拉盖尔高斯光束_厄米高斯光束MATLAB仿真

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 don't

%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 13021