A fourth-order symplectic finite-difference time-domain (FDTD) method for light scattering and a 3D Monte Carlo code for radiative transfer in scattering systems

When the finite-difference time-domain (FDTD) method is applied to light scattering computations, the far fields can be obtained by either a volume integration method, or a surface integration method. In the first study, we investigate the errors associated with the two near-to-far field transform methods. For a scatterer with a small refractive index, the surface approach is more accurate than its volume counterpart for computing the phase functions and extinction efficiencies; however, the volume integral approach is more accurate for computing other scattering matrix elements. If a large refractive index is involved, the results computed from the volume integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation of a small refractive index. In my second study, a fourth order symplectic FDTD method is applied to the problem of light scattering by small particles. The total-field/ scattered-field (TF/SF) technique is generalized for providing the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. Numerical examples demonstrate that the fourthorder symplectic FDTD scheme substantially improves the precision of the near field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than the conventional second-order FDTD scheme if the same grid size is used. My third study is on multiple scattering theory. We develop a 3D Monte Carlo code for the solving vector radiative transfer equation, which is the equation governing the radiation field in a multiple scattering medium. The impulse-response relation for a plane-parallel scattering medium is studied using our 3D Monte Carlo code. For a collimated light beam source, the angular radiance distribution has a dark region as the detector moves away from the incident point. The dark region is gradually filled as multiple scattering increases. We have also studied the effects of the finite size of clouds. Extending the finite size of clouds to infinite layers leads to underestimating the reflected radiance in the multiple scattering region, especially for scattering angles around 90 degrees. The results have important applications in the field of remote sensing