04a19d223277d42ef0c6bb517085e6e7.svg\" alt=\"$r=a$\" data-tex=\"inline\"\/><\/math> \u2014 \u0442\u0430\u043d\u0433\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b, \u2014 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f: \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a23\/bf5\/5fc\/a23bf55fcef0a988491109527d1c94c8.svg\" alt=\"$r &lt; a$\" data-tex=\"inline\"\/><\/math> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0411\u0435\u0441\u0441\u0435\u043b\u044f <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/701\/8a7\/05d\/7018a705d35a6afb9be21b61b976f071.svg\" alt=\"$J_{\\nu}(\\rho_1)$\" data-tex=\"inline\"\/><\/math>, \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3e8\/812\/4b1\/3e88124b17f0ab49428890f31ed04d50.svg\" alt=\"$r &gt; a$\" data-tex=\"inline\"\/><\/math> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u041c\u0430\u043a\u0434\u043e\u043d\u0430\u043b\u044c\u0434\u0430 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/788\/a03\/050\/788a03050d0968a505f283be990f69bb.svg\" alt=\"$K_{\\nu}(\\rho_2)$\" data-tex=\"inline\"\/><\/math>. <\/p>\n<p>  \u0418\u0437 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e \u0441\u0435\u0440\u0434\u0446\u0435\u0432\u0438\u043d\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u0431\u043e\u043b\u0435\u0435 \u043e\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0439, \u0447\u0435\u043c \u043e\u0431\u043e\u043b\u043e\u0447\u043a\u0430, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/982\/924\/b5c\/982924b5cca58fd9769c6e61fc5834e5.svg\" alt=\"$\\varepsilon_1 &gt; \\varepsilon_2$\" data-tex=\"inline\"\/><\/math>:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/259\/eb5\/272\/259eb5272148ee9a9b93db894702041c.svg\" alt=\"$ \\frac{\\varepsilon_1\\mu}{c^2}\\omega^2 - k_z^2 &gt; 0, \\, k_z^2 - \\frac{\\varepsilon_2\\mu}{c^2}\\omega^2 &gt; 0,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/43b\/cb1\/ba9\/43bcb1ba9178286664b333342f65a639.svg\" alt=\"$ \\frac{\\varepsilon_1\\mu}{c^2}\\omega^2 &gt; k_z^2, \\, k_z^2 &gt; \\frac{\\varepsilon_2\\mu}{c^2}\\omega^2,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/dcd\/42a\/75b\/dcd42a75b1bbbffb43194854a5bcb9ac.svg\" alt=\"$ \\frac{\\varepsilon_1\\mu}{c^2}\\omega^2 &gt; \\frac{\\varepsilon_2\\mu}{c^2}\\omega^2,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/01e\/233\/cb0\/01e233cb00fef230a68a1a5adc354289.svg\" alt=\"$ \\varepsilon_1 &gt; \\varepsilon_2.$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>6. \u041e\u0431\u0449\u0438\u0439 \u0432\u0438\u0434 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/468\/5c9\/069\/4685c906953725958227b0317261b556.svg\" alt=\"$e_z,\\,b_z$\" data-tex=\"inline\"\/><\/math><\/h1>\n<p>  \u0412\u0432\u0435\u0434\u044f \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3a8\/d98\/ba5\/3a8d98ba51bfdba61e6ef13ddbad3bcf.svg\" alt=\"$\\gamma^2 = \\frac{\\varepsilon_1\\mu_1}{c^2}\\omega^2 - k_z^2, \\, \\kappa^2 = k_z^2 - \\frac{\\varepsilon_2\\mu_2}{c^2}\\omega^2,$\" data-tex=\"inline\"\/><\/math> \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/468\/5c9\/069\/4685c906953725958227b0317261b556.svg\" alt=\"$e_z,\\,b_z$\" data-tex=\"inline\"\/><\/math> \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0432 \u0432\u0438\u0434\u0435:  <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a23\/b13\/915\/a23b139154a7c0f78aa79fbf51cecc50.svg\" alt=\"$e_{z,1} = A_eJ_{|\\nu|}(\\gamma r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&lt;a,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/d47\/66d\/a50\/d4766da507298ff829a34fc339617d90.svg\" alt=\"$e_{z,2} = B_eK_{|\\nu|}(\\kappa r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&gt;a,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/509\/40c\/833\/50940c833acfe5be1b0437770021575e.svg\" alt=\"$b_{z,1} = A_bJ_{|\\nu|}(\\gamma r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&lt;a, $\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a92\/dc6\/cc9\/a92dc6cc9b8a99ed6d5861cdc9478403.svg\" alt=\"$b_{z,2} = B_bK_{|\\nu|}(\\kappa r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&gt;a. $\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u0417\u0434\u0435\u0441\u044c \u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/299\/32c\/040\/29932c0405c426b62ccdc7f5e18e4bb0.svg\" alt=\"$\\nu =\\ldots -2,-1,0,1,2\\ldots$\" data-tex=\"inline\"\/><\/math> (\u043c\u043e\u0436\u0435\u0442 