{"id":239,"date":"2019-03-21T18:36:29","date_gmt":"2019-03-21T10:36:29","guid":{"rendered":"\u6700\u8fd1\u4eff\u771f\u9700\u8981\u7528\u5230\u9ad8\u65af\u5149\u675f\uff0c\u5b66\u4e60\u4e86\u4e00\u4e0b\u9ad8\u65af\u5149\u675f\u7684\u8bbe\u7f6e\u548c\u76f8\u5173\u7406\u8bba\u3002\n\n\u5728\u4e00\u5b9a\u9891\u7387\u4e0b\uff0cMaxwell\u65b9\u7a0b\u5e76\u4e0d\u72ec\u7acb\u5b8c\u5168\u72ec\u7acb\uff0c\u53ea\u6709\u6cd5\u62c9\u7b2c\u5b9a\u5f8b\u548c\u5b89\u57f9\u5b9a\u5f8b\uff08\u52a0\u4f4d\u79fb\u7535\u6d41\uff09\u7684\u4e24\u4e2a\u65b9\u7a0b\u72ec\u7acb\u3002\u6c42\u89e3\u7535\u573a\u6216\u78c1\u573a\u53ef\u4ee5\u5f97\u5230Helmholtz\u65b9\u7a0b\uff0c\u662f\u4e00\u5b9a\u9891\u7387\u4e0b\u7535\u78c1\u6ce2\u7684\u57fa\u672c\u65b9\u7a0b\u3002\u5176\u89e3\u662f\u7535\u573a\u4ee3\u8868\u7535\u78c1\u6ce2\u573a\u5f3a\u5728\u7a7a\u95f4\u4e2d\u7684\u5206\u5e03\uff0c\u6bcf\u79cd\u53ef\u80fd\u7684\u5f62\u5f0f\u6210\u4e3a\u4e00\u79cd\u6ce2\u6a21\u3002\n\n\u57fa\u672c\u7684\u89e3\u6709\u5e73\u9762\u6ce2\u3001\u7403\u9762\u6ce2\u548c\u9ad8\u65af\u5149\u675f\u3002\u9ad8\u65af\u5149\u675f\u5728\u675f\u8170\u53ef\u4ee5\u770b\u4f5c\u5e73\u9762\u6ce2\uff0c\u800c\u5728\u8fdc\u79bb\u675f\u8170\u7684\u5730\u65b9\u53ef\u4ee5\u770b\u4f5c\u7403\u9762\u6ce2\uff0c\u662f\u8fde\u63a5\u5e73\u9762\u6ce2\u548c\u7403\u9762\u6ce2\u7684\u4e00\u79cd\u8fc7\u6e21\u7684\u5f62\u5f0f\u3002\n\n\u9ad8\u65af\u5149\u675f\u7684\u65b9\u7a0b\u4e3a\uff1a\n$ \\frac{E(r,z,t"},"modified":"2019-03-21T18:36:29","modified_gmt":"2019-03-21T10:36:29","slug":"%e9%ab%98%e6%96%af%e5%85%89%e6%9d%9f","status":"publish","type":"post","link":"https:\/\/blog.francis67.cc\/?p=239","title":{"rendered":"\u9ad8\u65af\u5149\u675f"},"content":{"rendered":"

\u6700\u8fd1\u4eff\u771f\u9700\u8981\u7528\u5230\u9ad8\u65af\u5149\u675f\uff0c\u5b66\u4e60\u4e86\u4e00\u4e0b\u9ad8\u65af\u5149\u675f\u7684\u8bbe\u7f6e\u548c\u76f8\u5173\u7406\u8bba\u3002<\/p>\n

