% A gradient-index lens: no interface at all, just a region where sound
% travels more slowly.
%
% The speed dips smoothly to c0*(1 - dn) at the centre of a Gaussian of width
% `w` metres, so a plane wave crossing it is retarded most in the middle and
% the wavefront curves. The focus lands a little way past the lens and is
% much brighter than anything else on the grid, which is worth remembering
% when reading the colour scale.
%
% This is the case where a sharp-interface scatterer has nothing to say: there
% is no reflection to speak of, only refraction, and the field is smooth
% everywhere. It is also the easiest scene for the solver, since nothing on
% the grid is under-resolved.
function [c, sig] = medium(x, y, L, h, c0, dn, w, x0)
  r2 = ((x - x0).^2 + y.^2) / (w*w);
  c = c0 * (1 - dn * exp(-r2));
  sig = sponge(x, y, L, 0.2*L, 1700);
end