w0无法识别是怎么回事
clc
clear all
close all
%% 环形涡旋光束
N = 200;
lambda = 632e-9; %波长为632nm
k = 2*pi/lambda; %波数
w0 = 3; %束腰半径
x = linspace(-10,10,N);
y = linspace(-10,10,N);
[X,Y] = meshgrid(x,y);
[theta,r] = cart2pol(X,Y);
beta = 50*pi/180;
figure;
for m = -4 : 4
subplot(3,3,m+5)
E1 = (r/w0).^abs(m).*exp(-r.^2/w0^2)*exp(1i*beta).*exp(-1i*m*theta);
I1 = E1.*conj(E1); I1 = I1/max(max(I1));
h1 = pcolor(X,Y,I1);
colorbar;
set(h1,'edgecolor','none','facecolor','interp');
title(['m = ',num2str(m)]);
%colormap(gray); %输出灰度图像
axis square;
%mesh(X,Y,I1) %三维
end
suptitle('环形涡旋光束：不同拓扑荷数(m)') %为图一添加总标题
%% 贝塞尔-高斯光束
N = 200;
lambda = 632e-9; %波长为632nm
k = 2*pi/lambda; %波数
w0 = 3; %束腰半径
x = linspace(-2e-6,2e-6,N);
y = linspace(-2e-6,2e-6,N);
[X,Y] = meshgrid(x,y);
[theta,r] = cart2pol(X,Y);
figure;
alpha = sqrt(k^2-theta.^2);
for m = -4 : 4
subplot(3,3,m+5)
E2 = besselj(m,alpha.*r).*exp(-r.^2/w0^2).*exp(-1i*m*theta); %使用了matlab内置的贝塞尔函数
I2 = E2.*conj(E2); I2 = I2/max(max(I2));
h2 = pcolor(X,Y,I2);
colorbar;
set(h2,'edgecolor','none','facecolor','interp');
title(['m = ',num2str(m)]);
%colormap(gray); %输出灰度图像
axis square;
%mesh(X,Y,I2) %三维
end
suptitle('贝塞尔-高斯光束：不同拓扑荷数(m)') %为图二添加总标题
%% 拉盖尔-高斯光束
N = 200;
lambda = 632e-9; %波长为632nm
k = 2*pi/lambda; %波数
w0 = 3; %光斑尺寸
x = linspace(-10,10,N);
y = linspace(-10,10,N);
[X,Y] = meshgrid(x,y);
[theta,r] = cart2pol(X,Y);
figure;
%p = 0, 1, 2;
p = 2;
for m = -4 : 4
subplot(3,3,m+5)
E3 = 1/w0*(sqrt(2)*r/w0).^abs(m).*laguerre(p,2*r.^2/w0^2).*exp(-r.^2/w0^2).*exp(1i*m*theta);
I3 = E3.*conj(E3); I3 = I3/max(max(I3));
h3 = pcolor(X,Y,I3);
colorbar;
set(h3,'edgecolor','none','facecolor','interp');
title(['m = ',num2str(m)]);
%colormap(gray); %输出灰度图像
axis square;
%mesh(X,Y,I3) %三维
end
suptitle('拉盖尔-高斯光束：不同拓扑荷数(m) p = 2') %为图三添加总标题
%拉盖尔多项式
function result = laguerre(p,x)
result = 0;
switch p
case 0
result = 1;
case 1
for l = -p : p
result = result+l+1-x;
end
case 2
for l = -p : p
result = result+0.5*(l+1)*(l+2)-(l+2)*x+0.5*x.^2;
end
end
end