拉盖尔高斯光束_厄米高斯光束MATLAB仿真.pdf
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激光原理by 贾而穑 130212114
厄米高斯光束MATLAB 仿真
其中主程序文件：plotHermiteGaussianBeams.m
子程序文件：HermitePoly.m
程序如下：
plotHermiteGaussianBeams.m
%%
% auther：Erse Jia
% Student ID 130212114
%%
%% Hermite Gaussian Beams
%% SET PARAMETERS
% Physical parameters
lambda = 500; % nm
k = 2*pi/lambda;
% The two parameters for the gaussian beam (and derived quantities)
z0 = 1;
A0 = 1;
W0 = sqrt(lambda*z0/pi);
W = @(z) W0*sqrt(1+(z/z0)^2);
R = @(z) z*(1+(z/z0)^2);
Zeta = @(z) atan(z/z0);
% The coefficients for the Hermite-Gaussian (HG) beam of order (l,m)
A = [ 1 0 0 0;
1 1 0 0;
0 0 0 0;
0 0 .2 0];
% Display Parameters
res = 800;
z = 1e-9;
x = linspace(-2*W(z),2*W(z),res);
y = linspace(-2*W(z),2*W(z),res);
[X Y] = meshgrid(x,y);
X = X(:);
Y = Y(:);
%% RUN THE SIMULATION
% Preallocate Memory
U = zeros(length(X),1);
Utemp = zeros(length(X),1);
Utemp2 = zeros(length(X),1);
% Calculate Values that are independent of HG Polynomial order
lpf = exp(-1i*k*z - 1i*k*(X.^2 + Y.^2)/(2*R(z))); %lateral phase factor
u = sqrt(2)*X/W(z);
v = sqrt(2)*Y/W(z);
for l = 1:size(A,1)
%if there are any terms of this order, calculate the x-HG (so you dont
%need to repeat for each value of m
if sum(A(l,:) ~= 0) ~= 0
Utemp2 = (W0/W(z))*polyval(HermitePoly(l-1),u).*exp(-u.^2/2);
else
continue;
end
for m = 1:size(A,2)
if A(l,m) ~= 0
Utemp = Utemp2.*(polyval(HermitePoly(m-1),v)).*exp(-v.^2/2);
Utemp = A(l,m)*Utemp.*lpf*exp(1i*(l+m+1)*Zeta(z));
U = U + Utemp;
end
end
end
%% DRAW PLOTS
figure;
U = reshape(U,res,res);
imagesc(x,y,abs(U).^2);
axis square;
set(1,color,w);
title(Hermite-Gaussian Beam of Order);
xlabel(x (nm));
ylabel(y (nm));
HermitePoly.m
%%
% HermitePoly.m by Erse Jia
% Student ID 130212114
% Gi
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