Using the grating order transmission monitor, we can plot the far-field Electric field as a function of angle for periodic structures (normal incidence with periodic or bloch boundary conditions with BFAST or nomal plane wave source). eg: https://kb.lumerical.com/en/diffractive_optics_gratings_order_transmission.html. There is always an angle spread for any diffraction lobe. Even the 0th order transmission has some spread in angle space. Ideally, a periodic system shouldnt have any spread but realistic systems which are finite do have a spread. The width ( in angle space) of the lobe decreases if the size of the periodic unit cell is increased but it is independent of the mesh size used with in the periodic cell. Also the angle spread increase as the beam going away from 0degrees which may or maynot increase as a function of wavelength.
I was curious if the way FDTD works has some physical significance. Is there a way to extract just the angle of the diffraction order as a function of wavelength without showing any angle spread.