Matlab：拉盖尔高斯光束的干涉

2024-07-06 08:25| 来源: 网络整理| 查看: 265

代码：

clc clear all close all %% 拉盖尔-高斯光束与平面光波干涉 N = 300; %取样点数 lambda = 632e-9; %波长632nm k = 2*pi/lambda; %波数 w0 = 3; x = linspace(-1e-4,1e-4,N); y = x; [X,Y] = meshgrid(x,y); [theta,r] = cart2pol(X,Y); p = 0; Z_R = pi*w0^2/lambda; %瑞利长度 z = 0; w_z = w0*sqrt(1+(z/Z_R)^2);%光束在z位置的半径 figure; for m = -4:4 E1 = exp(-1i*k*X); %平面波 E2 = sqrt(2*factorial(p)/pi/(p+factorial(abs(m))))*(1/w_z)*(sqrt(2)*r/w_z).^abs(m)... .*exp(-r.^2/w_z^2).*laguerre(p,abs(m),2*r.^2/w_z^2).*exp(-1i*m*theta).*exp(-1i*k*z)... .*exp(-1i*k*r.^2*z/2/(z^2+Z_R^2))*exp(-1i*(2*p+abs(m)+1)*atan(z/Z_R)); c1 = E1+E2; E_1 = c1.*conj(c1); subplot(3,3,m+5) h1 = pcolor(X,Y,E_1); colorbar; set(h1,'edgecolor','none','facecolor','interp'); title(['m = ',num2str(m)]); colormap(gray); axis square; end suptitle('拉盖尔-高斯光束与平面光波干涉') %为图一添加总标题 %% 涡旋光束与球面光波干涉 N = 200; %取样点数 lambda = 632e-9; %波长632nm k = 2*pi/lambda; %波数 x = linspace(-2e-3,2e-3,N); y = x; [X,Y] = meshgrid(x,y); [theta,r] = cart2pol(X,Y); Z = 1; Z_R = pi*w0^2/lambda; %瑞利长度 z = 0; w_z = w0*sqrt(1+(z/Z_R)^2);%光束在z位置的半径 figure; for m = -4:4 E3 = exp(-1i*k*Z*(1+0.5*X.^2/Z^2+0.5*Y.^2/Z^2)); %球面波 E4 = sqrt(2*factorial(p)/pi/(p+factorial(abs(m))))*(1/w_z)*(sqrt(2)*r/w_z).^abs(m)... .*exp(-r.^2/w_z^2).*laguerre(p,abs(m),2*r.^2/w_z^2).*exp(-1i*m*theta).*exp(-1i*k*z)... .*exp(-1i*k*r.^2*z/2/(z^2+Z_R^2))*exp(-1i*(2*p+abs(m)+1)*atan(z/Z_R)); c2 = E3+E4; E_2 = c2.*conj(c2); subplot(3,3,m+5) h2 = pcolor(X,Y,E_2); colorbar; set(h2,'edgecolor','none','facecolor','interp'); title(['m = ',num2str(m)]); colormap(gray); axis square; end suptitle('拉盖尔高斯光束与球面光波干涉') %为图二添加总标题 %% 拓扑荷数相反的拉盖尔高斯光束互相干涉 N = 200; %取样点数 lambda = 632e-9; %波长632nm k = 2*pi/lambda; %波数 x = linspace(-8,8,N); y = x; [X,Y] = meshgrid(x,y); [theta,r] = cart2pol(X,Y); Z_R = pi*w0^2/lambda; %瑞利长度 z = 0; w_z = w0*sqrt(1+(z/Z_R)^2);%光束在z位置的半径 figure; for m = 1:9 E5 = sqrt(2*factorial(p)/pi/(p+factorial(abs(-m))))*(1/w_z)*(sqrt(2)*r/w_z).^abs(-m)... .*exp(-r.^2/w_z^2).*laguerre(p,abs(-m),2*r.^2/w_z^2).*exp(-1i*(-m)*theta).*exp(-1i*k*z)... .*exp(-1i*k*r.^2*z/2/(z^2+Z_R^2))*exp(-1i*(2*p+abs(-m)+1)*atan(z/Z_R)); E6 = sqrt(2*factorial(p)/pi/(p+factorial(abs(m))))*(1/w_z)*(sqrt(2)*r/w_z).^abs(m)... .*exp(-r.^2/w_z^2).*laguerre(p,abs(m),2*r.^2/w_z^2).*exp(-1i*m*theta).*exp(-1i*k*z)... .*exp(-1i*k*r.^2*z/2/(z^2+Z_R^2))*exp(-1i*(2*p+abs(m)+1)*atan(z/Z_R)); c2 = E5+E6; E_3 = c2.*conj(c2); subplot(3,3,m) h3 = pcolor(X,Y,E_3); colorbar; set(h3,'edgecolor','none','facecolor','interp'); title(['m = ',num2str(m)]); colormap(gray); axis square; end suptitle('拓扑荷数相反的拉盖尔高斯光束互相干涉') %为图三添加总标题 %% 拉盖尔多项式(文献3中的公式) function result = laguerre(p,l,x) result = 0; if p == 0 result = 1; elseif p == 1 result = 1+abs(l)-x; else result = (1/p)*((2*p+l-1-x).*laguerre(p-1,abs(l),x)-(p+l-1)*laguerre(p-2,abs(l),x)); end end

运行结果：在这里插入图片描述参考文献： [1]徐丽娟. 涡旋光束的产生及特性研究[D]. 浙江大学, 2014. [2]赵麒, 白忠臣, 周骅,等. 拉盖尔-高斯光束作用下熔石英温度及应力研究%Research of temperature and thermal stress of fused silica irradiated by Laguerre-Gaussian beam[J]. 激光技术, 2018, 042(001):121-126. [3]石业娇. 面向Fredholm微分方程的广义拉盖尔多项式求解方法[J]. 湘潭大学自然科学学报, 2018, 040(001):31-35.

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