# 二维轴对称模型中的电磁散射

2022年 4月 12日

### 柱坐标中的平面波展开

\bm{E_b}=\bm{E_0}e^{i(\omega t-\bm{k} \cdot \bm{r})}

\bm{E_b}
= E_0 ( cos\theta e^{-ikrsin\theta cos\phi} e^
{ikzcos\theta} \bm{\hat{x}} + sin\theta e^{-ikrsin\theta cos\phi} e^{ikzcostheta}
\bm{\hat{z}})

e^{-i k r cos\phi} = \sum_{m=-\infty}^{\infty} (-i)^m J_m(kr)e^{-im\phi}

\bm{\hat{x}} = \frac{1}{2} [e^{i\phi} (\bm{\hat{r}} + i\bm{\hat{\phi}}) + e^{-i\phi} (\bm{\hat{r}} – i\bm{\hat{\phi}})]

\bm{E_b} = E_0e^{ikzcos\theta} \{ \frac{1}{2}cos\theta \sum_{m=-\infty}^{\infty} [(-i)^{m-1} J_{m-1} (krsin\theta) + (-i)^{m+1}J_{m+1}(krsin\theta)]e^{-im\phi} \bm{\hat{r}} \\
-\frac{i}{2}cos\theta \sum_{m=-\infty}^{\infty} [(-i)^{m-1} J_{m-1} (krsin\theta) – (-i)^{m+1}J_{m+1}(krsin\theta)] e^{-im\phi}\bm{\hat{\phi}} \\
+sin\theta \sum_{m=-\infty}^{\infty} (-i)^m J_m (krsin\theta)e^{-im\phi} \bm{\hat{z}} \}

\bm{E_r} = \frac{1}{2} E_0 e^{ikzcos\theta} cos\theta \sum_{m=0}^{\infty} \chi(m)[(-i)^{m-1}J_{m-1}(krsin\theta) + (-i)^{m+1} J_{m+1} (krsin\theta)]cos(m\phi) \bm{\hat{r}}

### 研究长椭球体的散射

sqrt(abs(sum(withsol('sol1', ewfd.relEz*cos(m*0), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2 + abs(sum(withsol('sol1', ewfd.relEr*cos(m*0), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2 + abs(sum(withsol('sol1', j*ewfd.relEphi*sin(m*0), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2)

sqrt(abs(sum(withsol('sol1', ewfd.relEz*cos(m*rev1phi), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2 + abs(sum(withsol('sol1', ewfd.relEr*cos(m*rev1phi), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2 + abs(sum(withsol('sol1', j*ewfd.relEphi*sin(m*rev1phi), setind(m,index),setval(freq,30[THz])), index, 1, N+1))^2)

-withsol('sol1', sigma_sc, setval(m,0),setval(freq, freq))-sum(withsol('sol1', 0.5*sigma_sc, setval(m,val),setval(freq, freq)),val,1,N)

### 动手尝试

#### 评论 (2)

2024-06-26

##### Min Yuan
2024-07-05 COMSOL 员工