\u5728\u4e00\u5b9a\u9891\u7387\u4e0b\uff0cMaxwell\u65b9\u7a0b\u5e76\u4e0d\u72ec\u7acb\u5b8c\u5168\u72ec\u7acb\uff0c\u53ea\u6709\u6cd5\u62c9\u7b2c\u5b9a\u5f8b\u548c\u5b89\u57f9\u5b9a\u5f8b\uff08\u52a0\u4f4d\u79fb\u7535\u6d41\uff09\u7684\u4e24\u4e2a\u65b9\u7a0b\u72ec\u7acb\u3002\u6c42\u89e3\u7535\u573a\u6216\u78c1\u573a\u53ef\u4ee5\u5f97\u5230Helmholtz\u65b9\u7a0b\uff0c\u662f\u4e00\u5b9a\u9891\u7387\u4e0b\u7535\u78c1\u6ce2\u7684\u57fa\u672c\u65b9\u7a0b\u3002\u5176\u89e3\u662f\u7535\u573a\u4ee3\u8868\u7535\u78c1\u6ce2\u573a\u5f3a\u5728\u7a7a\u95f4\u4e2d\u7684\u5206\u5e03\uff0c\u6bcf\u79cd\u53ef\u80fd\u7684\u5f62\u5f0f\u6210\u4e3a\u4e00\u79cd\u6ce2\u6a21\u3002<\/p>\n

\u57fa\u672c\u7684\u89e3\u6709\u5e73\u9762\u6ce2\u3001\u7403\u9762\u6ce2\u548c\u9ad8\u65af\u5149\u675f\u3002\u9ad8\u65af\u5149\u675f\u5728\u675f\u8170\u53ef\u4ee5\u770b\u4f5c\u5e73\u9762\u6ce2\uff0c\u800c\u5728\u8fdc\u79bb\u675f\u8170\u7684\u5730\u65b9\u53ef\u4ee5\u770b\u4f5c\u7403\u9762\u6ce2\uff0c\u662f\u8fde\u63a5\u5e73\u9762\u6ce2\u548c\u7403\u9762\u6ce2\u7684\u4e00\u79cd\u8fc7\u6e21\u7684\u5f62\u5f0f\u3002<\/p>\n

\u9ad8\u65af\u5149\u675f\u7684\u65b9\u7a0b\u4e3a\uff1a
\n$ \\frac{E(r,z,t)}{E_0}=\\frac{w_0}{w(z)}exp[-(\\frac{r}{w(z)})^2]exp[i(\\omega t-\\Phi _T-\\Phi _L)]$<\/p>\n

\u9ad8\u65af\u5149\u675f\u7684\u57fa\u672c\u53c2\u6570\u6709\uff1a
\n– Beam radius : $w(z)=w_0\\sqrt{1+(\\frac{z}{z_R})^2}$\uff0c\u4ee3\u8868z\u70b9\u5904\u5149\u6591\u534a\u5f84
\n– Radius of curvature of phase front : $R(z)=z[1+(\\frac{z_R}{z})^2]$\uff0c\u4ee3\u8868\u7b49\u76f8\u4f4d\u9762
\n– Transverse phase \uff1a $\\Phi T(r,z)=\\frac{kr^2}{2R(z)}$
\n– longitudinal phase : $\\Phi _L(z)=k_z-arctan(\\frac{z}{z_R})$
\n– Rayleigh Length \uff1a $ z_R=\\frac{\\pi w_0^2}{\\lambda }$\uff0c\u4e5f\u79f0\u4e3a\u9ad8\u65af\u5149\u675f\u7684\u5171\u7126\u53c2\u6570
\n– Divergence angle \uff1a $\\Theta =2\\theta =2\\times \\lim<\/em>{z \\to \\infty } arctan(\\frac{w(z)}{z})\\simeq \\frac{\\lambda _0}{\\pi nw_0}$\uff0c\u4ee3\u8868\u8fdc\u573a\u53d1\u6563\u89d2<\/p>\n

\"\"<\/p>\n

\u53c2\u8003\uff1a
\n1. Understanding the Paraxial Gaussian Beam Formula<\/a>
\n2. Gaussian beam – wikipedia<\/a>
\n3. Gaussian beam – Youtube<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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