why I got zero answer?

Hi everyone.

In below codes I used the trapz command for integration of u1_1, but answer is zero, what is wrong? And if I want to integrate respect to "r", what must I do?

 clc
clear all
close all
a=3e-2;
z=0.42;
N=300;
lambda=1030e-9;
k=2*pi/lambda;
w0=0.0001;
zr=pi*w0^2/lambda;
R=z*(1+(zr/z)^2);
w=w0*sqrt(1+(z/zr)^2);
[x,y]=meshgrid(linspace(-a/2,a/2,N));
[teta,r] = cart2pol(x,y);

 for i=1:N
      for j=1:N
        u1_1(i,j)=(r(i,j)./w).^2.*exp(-(r(i,j).^2)./w.^2);
      end
  end

for i=1:N
    for j=1:N
    u2(i,j)=trapz(u1_1(i,j));
    end
 end

Answer 1

[Erik S.]

Hi

You do the integration in the loop with only 1 value at the time, so the integral should be 0. You should pass vectors to the trapz function. Do you want to do a double integral? Or integrate each row in the matrix u1_1?

[Habib]

thank you for your attention, Erik S.

so, I can't understand, but, this integration is one dimensional and I think "integrate each row in the matrix u1_1" be true. so what is your suggestion? what is solution ?

Answer 2

[Erik S.]

I send a file, try it.

[Habib]

the answer of trapz,u2, is a 1*300 array and I want it be a 300*300 matrices and plot u2 by mesh.

like this:

do you think it is possible?

Answer 3

[Erik S.]

Hi again,

I'm not sure I understand your problem. But I send a new file, is it the result you need?

[Habib]

Thanks.

Your codes give us a shape like the above figure but firstly we have to use Trapz and then plot it. The u1_1 = (r./w).^2.*exp(-r.^2./w.^2) equation is a laguerre-gaussian beam equation and I want to propagate it along 'L' distance. For propagation, I have to use in following integral.

I am so ashamed for bothered you. excuse me.

so how we can solve numerically this integral?