使用matlab求解二维声子晶体能带结构的代码

以下是一个简单的 Matlab 代码，用于求解二维声子晶体的能带结构：

% 二维声子晶体能带结构计算代码
% 参考文献：M. Florescu, et al., "Ultracompact photonic crystal waveguide 
% bends with high transmission,"  Optics Letters, vol. 31, no. 10, pp. 1449-1451, May 2006.

clc;
clear all;

% 设置晶格常数和布拉格矢量
a = 1;
b = a*sqrt(3);
Kx = (4*pi)/(3*a);
Ky = (2*pi)/(sqrt(3)*b);

% 设置频率范围和步长
f_min = 0;
f_max = 100;
f_step = 0.1;

% 初始化能量矩阵
E = zeros(2000,2000);

% 计算能带结构
for i = 1:2000
    for j = 1:2000
        kx = ((i-1000)*0.01*Kx);
        ky = ((j-1000)*0.01*Ky);
        d1 = sqrt(3)/2*a;
        d2 = a/2;
        G1 = [2*pi/a; -2*pi/(3*b)];
        G2 = [0; 4*pi/(3*b)];
        M = [kx/2 - ky/(2*sqrt(3)); ky*sqrt(3)/2 - kx/2];
        N = [-kx/(2*sqrt(3)); ky/2 + kx/2];
        A = [0; 0];
        B = [d2; d1];
        C = [d2; -d1];
        D = [0; -2*d1];
        E1 = [d2; -3*d1];
        F = [-d2; -2*d1];
        G = [-d2; 0];
        H = [-d2; 2*d1];
        E2 = [0; 3*d1];
        r1 = norm(M);
        r2 = norm(N);
        r3 = norm(A-M);
        r4 = norm(B-M);
        r5 = norm(C-M);
        r6 = norm(D-M);
        r7 = norm(E1-M);
        r8 = norm(F-M);
        r9 = norm(G-M);
        r10 = norm(H-M);
        r11 = norm(E2-M);
        r12 = norm(N-A);
        r13 = norm(B-A);
        r14 = norm(C-A);
        r15 = norm(D-A);
        r16 = norm(E1-A);
        r17 = norm(F-A);
        r18 = norm(G-A);
        r19 = norm(H-A);
        r20 = norm(E2-A);
        r21 = norm(N-B);
        r22 = norm(C-B);
        r23 = norm(D-B);
        r24 = norm(E1-B);
        r25 = norm(F-B);
        r26 = norm(G-B);
        r27 = norm(H-B);
        r28 = norm(E2-B);
        r29 = norm(N-C);
        r30 = norm(D-C);
        r31 = norm(E1-C);
        r32 = norm(F-C);
        r33 = norm(G-C);
        r34 = norm(H-C);
        r35 = norm(E2-C);
        r36 = norm(N-D);
        r37 = norm(E1-D);
        r38 = norm(F-D);
        r39 = norm(G-D);
        r40 = norm(H-D);
        r41 = norm(E2-D);
        r42 = norm(E1-E2);
        r43 = norm(F-E2);
        r44 = norm(G-E2);
        r45 = norm(H-E2);
        r46 = norm(F-E1);
        r47 = norm(G-E1);
        r48 = norm(H-E1);
        r49 = norm(G-F);
        r50 = norm(H-F);
        r51 = norm(H-G);
        if (r1 <= 1) || (r2 <= 1) || (r3 <= 1) || (r4 <= 1) || (r5 <= 1) || (r6 <= 1) || (r7 <= 1) || (r8 <= 1) || (r9 <= 1) || (r10 <= 1) || (r11 <= 1) || (r12 <= 1) || (r13 <= 1) || (r14 <= 1) || (r15 <= 1) || (r16 <= 1) || (r17 <= 1) || (r18 <= 1) || (r19 <= 1) || (r20 <= 1) || (r21 <= 1) || (r22 <= 1) || (r23 <= 1) || (r24 <= 1) || (r25 <= 1) || (r26 <= 1) || (r27 <= 1) || (r28 <= 1) || (r29 <= 1) || (r30 <= 1) || (r31 <= 1) || (r32 <= 1) || (r33 <= 1) || (r34 <= 1) || (r35 <= 1) || (r36 <= 1) || (r37 <= 1) || (r38 <= 1) || (r39 <= 1) || (r40 <= 1) || (r41 <= 1) || (r42 <= 1) || (r43 <= 1) || (r44 <= 1) || (r45 <= 1) || (r46 <= 1) || (r47 <= 1) || (r48 <= 1) || (r49 <= 1) || (r50 <= 1) || (r51 <= 1)
            E(i,j) = NaN;
        else
            E(i,j) = sqrt(abs(1 + exp(i*G1(1)*a + j*G1(2)*b) + exp(i*G2(1)*a + j*G2(2)*b) + exp((i*G1(1) + j*G1(2))*a + (i*G2(1) + j*G2(2))*b)));
        end
    end
end

% 绘制能带结构图
figure;
hold on;
axis([-1 1 -1 1]);
for f = f_min:f_step:f_max
    contour(sin(Kx*linspace(-pi,pi,2000)), sin(Ky*linspace(-pi,pi,2000)), E, [f f], 'LineColor', 'blue');
end
xlabel('k_x');
ylabel('k_y');
title('二维声子晶体能带结构');

请注意，此代码仅提供了一个简单的框架，您需要根据自己的需要进行修改和优化。此外，由于该算法的计算量较大，可能需要一些时间才能生成完整的能带结构图。