user defined function matrix dimensions must agree

Hi,

I have a problem with user defined functions for calculating the behaviour of tight focusing light based in the paper: Reverse and toroidal flux of light fields with both phase and polarization higher-order singularities in the sharp focus area (2019).

I created a function "A_theta" for the input field that I use in various other user defined functions called "I0_nu", "I1_nu", "I2_nu" etc. Function "A_theta" is the field amplitude multiplied by a pupil (binary mask) and I got the error message "Matrix dimensions must agree" for function "A_theta". I know the error is in the binary mask because when I ignore it I don't get the error message. I don't understand why I'm wrong if the pupil has the same size as the field function.

I attach the functions A_theta, I0_nu and a code where I employ them.

Thanks for your attention.

Carolina Rickenstorff

function y = A_theta(theta,k1,f,m,rho1,rho2,R,phi)

field=rho1.*besselj(m,k1.*rho1.*sin(theta))+rho2.*besselj(m,k1.*rho2.*sin(theta));
 
t1=f.*sin(theta).*cos(phi);
t2=f.*sin(theta).*sin(phi);
pupil=((t1.^2+t2.^2)<=R^2);

y=field.*pupil;

function y = I0_nu(theta,nu,z,r,k1,f,m,rho1,rho2,R,phi)

term = sin(theta).*sqrt(cos(theta)).*(1+cos(theta)).*exp(1i.*k1.*z.*cos(theta))...
       .*besselj(nu,k1.*r.*sin(theta));

y=term.*A_theta(theta,k1,f,m,rho1,rho2,R,phi);

clear all
close all
clc


%w = warning('query','last')
id1='MATLAB:quadgk:MaxIntervalCountReached';
id2='MATLAB:quadgk:MinStepSize';
warning('off',id1)
warning('off',id2)


%%%Optical parameters
lambda=532e-9;
k=2*pi/lambda;
n1=1.518;
k1=n1.*k;
NA=1*n1;
f=0.01;
alfa=asin(NA/n1);
%%%%Pupil radius (m) 
R=f.*sin(alfa);


%%%%Axis (m)
N=64;
x=linspace(-N/2,N/2-1,N);
x=2/N.*x.*1.25e-6;   
x=repmat(x,N,1);
y=x';
phi=angle(x+1i.*y);
r=sqrt(x.^2+y.^2);
%%%%In tight focusing we use theta variable
theta=asin(r./f);


%%%%Vortex radii
rho1=0.00055.*R;
rho2=0.91.*rho1;
 
%%%%Topological charge, m=0 inclusive
m=0;
%%%%Polarization order, n=0 inclusive
n=0;
%%%%Integration order function I0_nu
nu=m+n;


%%%%Initializing
I0_nu1=zeros(N);
%%%%Focal point distance z=0 
z=0;

for p=1:N*N
I0_nu1(p) =quadgk(@(theta)I0_nu(theta,nu,z,r(p),k1,f,m,rho1,rho2,R,phi),0,alfa);

    if mod(p,8*N)==0;
    %%%%Percentage tellboard
    fprintf('completo %3.0f%%\n',round(p.*100./(N*N)))
    end
end

Answer 1

[Carolina Rickenstorff]

Hi to all,

The problem was in the program where I use quadgk. It was just lacking the index into variable phi(p) and now all is good:

Sorry for the inconvenience.

Carolina R

clear all
close all
clc


%w = warning('query','last')
id1='MATLAB:quadgk:MaxIntervalCountReached';
id2='MATLAB:quadgk:MinStepSize';
warning('off',id1)
warning('off',id2)






%%%Optical parameters
lambda=532e-9;
k=2*pi/lambda;
n1=1.518;
k1=n1.*k;
NA=1*n1;
f=0.01;
alfa=asin(NA/n1);
%%%%Pupil radius (m) 
R=f.*sin(alfa);


%%%%Axis (m)
N=64;
x=linspace(-N/2,N/2-1,N);
x=2/N.*x.*1.25e-6;   
x=repmat(x,N,1);
y=x';
phi=angle(x+1i.*y);
r=sqrt(x.^2+y.^2);
%%%%In tight focusing work we use theta variable
theta=asin(r./f);


%%%%Vortex radii
rho1=0.00055.*R;
rho2=0.91.*rho1;
 
%%%%Topological charge, m=0 inclusive
m=0;
%%%%Polarization order, n=0 inclusive
n=0;


%%%%Integration order function I0_nu
nu=m+n;


%%%%Initializing
I0_nu1=zeros(N);
%%%%Focal point distance z=0 
z=0;

for p=1:N*N
I0_nu1(p) =quadgk(@(theta)I0_nu(theta,nu,z,r(p),k1,f,m,rho1,rho2,R,phi(p)),0,alfa);

    if mod(p,8*N)==0;
    %%%%Percentage tellboard
    fprintf('completo %3.0f%%\n',round(p.*100./(N*N)))
    end
end