We simulate Mie scattering from a two dimensions dielectric cylinder. Angular scattering results from the FDTD simulation are compared to the analytic solution.
Open and run the simulation file named mie_theory_2d.fsp. The simulation creates the mpeg movie below. The Total-Field Scattered-Field (TFSF) source is used to create a plane wave incident on a dielectric cylinder. Only light scattered by the cylinder propagates beyond the TFSF boundary.
After running the simulation, run the script file named mie_theory_2d.lsf. The script file computes a series of far field projections at 2 wavelengths, and compares the results to the analytic data for scattering from a dielectric cylinder that are stored in the file cylinder.txt. Note that the monitors record 25 wavelengths, but the script in the analysis group selects the monitor data at 1 and 2 microns. The resultant plot (logarithmic scale) is shown below. The analytic and simulated results agree very well at all angles, over more than 5 orders of magnitude.
The script can also calculate the scattering and absorption cross sections. The absorption will be zero, since the cylinder is a composed of a dielectric with no absorption. To calculate the cross sections, edit the script and set the do_cross_sections variable to 1.
H C van de Hulst, "Light Scattering by Small Particles", John Wiley, (1957). The 1981 edition is available through Google Books.