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f), \u043f\u043e\u0442\u043e\u043c\u0443 \u0432 \u0438\u043d\u0434\u0435\u043a\u0441\u0430\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u0440\u0438\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0437\u043d\u0430\u043a \u043c\u043e\u0434\u0443\u043b\u044f (\u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0411\u0435\u0441\u0441\u0435\u043b\u044f \u0438\u043c\u0435\u0435\u0442 \u043c\u0435\u0441\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/152\/8de\/5b4\/1528de5b495ea7fc923b47a280115aeb.svg\" alt=\"$\\nu^2$\" data-tex=\"inline\"\/><\/math>, \u0437\u043d\u0430\u043a \u0438\u043d\u0434\u0435\u043a\u0441\u0430 \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439). \u0414\u0430\u043b\u0435\u0435 \u0437\u043d\u0430\u043a \u043c\u043e\u0434\u0443\u043b\u044f \u0432 \u0438\u043d\u0434\u0435\u043a\u0441\u0430\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043e\u043f\u0443\u0441\u043a\u0430\u0435\u0442\u0441\u044f, \u043d\u043e \u043f\u043e\u0434\u0440\u0430\u0437\u0443\u043c\u0435\u0432\u0430\u0435\u0442\u0441\u044f.<\/p>\n<p>  \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u0432\u0435\u0434\u0435\u043d \u0438\u043d\u0434\u0435\u043a\u0441 \u0434\u043b\u044f \u043c\u0430\u0433\u043d\u0438\u0442\u043d\u043e\u0439 \u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u043e\u0441\u0442\u0438: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/762\/35d\/35f\/76235d35fbe01b8d0f8ab69f0b05c2ec.svg\" alt=\"$\\mu_1$\" data-tex=\"inline\"\/><\/math> \u2014 \u0432 \u0441\u0435\u0440\u0434\u0446\u0435\u0432\u0438\u043d\u0435, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/caf\/aea\/bfc\/cafaeabfcc0378fad0de03fa3ababbde.svg\" alt=\"$\\mu_2$\" data-tex=\"inline\"\/><\/math> \u2014 \u0432 \u043e\u0431\u043e\u043b\u043e\u0447\u043a\u0435.<\/p>\n<h1>7. \u0421\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/1c3\/162\/8d1\/1c31628d13401215f814a41d313516ee.svg\" alt=\"$A_e,\\,A_b,\\,B_e,\\,B_b$\" data-tex=\"inline\"\/><\/math><\/h1>\n<p>  \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0437\u0430\u043a\u043e\u043d<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/5bd\/551\/cd0\/5bd551cd0c47cabd918841c620ce8df0.svg\" alt=\"$\\textbf{b}_{\\bot} = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\operatorname{grad}_{\\bot}b_z + \\varepsilon\\mu\\frac{\\omega}{c}\\left[ \\hat{\\textbf{z}}\\times\\operatorname{grad}_{\\bot}e_z\\right] \\right\\rbrace, \\, \\textbf{e}_{\\bot} = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\operatorname{grad}_{\\bot}e_z - \\frac{\\omega}{c}\\left[ \\hat{\\textbf{z}}\\times\\operatorname{grad}_{\\bot}b_z\\right] \\right\\rbrace,$\" data-tex=\"display\"\/><\/math><\/p>\n<p> \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/55a\/06d\/4d6\/55a06d4d69031d583a04a932fd3345a2.svg\" alt=\"$e_{\\varphi,1},\\,e_{\\varphi,2},\\,h_{\\varphi,1},\\,h_{\\varphi,2}$\" data-tex=\"inline\"\/><\/math>, \u0438\u043c\u0435\u044f \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0432 \u0432\u0438\u0434\u0443, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/7bc\/d70\/a60\/7bcd70a604125542965e2c7b61dd179f.svg\" alt=\"$\\textbf{h}=\\textbf{b}\/\\mu$\" data-tex=\"inline\"\/><\/math>.<br \/>  \u041a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432 \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0442\u0430\u043d\u0433\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ac7\/f04\/c5f\/ac7f04c5f862cac8def2a80d02dedaca.svg\" alt=\"$e_{z,1}\\bigg|_{r=a}=e_{z,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/0c6\/158\/8ea\/0c61588ea3a92308d7d43f902075f040.svg\" alt=\"$e_{\\varphi,1}\\bigg|_{r=a}=e_{\\varphi,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/feb\/a49\/923\/feba499237f826d2bedd039e947d2eb1.svg\" alt=\"$h_{z,1}\\bigg|_{r=a}=h_{z,2}\\bigg|_{r=a},$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/274\/a13\/9b2\/274a139b26d0e0bdbf8ffbb3df942d52.svg\" alt=\"$h_{\\varphi,1}\\bigg|_{r=a}=h_{\\varphi,2}\\bigg|_{r=a}.