98 lines
3.1 KiB
Matlab
98 lines
3.1 KiB
Matlab
clc; clear; close all;
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% ================= 1. 物理参数定义 =================
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r = 0.1; % 圆柱半径
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eps_r = 5.0; % 相对介电常数
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m = sqrt(eps_r); % 相对折射率 m = ~1.414
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k0 = 50; % 背景真空中波数 (k=6)
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k1 = k0 * m; % 圆柱内部波数
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x_size = k0 * r; % 尺寸参数 x = k0*a
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% ================= 2. 计算域网格设置 =================
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x_range = 1;
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y_range = 1;
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Nx = 500;
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Ny = 500;
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x_vec = linspace(0, x_range, Nx);
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y_vec = linspace(0, y_range, Ny);
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[X, Y] = meshgrid(x_vec, y_vec);
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xc = 0.5; yc = 0.5;
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[Phi, R] = cart2pol(X - xc, Y - yc); % 转换为极坐标
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% ================= 3. 场初始化 =================
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E_scat = zeros(size(X)); % 散射场
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E_int = zeros(size(X)); % 内部场
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% Wiscombe 截断准则（决定级数展开需要算到第几阶）
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N_trunc = round(x_size + 4.05 * x_size^(1/3) + 2);
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% ================= 4. 2D Mie 级数展开计算 =================
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% 2D 圆柱级数从 -N 到 +N
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for n = -N_trunc : N_trunc
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% 边界处的贝塞尔函数值
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J_nx = besselj(n, x_size);
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J_nmx = besselj(n, k1 * r);
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H_nx = besselh(n, 1, x_size);
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% 边界处的导数值 (利用递推公式 Z_n' = 0.5 * (Z_{n-1} - Z_{n+1}))
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J_nx_p = 0.5 * (besselj(n-1, x_size) - besselj(n+1, x_size));
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J_nmx_p = 0.5 * (besselj(n-1, k1*r) - besselj(n+1, k1*r));
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H_nx_p = 0.5 * (besselh(n-1, 1, x_size) - besselh(n+1, 1, x_size));
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% 计算 TM 偏振下的散射系数 a_n (对应 E_z)
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num_a = m .* J_nx .* J_nmx_p - J_nx_p .* J_nmx;
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den_a = J_nmx .* H_nx_p - m .* J_nmx_p .* H_nx;
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a_n = num_a ./ den_a;
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% 计算内部透射系数 c_n
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num_c = J_nx .* H_nx_p - J_nx_p .* H_nx; % 这其实是 Wronskian
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c_n = num_c ./ den_a;
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% 空间相位因子: i^n * exp(i*n*phi)
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phase = (1i)^n * exp(1i * n * Phi);
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% 累加外部散射场 (仅在 R >= r 区域有效)
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out_idx = R >= r;
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E_scat(out_idx) = E_scat(out_idx) + a_n .* besselh(n, 1, k0 * R(out_idx)) .* phase(out_idx);
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% 累加内部总场 (仅在 R < r 区域有效)
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in_idx = R < r;
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E_int(in_idx) = E_int(in_idx) + c_n .* besselj(n, k1 * R(in_idx)) .* phase(in_idx);
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end
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% ================= 5. 组装全场并绘图 =================
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% 入射平面波: u_inc = exp(i*k0*x)
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phase_shift = exp(1i * k0 * xc);
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E_scat = E_scat .* phase_shift;
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E_int = E_int .* phase_shift;
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E_inc = exp(1i * k0 * X);
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% 总场 = 外部(入射 + 散射) + 内部场
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% 组装总场
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E_total = zeros(size(X));
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E_total(R >= r) = E_inc(R >= r) + E_scat(R >= r);
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E_total(R < r) = E_int(R < r);
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%
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% % 提取最大场强做对比
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% max_E_val = max(abs(E_total(:)));
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% fprintf('2D 理论解析解中心区域最大场强 (max |E_total|): %.4f\n', max_E_val);
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% 绘图
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figure('Color','w');
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pcolor(X, Y, abs(E_total-E_inc));
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max_E_real = max(max(abs(E_total-E_inc)));
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shading interp;
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axis equal tight;
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colorbar;
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colormap jet;
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title(sprintf('2D Cylinder Mie Scattering |E_{scatter}| (Max = %.4f)', max_E_real));
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% 绘制圆柱边界
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hold on;
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theta_circle = linspace(0, 2*pi, 100);
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plot(xc + r * cos(theta_circle), yc + r * sin(theta_circle), 'k--', 'LineWidth', 1.5);
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hold off;
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