General finite-difference time-domain solution of an arbitrary electromagnetic source interaction with an arbitrary dielectric surface

摘要

In this study, we develop a numerical algorithm to calculate the interaction of an arbitrary electromagnetic beam with an arbitrary dielectric surface as one of the tools necessary to design and build a detector network based on surface-enhanced Raman scattering (SERS). By using the scattered-field finite-difference time-domain (FDTD) method with incident source terms in the FDTD equations, this development enables an arbitrary incident beam to be implemented onto an arbitrary dielectric surface or particle. Most importantly, in this study a scattered-field uniaxial perfectly matched layer (SF-UPML) absorbing boundary condition (ABC) is developed to truncate the computational domain of the scattered-field FDTD grid. The novel SF-UPML for the scattered-field FDTD algorithm should have a numerical accuracy similar to that of the conventional uniaxial perfectly matched layer for the source-free FDTD equations. Using the new ABC, the scattered-field FDTD method can accurately calculate electromagnetic wave scattering by an arbitrary dielectric surface or particles illuminated by an arbitrary incident beam.