$\" data-tex=\"display\"\/><\/math><\/p>\n<p>  \u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0441\u0443\u0442\u044c \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/1c3\/162\/8d1\/1c31628d13401215f814a41d313516ee.svg\" alt=\"$A_e,\\,A_b,\\,B_e,\\,B_b$\" data-tex=\"inline\"\/><\/math>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/d75\/c87\/327\/d75c8732725193c1ebe64269c620a811.svg\" alt=\"$\\left( \\begin{array}{cccc} J_{\\nu}(\\gamma a) &amp; -K_{\\nu}(\\kappa a) &amp; 0 &amp; 0 \\\\ 0 &amp; 0 &amp; \\frac{1}{\\mu_1}J_{\\nu}(\\gamma a) &amp; -\\frac{1}{\\mu_2}K_{\\nu}(\\kappa a) \\\\ \\frac{\\nu k_z}{a\\gamma^2} J_{\\nu}(\\gamma a) &amp; \\frac{\\nu k_z}{a\\kappa^2} K_{\\nu}(\\kappa a) &amp; \\frac{i}{\\gamma^2}\\frac{\\omega}{c}\\gamma J^{\\prime}_{\\nu}(\\gamma a) &amp; \\frac{i}{\\kappa^2} \\frac{\\omega}{c} \\kappa K^{\\prime}_{\\nu}(\\kappa a) \\\\ i\\frac{\\varepsilon\\mu}{\\gamma^2\\mu_1}\\frac{\\omega}{c}\\gamma J^{\\prime}_{\\nu}(\\gamma a) &amp; \\frac{i}{\\mu_2\\kappa^2}\\varepsilon\\mu\\frac{\\omega}{c}\\kappa K^{\\prime}_{\\nu}(\\kappa a) &amp; -\\frac{k_z \\nu}{a\\gamma^2 \\mu_1} J_{\\nu}(\\gamma a) &amp; - \\frac{\\nu k_z}{\\mu_2a\\kappa^2}K_{\\nu}(\\kappa a) \\end{array} \\right) \\left( \\begin{array}{c} A_e\\\\ B_e\\\\ A_b\\\\ B_b \\end{array} \\right) = 0,$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>8. \u0414\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u043e\u043d\u043d\u043e\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435<\/h1>\n<p>  \u0414\u043b\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0434\u043e\u043b\u0436\u0435\u043d \u0440\u0430\u0432\u043d\u044f\u0442\u044c\u0441\u044f \u043d\u0443\u043b\u044e: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/817\/caa\/6f6\/817caa6f6ff494af9afd6b9c3232ac49.svg\" alt=\"$\\left( \\frac{\\varepsilon_1\\mu_1}{x^2}+\\frac{\\varepsilon_2\\mu_2}{y^2}\\right) \\left( \\frac{1}{x^2} + \\frac{1}{y^2}\\right)\\nu^2 = \\left[ \\mu_2 g(y)+\\mu_1 f(x)\\right] \\left[ \\varepsilon_2g(y) + \\varepsilon_1 f(x)\\right] .$\" data-tex=\"display\"\/><\/math><\/p>\n<p> \u0412 \u044d\u0442\u043e\u0439 \u0437\u0430\u043f\u0438\u0441\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0434\u0435\u0442\u0435\u0440\u043c\u0438\u043d\u0430\u043d\u0442\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u044b \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/fcf\/5f9\/ffb\/fcf5f9ffb4659143019233205b62b9d8.svg\" alt=\"$f(x) = \\frac{J^{\\prime}_{\\nu}(x)}{xJ_{\\nu}(x)}, \\, g(y) = \\frac{K^{\\prime}_{\\nu}(y)}{yK_{\\nu}(y)},$\" data-tex=\"inline\"\/><\/math> <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/5f0\/c81\/ae7\/5f0c81ae727abae3084a82e038a2ec1e.svg\" alt=\"$x=\\gamma a,\\,y=\\kappa a$\" data-tex=\"inline\"\/><\/math> \u0438 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/027\/3da\/f01\/0273daf01f658afcbf45b1d982151362.svg\" alt=\"$\\frac{\\omega^2}{c^2} = \\frac{\\kappa^2+\\gamma^2}{\\varepsilon_1\\mu_1 - \\varepsilon_2\\mu_2},\\,k_z^2 = \\frac{\\varepsilon_1\\mu_1\\kappa^2+\\varepsilon_2\\mu_2\\gamma^2}{\\varepsilon_1\\mu_1 - \\varepsilon_2\\mu_2}$\" data-tex=\"inline\"\/><\/math>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0442 \u0438\u0437 \u0432\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0445 \u0440\u0430\u043d\u0435\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/0b2\/657\/40a\/0b265740aaf94260bf14db7cc1e16626.svg\" alt=\"$\\gamma^2 = \\frac{\\varepsilon_1\\mu_1}{c^2}\\omega^2 - k_z^2, \\, \\kappa^2 = k_z^2 - \\frac{\\varepsilon_2\\mu_2}{c^2}\\omega^2$\" data-tex=\"inline\"\/><\/math>.<\/p>\n<p>  \u0412\u0435\u043b\u0438\u0447\u0438\u043d\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/c59\/6de\/554\/c596de55413b0d71dc9948f41a09d89d.svg\" alt=\"$x,\\,y$\" data-tex=\"inline\"\/><\/math> \u2014 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0435\u0449\u0435 \u043e\u0434\u043d\u0438\u043c \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e\u043c, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0438\u0437 \u0434\u0432\u0443\u0445 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0438 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u044f, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b3b\/a34\/750\/b3ba34750c977801ab284655b95d3e30.svg\" alt=\"$k_z$\" data-tex=\"inline\"\/><\/math> \u2014 \u0435\u0434\u0438\u043d\u0430 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/0c6\/0e3\/618\/0c60e36181c71165af3a93c4c535d67a.svg\" alt=\"$x^2+y^2 = (\\varepsilon_1\\mu_1 - \\varepsilon_2\\mu_2)a^2\\frac{\\omega^2}{c^2}.