How to plot the 2d complex function with amplitude and phase

I have a 2d complex function as follows

psi=sqrt(x^2+y^2)*exp(-(x^2+y^2)/16)*exp(i*atan2(y,x));

How to realize the following figure by using Matlab?

In this image, the color on the ring presents the changes of phase of the function from small to big.

[Paul]

The phase of psi is a function of two variables (x and y). How is "changes of phase" defined? Change wrt x holding y constant (del f / del x)? Change wrt y holding x constant (del f / del y)? Something else?

Answer 1

[Hiro Yoshino]

Run the following code and see if this fits your thought.

meshgrid is a key here.

x=-1:0.01:1;
y=-1:0.01:1;
[X,Y] = meshgrid(x,y);

phi = sqrt(X.^2+Y.^2).*exp(-(X.^2+Y.^2)/16).*exp(1i*atan2(Y,X));
rPhi = real(phi);
iPhi = imag(phi);
phiPhase = angle(phi);
%phiPhaseW = unwrap(phiPhase);

s2 = surf(X,Y,phiPhase,'LineStyle','none');

xlabel('X')
ylabel('Y')
zlabel('phiPhase')
title('X vs. Y vs. phiPhase')