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

摘要

When the finite-difference time-domain (FDTD) method is applied to light scatteringcomputations, 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 associatedwith the two near-to-far field transform methods. For a scatterer with a smallrefractive index, the surface approach is more accurate than its volume counterpartfor computing the phase functions and extinction efficiencies; however, the volumeintegral approach is more accurate for computing other scattering matrix elements. Ifa large refractive index is involved, the results computed from the volume integrationmethod become less accurate, whereas the surface method still retains the same orderof accuracy as in the situation of a small refractive index.In my second study, a fourth order symplectic FDTD method is applied to theproblem 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 symplecticFDTD (SFDTD) scheme. Numerical examples demonstrate that the fourthordersymplectic FDTD scheme substantially improves the precision of the near fieldcalculation. The major shortcoming of the fourth-order SFDTD scheme is that itrequires 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 Carlocode for the solving vector radiative transfer equation, which is the equation governingthe radiation field in a multiple scattering medium. The impulse-response relation fora plane-parallel scattering medium is studied using our 3D Monte Carlo code. For acollimated light beam source, the angular radiance distribution has a dark region asthe detector moves away from the incident point. The dark region is gradually filledas multiple scattering increases. We have also studied the effects of the finite size ofclouds. Extending the finite size of clouds to infinite layers leads to underestimatingthe reflected radiance in the multiple scattering region, especially for scattering anglesaround 90 degrees. The results have important applications in the field of remote sensing.