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[求助]
金属狭缝内的有效折射率的方程求解
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不知道matlab大神能不能帮我解一下这个方程，我之前找同学帮忙，结果他说这个方程除非化简成y=ax的形式他才能解，但是这个方程既有复数，又有双曲函数，完全不会接，就想看看有没有大神能直接摆那个程序接一下，金币不够你说，我在加到你满意 其中k0,介电常数都是给定的，主要想看一看有效折射率n，随缝宽w的变化。  有效折射率方程2.jpg |
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想要_回家: 金币+100, ★★★很有帮助, 解决了我的问题 2013-07-15 15:01:52
想要_回家: 金币+100, ★★★很有帮助, 解决了我的问题 2013-07-15 15:01:52
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我用的比较传统的直接解方程的办法，算出不同w对应的n，然后作图，作图的时候，n的虚数部分去掉。 可见看见在w=0和50nm处有跳跃。程序如下： function sn_20130715 clear all;clc global w k0 ed em k0=6.082e6; ed=1; em=-42.7616-1.308*1i; format long n0=0.1; w=0; for i=1:101 n(i)=fsolve(@refraction,n0); w=w+1e-9; end w=0:1e-9:100e-9; [w' n'] figure plot(w',n','bo-') function y=refraction(n) global w k0 ed em y=tanh(w*k0/2*sqrt(n^2-ed))+ed*sqrt(n^2-em)/em/sqrt(n^2-ed); 结果： w n 0 0.099999959741578 + 6.539999121449442i 0.000000001000000 0.096312251752139 + 6.790411526565819i 0.000000002000000 0.096707779627593 + 6.762641111012455i 0.000000003000000 4.642911438878475 + 0.053877233727280i 0.000000004000000 3.962660617247608 + 0.041300656950422i 0.000000005000000 3.525665802152372 + 0.033920995113969i 0.000000006000000 3.216581490280788 + 0.029034029856561i 0.000000007000000 2.983648081683195 + 0.025673453649347i 0.000000008000000 2.800743468367221 + 0.023172073950826i 0.000000009000000 2.652512509968276 + 0.021232609557716i 0.000000010000000 2.529538254154120 + 0.019554357109418i 0.000000011000000 2.425435001788252 + 0.018165144355004i 0.000000012000000 2.335971728020295 + 0.017013917367326i 0.000000013000000 2.258136757699678 + 0.016090235279249i 0.000000014000000 2.189778767247689 + 0.015217258105177i 0.000000015000000 2.129076172185004 + 0.014524751710617i 0.000000016000000 2.074768610545597 + 0.013810265306609i 0.000000017000000 2.025863353416570 + 0.013216186916386i 0.000000018000000 1.981563147230965 + 0.012673784991951i 0.000000019000000 1.941231116322375 + 0.012223991275707i 0.000000020000000 1.904296658761679 + 0.011756537606865i 0.000000021000000 1.870337630393248 + 0.011326860158899i 0.000000022000000 1.839040454804140 + 0.010968370287799i 0.000000023000000 1.810036260319961 + 0.010614583647135i 0.000000024000000 1.783095481222376 + 0.010274176168077i 0.000000025000000 1.757985895939245 + 0.009970519031675i 0.000000026000000 1.734540845621961 + 0.009687402452938i 0.000000027000000 1.712590436229947 + 0.009414924267260i 0.000000028000000 1.691979152449821 + 0.009161543473387i 0.000000029000000 1.672586928136418 + 0.008928065577144i 0.000000030000000 1.654310462030495 + 0.008708270753012i 0.000000031000000 1.637052109604773 + 0.008498210421664i 0.000000032000000 1.620723144513482 + 0.008294787737511i 0.000000033000000 1.605246720201364 + 0.008119958861623i 0.000000034000000 1.590562493942908 + 0.007940897654971i 0.000000035000000 1.576608580383508 + 0.007771734489512i 0.000000036000000 1.563321392247376 + 0.007603024610845i 0.000000037000000 1.550664927079865 + 0.007452783311542i 0.000000038000000 1.538587030987787 + 0.007304501413247i 0.000000039000000 1.527049474518354 + 0.007162602535289i 0.000000040000000 1.516015879011861 + 0.007026659469317i 0.000000041000000 1.505452511439111 + 0.006896429334978i 0.000000042000000 1.495330964568782 + 0.006771118273797i 0.000000043000000 1.485621773843522 + 0.006650840640318i 0.000000044000000 1.476300174141656 + 0.006535136468970i 0.000000045000000 1.467342938878898 + 0.006423791230058i 0.000000046000000 1.458728578591685 + 0.006316519195074i 0.000000047000000 1.450437457270150 + 0.006213046662400i 0.000000048000000 -1.442451248720188 - 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