why I got zero answer?

Question

Habib 2015-2-18

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评论： Habib 2015-2-19

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

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Answer 1

Erik S. 2015-2-18

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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?

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Habib 2015-2-18

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 ?

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Answer 2

Erik S. 2015-2-18

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helper.m

I send a file, try it.

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Habib 2015-2-18

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?

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Answer 3

Erik S. 2015-2-19

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https://ww2.mathworks.cn/matlabcentral/answers/179150-why-i-got-zero-answer#answer_168525

helper.m

Hi again,

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

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Habib 2015-2-19

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?

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