Analytical Jacobians of single scattering optical properties using the invariant imbedding T-matrix method

Abstract

Integrated and differential optical properties of a single particle, such as the scattering, absorption, and extinction cross sections, single scattering albedo, asymmetry factor, and scattering phase matrix, are derived from electromagnetic scattering theory. This process depends on microphysical inputs which include particle shape, refractive index, aspect ratio, and size parameter. In this work, we use the invariant imbedding T-matrix method (IITM) to derive analytic expressions for Jacobians of these optical properties with respect to the input parameters. These IITM-derived Jacobians for spheroids, cylinders, and hexagonal prisms are validated by comparison with results calculated with the extended boundary condition method (EBCM) and further validated using finite-difference estimates. We examine the dependencies of these Jacobians as functions of the input microphysical parameters, focusing again on spheroids, cylinders, and hexagonal prisms.