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

Area of Science:

• Electromagnetic theory
• Optical physics
• Computational physics

Background:

• Optical properties of single particles are crucial for understanding light-matter interactions.
• Deriving these properties relies on microphysical inputs like shape and refractive index.
• Accurate calculation of sensitivities to these inputs is essential for inverse problems.

Purpose of the Study:

• To derive analytic expressions for the Jacobians of optical properties with respect to microphysical parameters.
• To validate these derived Jacobians using established methods.
• To analyze the dependencies of these Jacobians on particle characteristics.

Main Methods:

• Invariant Imbedding T-Matrix Method (IITM) for analytic Jacobian derivation.
• Extended Boundary Condition Method (EBCM) for validation.
• Finite-difference estimation for further validation.

Main Results:

• Analytic expressions for optical property Jacobians were successfully derived using IITM.
• IITM-derived Jacobians were validated against EBCM and finite-difference methods for spheroids, cylinders, and hexagonal prisms.
• Dependencies of Jacobians on microphysical parameters were examined.

Conclusions:

• The invariant imbedding T-matrix method provides an effective means to calculate optical property sensitivities.
• Validated Jacobians are essential for accurate retrieval of particle properties from optical measurements.
• This work advances the computational tools for light scattering analysis.