$\" data-tex=\"display\"\/><\/math><\/p>\n<h1>9. \u041c\u043e\u0434\u044b<\/h1>\n<p>  \u0414\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/c59\/6de\/554\/c596de55413b0d71dc9948f41a09d89d.svg\" alt=\"$x,\\,y$\" data-tex=\"inline\"\/><\/math> \u0438\u0437 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ccb\/06c\/8e3\/ccb06c8e30cb3c6fe6d0da6c18dc754d.svg\" alt=\"$\\left( \\frac{\\varepsilon_1\\mu_1}{x^2}+\\frac{\\varepsilon_2\\mu_2}{y^2}\\right) \\left( \\frac{1}{x^2} + \\frac{1}{y^2}\\right)\\nu^2 = \\left[ \\mu_2 g(y)+\\mu_1 f(x)\\right] \\left[ \\varepsilon_2g(y) + \\varepsilon_1 f(x)\\right],$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8c6\/113\/948\/8c6113948b165f7be93825869bebb885.svg\" alt=\"$x^2+y^2 = (\\varepsilon_1\\mu_1 - \\varepsilon_2\\mu_2)a^2\\frac{\\omega^2}{c^2},$\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0437\u0430\u0434\u0430\u0442\u044c: <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/e11\/b42\/9bf\/e11b429bff0b220bc54a66e0fa1e13db.svg\" alt=\"$\\nu,\\,\\omega,\\,\\varepsilon_1,\\,\\mu_1,\\,\\varepsilon_2,\\,\\mu_2,\\,a$\" data-tex=\"inline\"\/><\/math>.<\/p>\n<p>  \u0421\u0432\u044f\u0437\u044c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8e0\/005\/755\/8e00057550e339090ed0478415a81408.svg\" alt=\"$x$\" data-tex=\"inline\"\/><\/math> \u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/edf\/1f4\/a3d\/edf1f4a3dcce216103ecd4beb5c7bbbc.svg\" alt=\"$y$\" data-tex=\"inline\"\/><\/math> \u043f\u0435\u0440\u0432\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0441\u0435\u0440\u0438\u044e \u043b\u0438\u043d\u0438\u0439 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 (\u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u0440\u0430\u0437\u0434\u0435\u043b\u0430 \u043c\u0435\u0436\u0434\u0443 \u0441\u0438\u043d\u0438\u043c \u0438 \u043a\u0440\u0430\u0441\u043d\u044b\u043c \u0446\u0432\u0435\u0442\u0430\u043c\u0438, \u0441\u043c. \u0440\u0438\u0441. \u043d\u0438\u0436\u0435). \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u043b\u0438\u043d\u0438\u0439 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8c0\/9be\/c86\/8c09bec86e984194d3f2f86b29281852.svg\" alt=\"$\\nu$\" data-tex=\"inline\"\/><\/math>.<\/p>\n<p>  \u0421\u0432\u044f\u0437\u044c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8e0\/005\/755\/8e00057550e339090ed0478415a81408.svg\" alt=\"$x$\" data-tex=\"inline\"\/><\/math> \u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/edf\/1f4\/a3d\/edf1f4a3dcce216103ecd4beb5c7bbbc.svg\" alt=\"$y$\" data-tex=\"inline\"\/><\/math> \u0432\u0442\u043e\u0440\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c \u0441 \u0440\u0430\u0434\u0438\u0443\u0441\u043e\u043c, \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u044f\u0449\u0438\u043c \u043e\u0442 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ac1\/7c5\/491\/ac17c549119a8b8b949d7612ef39b71d.svg\" alt=\"$a$\" data-tex=\"inline\"\/><\/math>. \u0422\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0439 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439.<br \/>  <img decoding=\"async\" src=\"https:\/\/habrastorage.org\/files\/5e7\/2ef\/eff\/5e72efeff1ef4eb59d77598d6771b490.png\"\/><\/p>\n<p>  \u041d\u0430\u0431\u043e\u0440 \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043f\u0430\u0440 \u0447\u0438\u0441\u0435\u043b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/aa3\/27c\/7a8\/aa327c7a85b0351f4eec27a9c6fc2108.svg\" alt=\"$(x_i,y_i)$\" data-tex=\"inline\"\/><\/math>. \u041a\u0430\u0436\u0434\u043e\u0439 \u0442\u0430\u043a\u043e\u0439 \u043f\u0430\u0440\u0435 \u0447\u0438\u0441\u0435\u043b \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043c\u0430\u0433\u043d\u0438\u0442\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0439 \u00ab\u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043c\u043e\u0434\u043e\u0439\u00bb.<\/p>\n<p>  \u041c\u043e\u0434\u0443 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0430 \u043f\u0440\u0438\u043d\u044f\u0442\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: \u0434\u0432\u0435 \u0431\u0443\u043a\u0432\u044b (<math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/f27\/f14\/75b\/f27f1475b8de0b7fb51f6866429b8163.svg\" alt=\"$E,\\,H$\" data-tex=\"inline\"\/><\/math>) \u2014 \u043d\u0430 \u043f\u0435\u0440\u0432\u043e\u043c \u043c\u0435\u0441\u0442\u0435 \u0431\u0443\u043a\u0432\u0430 \u0441 \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0435\u0439 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/cc8\/d0e\/2f0\/cc8d0e2f07ecd20ba078ad033270f1d0.svg\" alt=\"$z$\" data-tex=\"inline\"\/><\/math>-\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0439 \u0438 \u0434\u0432\u0430 \u0438\u043d\u0434\u0435\u043a\u0441\u0430: \u043d\u0430 \u043f\u0435\u0440\u0432\u043e\u043c \u043c\u0435\u0441\u0442\u0435 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/8c0\/9be\/c86\/8c09bec86e984194d3f2f86b29281852.svg\" alt=\"$\\nu$\" data-tex=\"inline\"\/><\/math>, \u043d\u0430 \u0432\u0442\u043e\u0440\u043e\u043c \u043d\u043e\u043c\u0435\u0440 \u0432\u0435\u0442\u0432\u0438 (\u043d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0430 \u0441\u0438\u043d\u0438\u043c \u0446\u0432\u0435\u0442\u043e\u043c). <\/p>\n<p>  \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f:<br \/>  <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/9dd\/0dc\/2ee\/9dd0dc2ee248df1bd34257443e505b58.svg\" alt=\"$HE_{11}$\" data-tex=\"inline\"\/><\/math> \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043e \u0442\u043e\u043c, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/608\/6ba\/840\/6086ba84043b0fbba07459272d4086ec.svg\" alt=\"$H_z$\" data-tex=\"inline\"\/><\/math> \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/c49\/317\/80b\/c4931780b8b6f0c551df5235c25a1408.svg\" alt=\"$E_z$\" data-tex=\"inline\"\/><\/math>, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/f84\/0f5\/4ac\/f840f54ac1676256434e1ac2dbd12393.svg\" alt=\"$\\nu=1$\" data-tex=\"inline\"\/><\/math>, \u0432\u044b\u0431\u0440\u0430\u043d\u0430 \u043f\u0430\u0440\u0430 (\u0441\u043c.\u0440\u0438\u0441. \u0432\u044b\u0448\u0435) <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/fab\/8ee\/014\/fab8ee014d6b0208ec01356a7d406e5d.svg\" alt=\"$(x_1,y_1)$\" data-tex=\"inline\"\/><\/math>,<br \/>  <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/4b8\/08c\/4e7\/4b808c4e7039cce26306ff7a59dbc4a8.svg\" alt=\"$EH_{13}$\" data-tex=\"inline\"\/><\/math> \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043e \u0442\u043e\u043c, \u0447\u0442\u043e <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/c49\/317\/80b\/c4931780b8b6f0c551df5235c25a1408.svg\" alt=\"$E_z$\" data-tex=\"inline\"\/><\/math> \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/608\/6ba\/840\/6086ba84043b0fbba07459272d4086ec.svg\" alt=\"$H_z$\" data-tex=\"inline\"\/><\/math>, <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/f84\/0f5\/4ac\/f840f54ac1676256434e1ac2dbd12393.svg\" alt=\"$\\nu=1$\" data-tex=\"inline\"\/><\/math>, \u0432\u044b\u0431\u0440\u0430\u043d\u0430 \u043f\u0430\u0440\u0430 (\u0441\u043c.\u0440\u0438\u0441. \u0432\u044b\u0448\u0435) <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/f90\/3b9\/4c1\/f903b94c1b61347740b0ad8471c720cc.svg\" alt=\"$(x_5,y_5)$\" data-tex=\"inline\"\/><\/math> (\u0442\u0440\u0435\u0442\u044c\u044f \u0441\u0438\u043d\u044f\u044f \u0432\u0435\u0442\u0432\u044c).<\/p>\n<h1>10. \u041f\u043e\u0440\u044f\u0434\u043e\u043a \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u043f\u043e\u043b\u044f<\/h1>\n<p>  \u041f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f:<\/p>\n<p>  01. \u0417\u0430\u0434\u0430\u0442\u044c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/e11\/b42\/9bf\/e11b429bff0b220bc54a66e0fa1e13db.svg\" alt=\"$\\nu,\\,\\omega,\\,\\varepsilon_1,\\,\\mu_1,\\,\\varepsilon_2,\\,\\mu_2,\\,a$\" data-tex=\"inline\"\/><\/math>;<br \/>  02. \u041d\u0430\u0439\u0442\u0438 \u043d\u0430\u0431\u043e\u0440\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/20c\/53f\/2d6\/20c53f2d633fad1cc91d6e50bffb9a39.svg\" alt=\"$(x,y)$\" data-tex=\"inline\"\/><\/math>, \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u043e\u0434\u0438\u043d, (\u043f.9);<br \/>  03. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/1ac\/5cd\/8b4\/1ac5cd8b47570cde3cf68a4653fecb5f.svg\" alt=\"$k_z,\\,\\gamma,\\,\\kappa$\" data-tex=\"inline\"\/><\/math>, (\u043f.8);<br \/>  04. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/1c3\/162\/8d1\/1c31628d13401215f814a41d313516ee.svg\" alt=\"$A_e,\\,A_b,\\,B_e,\\,B_b$\" data-tex=\"inline\"\/><\/math>, (\u043f.7).