Symbolic function Gaussian Beam

Actually I want to plot the intensity profile I(x,y,z,lambda,wo) of a gaussian beam. Some how I get confused with handle @(x,y..) and syms. May some one help.

r = @(x,y)          sqrt(x^2+y^2);        % Distance
k = @(lambda)       2*pi*lambda;          % Wavenumber
w = @(w0,z,z0)      w0*sqrt(1+(z/z0)^2);  % Beamradius
R = @(z,z0)         z*(1+(z0/z)^2);       % 
w0= @(lambda,z0)    sqrt(lambda*z0/pi);
z0= @(w0, lambda)   pi*w0^2/lambda;
xi= @(z, z0)        atan(z/z0);

E = @(x,y,z,E0) ...
    E0*w0(1,1) / w(1,z,z0(1,1))...
    * exp(-(r(x,y)/w(w0,z,z0(1,1)))^2) ...
    * exp(-1i*k(1)*z-xi(z, z0(1,1))) ...
    * exp(-1i*k(1)*r(x,y)^2/2/R(z,z0(1,1)));
I=@(x,z) E(x,1,z,1)^2;
figure()
fcontour(I)

Warning: Error updating FunctionContour.

Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To operate on each element of the matrix individually, use POWER (.^) for elementwise power.

Answer 1

[Star Strider]

You need to use element-wise operations. See the documentation on Array vs. Matrix Operations for details.

Also, you can use the hypot function for ‘r’.

For example, ‘R’ becomes:

R = @(z,z0) z.*(1+(z0./z).^2);

Addition, subtraction, and multiplication of an array by a scalar are element-wise by definition.

.

[De Le]

I am not shure this is the issue here. These ment to smybolic linear function, not arrays. Anyways using .* and .^ did not solve the issue. I guess, as Torsten mentionend, my problem here is that i dont know how to use variables and funtion handelns properly.

Answer 2

[Torsten]

w0 and z0 are function handles. You can't use them like variables in your definitions.

Further, E is a complex-valued function. fcontour can only plot real-valued functions.

[De Le]

Is this approched better in case of using variables and function handels properly?

% Variables
syms x y z 

% Coeffitents
% lambda w0 E0 

% Handels
% r k w R xi z0
lambda = 1;w0 =1;E0 =1;

r(x,y)      =   sqrt(x^2+y^2);        % Distance
k           =   2*pi*lambda;          % Wavenumber
z0          =   pi*w0^2/lambda;
w(z)        =   w0*sqrt(1+(z/z0)^2);  % Beamradius
R(z)        =   z*(1+(z0/z)^2);       % 
xi(z)       =   atan(z/z0);

E(x,y,z) =...
    E0*w0 / w(z)...
    * exp(-(r(x,y)/w(z))^2) ...
    * exp(-1i*k*z-xi(z) ...
    * exp(-1i*k*r(x,y)^2/2/R(z)));
I(x,z)= E(x,1,z)^2;
figure()
fcontour(I)


I(1,1)

Further E is complex, but since I=E^2, fcontour has to plot a real.

I(x,z)= E(x,1,z)^2;
figure()
fcontour(I)

Anayways some how it is still not working.

[Torsten]

lambda = 1;
w0 =1;
E0 =1;
z0 = pi*w0^2/lambda;
k  = 2*pi*lambda;          % Wavenumber
r  = @(x,y)sqrt(x.^2+y.^2);        % Distance
w  = @(z)w0*sqrt(1+(z/z0).^2);  % Beamradius
R  = @(z) z.*(1+(z0./z).^2);       % 
xi = @(z)atan(z/z0);
E  = @(x,y,z)...
     E0*w0 ./ w(z)...
    .* exp(-(r(x,y)./w(z)).^2) ...
    .* exp(-1i*k*z-xi(z)) ...
    .* exp(-1i*k*r(x,y).^2./2./R(z));
I = @(x,z)E(x,1,z).*conj(E(x,1,z));
fcontour(I,[-4 4 -30 1],'Fill','on' )
colorbar