Plotting Bessel function in MATLAB

Question

In MATLAB how do you plot

f(r) = { 2*J1(a*r) / r }^2

where a = 2*pi and J1 is Bessel function of the 1st kind and r = sqrt(x^2 + y^2)

This should plot in 3D, i.e. kind of be like a bubble (not sure how to do this)

Answer 1

Use besselj --- the Bessel function of first kind --- to generate J1. I suppose you have to vary a and r to generate the "bubble".

I generated the following by varying x and y from -1:0.01:1 and plotting meshing points (x,y,f), I don't know if this is what you want.

Code

a = 2*pi;
[X Y] = meshgrid(-1:0.01:1,-1:0.01:1);
R = sqrt(X.^2+Y.^2);
f = (2*besselj(1,a*R(:))./R(:)).^2;
mesh(X,Y,reshape(f,size(X)));
axis vis3d;

Log plot

Doresdoom suggestion, I replaced axis vis3d; with set(gca,'Zscale','Log').

alt text

Mesh

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• Doresoom: use set(gca,'Zscale','Log') instead of axis vis3d to get the 'bubble' effect
• duffymo: +1 - really nice job here. Worth an upvote just for the asthetic quality of the contour plots.
• Jacob: @duffymo: Yeah they are beautiful, but it's all thanks to MATLAB :)
• duffymo: @Jacob - last time I checked, MATLAB didn't run itself. Still requires a smart, motivated person to tell it what to do.
• user333204: Thanks. Is there a way to make the little oscillations at the base more pronounced? When I do it it looks basically flat when I graph. Also, how do you make the graph look different, for example plot it so that it is uniformly green or something or alternatively so you just see the gridlines?