<\/p>\n<p>  \u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f <b>\u0432 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0445<\/b> \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u043f\u043e\u043b\u044f:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/2d8\/ac1\/c77\/2d8ac1c77d2c8e231a114ba6bee4fec5.svg\" alt=\"$e_z = A_eJ_{\\nu}(\\gamma r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&lt;a, $\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/b3b\/e7e\/2ac\/b3be7e2acba3b7d88663841efaf97f25.svg\" alt=\"$e_z = B_eK_{\\nu}(\\kappa r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&gt;a, $\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3cf\/a02\/754\/3cfa02754418bdc170f7c801f51ef979.svg\" alt=\"$b_z = A_bJ_{\\nu}(\\gamma r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&lt;a, $\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/31b\/3e5\/e31\/31b3e5e31110fd15100a9a405f58e9fa.svg\" alt=\"$b_z = B_bK_{\\nu}(\\kappa r)\\exp\\left\\lbrace i\\nu \\varphi \\right\\rbrace,\\text{ \u043f\u0440\u0438 }r&gt;a. $\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u0414\u0430\u043b\u0435\u0435, \u043f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a23\/bf5\/5fc\/a23bf55fcef0a988491109527d1c94c8.svg\" alt=\"$r &lt; a$\" data-tex=\"inline\"\/><\/math>: <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/226\/cfa\/380\/226cfa3806b7f6519c422ae262b214d5.svg\" alt=\"$\\left( \\begin{array}{c} b_r\\\\ b_{\\varphi} \\end{array} \\right) = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\left( \\begin{array}{c} A_b \\gamma J^{\\prime}_{\\nu}(\\gamma r) \\\\ \\frac{1}{r} i \\nu A_b J_{\\nu}(\\gamma r) \\end{array} \\right) + \\varepsilon\\mu\\frac{\\omega}{c} \\left( \\begin{array}{c} -\\frac{1}{r} i\\nu A_e J_{\\nu}(\\gamma r)\\\\ A_e \\gamma J^{\\prime}_{\\nu}(\\gamma r) \\end{array} \\right) \\right\\rbrace \\exp(i\\nu \\varphi) ,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/710\/92a\/b4b\/71092ab4b0014f18ab9f114fa2b91d25.svg\" alt=\"$\\left( \\begin{array}{c} e_r\\\\ e_{\\varphi} \\end{array} \\right) = \\frac{i}{\\gamma^2}\\left\\lbrace k_z \\left( \\begin{array}{c} A_e \\gamma J^{\\prime}_{\\nu}(\\gamma r)\\\\ \\frac{1}{r} i\\nu A_e J_{\\nu}(\\gamma r) \\end{array} \\right) - \\frac{\\omega}{c} \\left( \\begin{array}{c} -\\frac{1}{r}A_b i\\nu J_{\\nu}(\\gamma r)\\\\ A_b \\gamma J^{\\prime}_{\\nu}(\\gamma r) \\end{array} \\right) \\right\\rbrace \\exp(i\\nu \\varphi).$\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u041f\u0440\u0438 <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/3e8\/812\/4b1\/3e88124b17f0ab49428890f31ed04d50.svg\" alt=\"$r &gt; a$\" data-tex=\"inline\"\/><\/math>:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/c77\/728\/cc0\/c77728cc023884cd7d201b833351d37f.svg\" alt=\"$\\left( \\begin{array}{c} b_r\\\\ b_{\\varphi} \\end{array} \\right) = -\\frac{i}{\\kappa^2}\\left\\lbrace k_z \\left( \\begin{array}{c} B_b \\kappa K^{\\prime}_{\\nu}(\\kappa r) \\\\ \\frac{1}{r} i \\nu B_b K_{\\nu}(\\kappa r) \\end{array} \\right) + \\varepsilon\\mu\\frac{\\omega}{c} \\left( \\begin{array}{c} -\\frac{1}{r} i\\nu B_e K_{\\nu}(\\kappa r)\\\\ B_e \\kappa K^{\\prime}_{\\nu}(\\kappa r) \\end{array} \\right) \\right\\rbrace \\exp(i\\nu \\varphi) ,$\" data-tex=\"display\"\/><\/math><\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/a12\/ed5\/5d3\/a12ed55d377f1cb247a16fec41c34c20.svg\" alt=\"$\\left( \\begin{array}{c} e_r\\\\ e_{\\varphi} \\end{array} \\right) = -\\frac{i}{\\kappa^2}\\left\\lbrace k_z \\left( \\begin{array}{c} B_e \\kappa K^{\\prime}_{\\nu}(\\kappa r)\\\\ \\frac{1}{r} i\\nu B_e K_{\\nu}(\\kappa r) \\end{array} \\right) - \\frac{\\omega}{c} \\left( \\begin{array}{c} -\\frac{1}{r}B_b i\\nu K_{\\nu}(\\kappa r)\\\\ B_b \\kappa K^{\\prime}_{\\nu}(\\kappa r) \\end{array} \\right) \\right\\rbrace \\exp(i\\nu \\varphi).$\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u0414\u0430\u043b\u0435\u0435 <\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/e03\/70a\/145\/e0370a14552e8ec5f34a8691f9ead02f.svg\" alt=\"$\\textbf{E}(x,y,z,t) = \\left( \\begin{array}{c} e_r(x,y)\\\\ e_{\\varphi}(x,y)\\\\ e_z(x,y) \\end{array} \\right) \\exp\\left\\lbrace ik_zz - i\\omega t \\right\\rbrace, \\quad \\textbf{B}(x,y,z,t) = \\left( \\begin{array}{c} b_r(x,y)\\\\ b_{\\varphi}(x,y)\\\\ b_z(x,y) \\end{array} \\right) \\exp\\left\\lbrace ik_zz - i\\omega t \\right\\rbrace.$\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u0437\u0430\u043c\u044b\u043a\u0430\u044e\u0449\u0438\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0435:<math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/658\/946\/714\/6589467148d5dd5636637a58504a21bf.svg\" alt=\"$\\textbf{D}=\\varepsilon_{1,2} \\textbf{E},\\, \\textbf{B}= \\mu_{1,2} \\textbf{H}$\" data-tex=\"inline\"\/><\/math>(\u0438\u043d\u0434\u0435\u043a\u0441\u044b \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043d\u0430 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0441\u0440\u0435\u0434\u044b).