plot three dimensional surface for this code

Hi every one.

I decided to plot three-dimensional surface for u3 but when i wrote mesh(r4,u3), the error of " Z must be a matrix not scalar or vector" is appeared. Now I want help to plot it, How can I do it?.please help me?

 clear all 
 close all
 clc

 r_1=linspace(-1,1,100);

 r_2=linspace(-1,1,100);

 [r1,r2]=meshgrid(linspace(-1,1,100));

 z2=4.2;                % is the axial distance from the beam's narrowest point

 z1=1;

 L=z2-z1;

 wvl=500;               % is wavelength

 k=2*pi./wvl;

 w0=sqrt(wvl.*z1./pi);  % is the waist size

 % is the radius at which the field amplitude and intensity 
 % drop to 1/e and 1/e2 of their axial values, respectively
 w1=w0.*sqrt(1+wvl.*z1./pi.*w0.^2);  
 w2=w0.*sqrt(1+wvl.*z2./pi.*w0.^2);                                                      

 % is the radius of curvature of the beam's wavefronts
 R1=z1.*(1+(pi.*w0.^2./wvl.*z1).^2);            
 R2=z2.*(1+(pi.*w0.^2./wvl.*z2).^2); 

 % mathematical form of Gaussian beam
 u1=w0./w1.*exp((-1./w1.^2+1i.*pi./wvl.*R1).*(r1.^2+r2.^2)-1i.*k.*z1); 

 figure(1)

 surf(r1,r2,real(u1))

 K=zeros(1,length(r1));

 u2=zeros(1,length(r1));

 u3=zeros(1,length(r1));

 r3=linspace(0,1,length(r1));

 r4=linspace(0,1,length(r1));

 for nn=1:100

    for mm=1:100

       K(nn,mm)=exp(-1i.*pi.*(r3(nn).^2+z1.^2+r4(mm).^2+z1.^2-2.*(r3(nn).*r4(mm)+z1.*z2))./(wvl.*L)-1i.*k.*L);

       u2(nn,mm)=w0./w1.*exp((-1./w1.^2+1i.*pi./wvl.*R1).*(r3(nn).^2+r4(mm).^2)-1i.*k.*z1);

    end

    u3(nn)=trapz(r3,K(nn,:).*u1(nn,:));

 end

 figure(2)

 mesh(r3,r4,u3)

Answer 1

[Chad Greene]

Indeed, r3, r4, and u3 are all 1x100 arrays. Change mesh(r3,r4,u3) to plot3(r3,r4,u3) to see for yourself. You'll have to find a way to make u3 into a 2D matrix representing a surface instead of a 1D array representing a line.

[Habib]

thank you for your attention.

good luck