I have a quick question (I'll probably be working it out myself as I go). I was looking at the basic scalar wave equation (laplacian(Field) - d^2Field/dt^2 = 0), and I was playing around with different scenarios on a computer sim. (I successfully set up situations for diffraction/reflection).
However, one thing has been bugging me. The acceleration of the field amplitude is proportional to the laplacian. And as long as there is some difference between the amplitude at two points, there should be divergence of the gradient.
So how do you get a collimated beam propogating, such as in light? It seems to me that points to either side of the beam path should themselves be experiencing divergence, oscillating, and spreading the beam.
Is this because I'm currently only looking at a simple scalar wave? (Maxwell's equations sim to come soon....) Could there be, for example, a collimated sound wave?