<\/p>\n<p>  \u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u044f <b>\u0432 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442<\/b> \u0447\u0435\u0440\u0435\u0437 \u0446\u0438\u043b\u0438\u043d\u0434\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0434\u043b\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442:<\/p>\n<p><math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ed3\/0f5\/9d3\/ed30f59d3447af501ccf41a39a8d41fa.svg\" alt=\"$\\left( \\begin{array}{c} E_x\\\\ E_y\\\\ E_z \\end{array} \\right) = \\left( \\begin{array}{ccc} \\cos\\varphi &amp; -\\sin\\varphi &amp; 0\\\\ \\sin\\varphi &amp; \\cos\\varphi &amp; 0\\\\ 0 &amp; 0 &amp; 1 \\end{array} \\right) \\left( \\begin{array}{c} E_r\\\\ E_{\\varphi}\\\\ E_z \\end{array} \\right).$\" data-tex=\"display\"\/><\/math><\/p>\n<p>\u0414\u043b\u044f \u043c\u0430\u0433\u043d\u0438\u0442\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0442\u0430 \u0436\u0435.<\/p>\n<h1>11. \u0417\u0430\u043c\u0435\u0447\u0430\u043d\u0438\u044f<\/h1>\n<p>  \u0412\u044b\u0431\u0438\u0440\u0430\u044f <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/ac1\/7c5\/491\/ac17c549119a8b8b949d7612ef39b71d.svg\" alt=\"$a$\" data-tex=\"inline\"\/><\/math> \u043c\u043e\u0436\u043d\u043e \u0434\u043e\u0431\u0438\u0442\u044c\u0441\u044f \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f:<br \/>  <img decoding=\"async\" src=\"https:\/\/habrastorage.org\/files\/2b9\/f16\/013\/2b9f160136cc4e3491be8742b9ce3576.png\"\/><br \/>  \u0422\u0430\u043a\u043e\u0435 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u043e \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u043c\u043e\u0434\u043e\u0432\u044b\u043c. \u041e\u0434\u043d\u0430\u043a\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u00ab\u043e\u0434\u043d\u043e\u043c\u043e\u0434\u043e\u0432\u043e\u0441\u0442\u044c\u00bb \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0447\u0430\u0441\u0442\u043e\u0442\u044b \u2014 \u0431\u043e\u043b\u0435\u0435 \u0432\u044b\u0441\u043e\u043a\u0438\u0435 \u0447\u0430\u0441\u0442\u043e\u0442\u044b \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u044f\u044e\u0442\u0441\u044f \u0432 \u00ab\u043e\u0434\u043d\u043e\u043c\u043e\u0434\u043e\u0432\u043e\u043c\u00bb \u0432\u043e\u043b\u043e\u043a\u043d\u0435 \u0432 \u0432\u0438\u0434\u0435 \u043d\u0430\u0431\u043e\u0440\u0430 \u043c\u043e\u0434.<\/p>\n<p>  \u0418\u043d\u043e\u0433\u0434\u0430 \u0433\u043e\u0432\u043e\u0440\u044f\u0442 \u043e \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u0438\u0438 \u043f\u043e\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0432 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0435, \u0438\u043c\u0435\u044f \u0432 \u0432\u0438\u0434\u0443 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u044f \u043c\u043e\u0434\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/9dd\/0dc\/2ee\/9dd0dc2ee248df1bd34257443e505b58.svg\" alt=\"$HE_{11}$\" data-tex=\"inline\"\/><\/math>: \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u043f\u043e\u043b\u044f \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u043e\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b. \u041e\u0434\u043d\u0430\u043a\u043e, \u043e\u0431\u0449\u0430\u044f \u043a\u0430\u0440\u0442\u0438\u043d\u0430 \u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438 (\u0441\u043c. \u0432\u0438\u0434\u0435\u043e \u043d\u0438\u0436\u0435), \u2014 \u043e \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u0438\u0438 \u043f\u043e\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0432 \u0442\u0430\u043a\u043e\u043c \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c \u043d\u0435 \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u0442\u0441\u044f.  <\/p>\n<div class=\"oembed\">\n<div>\n<div style=\"left: 0px; width: 100%; height: 0px; position: relative; padding-bottom: 56.2493%;\"><iframe src=\"https:\/\/www.youtube.com\/embed\/MxNeBcm7hqI?rel=0&amp;showinfo=1\" frameborder=\"0\" allowfullscreen=\"true\" webkitallowfullscreen=\"true\" mozallowfullscreen=\"true\" style=\"top: 0px; left: 0px; width: 100%; height: 100%; position: absolute;\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<p>  \u0414\u043b\u044f \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0430 \u043d\u0438\u0436\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u0430 \u044d\u0432\u043e\u043b\u044e\u0446\u0438\u044f \u0432 \u0442\u0435\u0447\u0435\u043d\u0438\u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0435\u0440\u0438\u043e\u0434\u0430 \u043c\u043e\u0434\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/9dd\/0dc\/2ee\/9dd0dc2ee248df1bd34257443e505b58.svg\" alt=\"$HE_{11}$\" data-tex=\"inline\"\/><\/math>  <\/p>\n<div class=\"oembed\">\n<div>\n<div style=\"left: 0px; width: 100%; height: 0px; position: relative; padding-bottom: 56.2493%;\"><iframe src=\"https:\/\/www.youtube.com\/embed\/mcHTMx_9Yp0?rel=0&amp;showinfo=1\" frameborder=\"0\" allowfullscreen=\"true\" webkitallowfullscreen=\"true\" mozallowfullscreen=\"true\" style=\"top: 0px; left: 0px; width: 100%; height: 100%; position: absolute;\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<p>  \u0438 \u043c\u043e\u0434\u044b <math><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/geektimes\/post_images\/24d\/bed\/5f6\/24dbed5f6c12d672428765d37ae30722.svg\" alt=\"$HE_{31}$\" data-tex=\"inline\"\/><\/math>  <\/p>\n<div class=\"oembed\">\n<div>\n<div style=\"left: 0px; width: 100%; height: 0px; position: relative; padding-bottom: 56.2493%;\"><iframe src=\"https:\/\/www.youtube.com\/embed\/tLDYykL1f7w?rel=0&amp;showinfo=1\" frameborder=\"0\" allowfullscreen=\"true\" webkitallowfullscreen=\"true\" mozallowfullscreen=\"true\" style=\"top: 0px; left: 0px; width: 100%; height: 100%; position: absolute;\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<p> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/geektimes.ru\/post\/287990\/\"> https:\/\/geektimes.ru\/post\/287990\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/files\/fbc\/d5e\/b09\/fbcd5eb09cc74856ad8f598719959831.png\"\/><br \/>  \u041a\u0430\u043a-\u0442\u043e \u043c\u043d\u0435 \u043f\u043e\u043d\u0430\u0434\u043e\u0431\u0438\u043b\u0430\u0441\u044c &quot;<b>\u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043c\u043e\u0434\u0430 \u043e\u043f\u0442\u043e\u0432\u043e\u043b\u043e\u043a\u043d\u0430<\/b>&quot;. \u041d\u043e \u044f \u043d\u0438\u0433\u0434\u0435 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b <b>\u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043c\u0430\u0433\u043d\u0438\u0442\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f<\/b>. \u041d\u0443 \u0438 \u00ab\u0441\u0434\u0435\u043b\u0430\u043b \u0441\u0430\u043c\u00bb, \u0440\u0430\u0437 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b, \u0438 <b>\u043e\u0444\u043e\u0440\u043c\u0438\u043b \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0442\u0443\u0442, \u0432 \u0441\u0442\u0430\u0442\u044c\u0435<\/b>. \u0422\u0430\u043a \u0447\u0442\u043e, \u0441\u043a\u043e\u0440\u0435\u0435 \u0432\u0441\u0435\u0433\u043e, \u043d\u0438\u0433\u0434\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0432\u044b \u0442\u0430\u043a\u043e\u0433\u043e \u043d\u0435 \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u0435 \u2014 \u0443\u043d\u0438\u043a\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0430\u044f \u0432\u0435\u0449\u044c! \u0412 \u043a\u043d\u0438\u0436\u043a\u0430\u0445 \u044d\u0442\u043e \u043d\u0435 \u043f\u0438\u0448\u0443\u0442, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d\u043e \u0434\u043b\u0438\u043d\u043d\u043e\u0435 \u2014 \u043e\u0431\u044b\u0447\u043d\u043e \u043f\u0438\u0448\u0443\u0442 \u0441\u0430\u043c\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0435, \u0430 \u043f\u0440\u043e \u043e\u0431\u0449\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u044e\u0442 \u0432\u0441\u043a\u043e\u043b\u044c\u0437\u044c. \u041d\u0443 \u0432\u043e\u0442 \u043e\u043d, \u043e\u0431\u0449\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439, \u043f\u043e\u0434 \u043a\u0430\u0442\u043e\u043c.  <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-284833","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/284833","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=284833"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/284833\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=284833"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=284833"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=284833"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}