Matlab code for beam propagation with variable ,rectangular grid spacing

Hi, I would like to request somebody to help me in the following Matlab problem:

I want to propagate a converging optical beam down its focus. I have started with a 1024 x 1024 number of grid points across the beam ( an uniform circle of white colour inside a background square of black colour------the size of the square is 6.5 mm x 6.5 mm and the diameter of the circle is 4.5 mm). The circular beam will come to a focal spot of 50 micron diameter within a distance of 20 mm. What I want is to propagate the circular beam in a high resolution grid so that the tiny focal spot contains a large number (the most) of grid points and at the same time propagate the background on a coarse grid so that only a few grid points span them. The overall size of the grid will be unchanged ( the white focal spot will be in the middle of a black square of size 6.5 mm x 6.5 mm ). effectively, the grid spacing will go on decreasing as the circle will converge forward and at the same time the grid spacing for the outer background (square) will go on increasing.

I am not sure how to implement this in Matlab. can anybody help me,please. Thanks. regards, sujit