If you have a photon travelling along the x-axis at (x,0,0) , with its E field along the y-axis at y=0, wouldn't the E field at z=±dz have to be contiunous with the photon's perturbation of the E field, thus giving a photon a finite width?

If this is true, is this basically why diffraction happens? And what shape does the E-field take along z? an exponential decay?
If this is false because the E field is like a delta function, where does diffraction come from?!