Applications of Maxwell's equations to light scattering by dielectric particles

In this chapter, we illustrate how Maxwell's equations can be used to compute the optical properties of dielectric particles. We first demonstrate an example of a straightforward application of Maxwell's equations for the solutions of the single-scattering properties of a dielectric particle, known as the finite-difference time-domain (FDTD) method. We also review the efficacy of electromagnetic volume or surface integral derived from Maxwell's equations, which can be used to compute the scattered electric fields in the radiation zone (i.e., far field) if the electric field inside a particle or the electric and magnetic field on a surface enclosing the particle is known. The extended boundary condition method (EBCM) based on electromagnetic surface integral equations and the invariant imbedding T-matrix method (IITM) derived from an electromagnetic volume integral equation can be used to compute the T-matrix of a scattering particle, which contains all the information about the single-scattering properties of the scattering particle. A synergistic combination of IITM and the physical geometric-optics method (PGOM) provides a practical approach for computing aerosol scattering properties for the size parameter region of practical interest in atmospheric radiation. Moreover, we briefly demonstrate the importance of accounting for the nonsphericity of particles in atmospheric remote sensing.