Plot 3D figure

Hello, I would like to plot this fugure (ro, Z, I), my code as below, could you please give me a help? Thanks a lot.

clear all; close all; clc

 for n = 1:1:100
    i = sqrt(-1);
    a = 0.62;
    NA = 0.29;
    wL = 772e-3; % micro meter
    
    R = linspace (-0.4,0.4,100); 
    ro = ((2*pi)/wL)*NA.*R;
    
    Z =  linspace(-1,1,100);
    mu = ((2*pi)/wL)*NA^2*Z;
    
    fun1 = @(r)r.*exp(-r.^2).* besselj(ro(n),r) .*exp(-(1.*i.*mu(n).*r.^2)./2);
    q1 = integral(fun1,0,1);
    q2 = integral(fun1,0,a);
    
    E(n) = (2/(1-exp(-1)))*q1- 2*(2/(1-exp(-1)))*q2; % electric field
    I(n) = abs(E(n)).^2; % intensity 
end

figure(2)
plot(R, I)

Answer 1

[Walter Roberson]

The scale factor between and Z or R values is not obvious. It is also not obvious why you used the ranges you did: the sample plot suggests that they should be reversed. However, I had to use those ranges to get any plot of note -- and you can see it is not the expected plot. The output was essentially unchanged with Z -- which suggests that possibly Z is the wrong scale.

a = 0.62;
NA = 0.29;
wL = 772e-3; % micro meter
    
num_R = 100;
num_Z = 101;
Zvals = linspace(-5,5,num_Z)/1e2;
Rvals = linspace(-40,40,num_R)/1e2;
 
for Ridx = 1 : num_R
    R = Rvals(Ridx);
    ro = ((2*pi)/wL)*NA.*R;
    for Zidx = 1 : num_Z
        Z = Zvals(Zidx);
        mu = ((2*pi)/wL)*NA^2*Z;
        fun1 = @(r)r .* exp(-r.^2) .* besselj(ro,r) .* exp(-(1.*i.*mu.*r.^2)./2);
        q1 = integral(fun1,0,1);
        q2 = integral(fun1,0,a);
        E(Ridx, Zidx) = (2/(1-exp(-1)))*q1 - 2*(2/(1-exp(-1)))*q2; % electric field
    end
end

I = abs(E).^2; % intensity 

figure(2)
surf(Zvals, Rvals, I, 'edgecolor', 'none')

[Tina Hsiao]

Thanks a lot. It works.

clear all; close all; clc

NA = 0.29;
wL = 772e-3; % micro meter
    
num_Z = 100;
num_R = 100;

Zvals= linspace(-40,40,num_Z);
Rvals = linspace(-5,5,num_R);
    
 for Zidx = 1 : num_Z
     Z = (Zvals(Zidx));
     mu = ((2*pi)/wL).*NA^2.*Z;
     
     for Ridx = 1 : num_R
         R = (Rvals(Ridx));
         ro = ((2*pi)/wL)*NA.*R;
         
         fun1 = @(r)r.* exp(-r.^2) .* besselj(0,ro*r).* exp(-(1.*i.*mu.*r.^2)./2);
         fun2 = @(a)a.* exp(-a.^2) .* besselj(0,ro*a).* exp(-(1.*i.*mu.*a.^2)./2);
         q1 = integral(fun1,0,1);
         q2 = integral(fun2,0,0.62);
        
         E(Ridx, Zidx) = (2/(1-exp(-1))).*q1 - 2*(2/(1-exp(-1))).*q2; % electric field     
    end
 end

phase = atan2(imag(E),real(E));
I = abs(E).^2; % intensity 

figure(2)
surf( Rvals, Zvals, I/max(max(I)), 'edgecolor', 'none')

[Walter Roberson]

Looks good, but what do you do with phase after you calculate it?