Scattering matrix of arbitrarily shaped objects: combining finite elements and vector partial waves.

Area of Science:

• Computational electromagnetics
• Electromagnetic scattering theory
• Numerical methods for wave phenomena

Background:

• Characterizing electromagnetic scattering is crucial for understanding light-matter interactions.
• Existing methods like T-matrix and Mie theory have limitations for complex geometries.
• Finite element methods offer detailed solutions but integrating them with scattering formalisms is challenging.

Purpose of the Study:

• To introduce and validate a hybrid numerical approach combining finite element calculations with vector partial wave formulation.
• To accurately determine the T-matrix elements and scattering matrix of individual scatterers.
• To provide an accessible, open-source tool for electromagnetic scattering analysis.

Main Methods:

• Employing finite element calculations (FEC) to model individual scatterers.
• Utilizing the vector partial wave (VPW) formulation to generate incident waves.
• Numerically calculating T-matrix elements by feeding VPW solutions into the FEC problem.
• Deriving recurrence relations for efficient VPW computation.

Main Results:

• Demonstrated high accuracy in determining the scattering matrix for spherical and spheroidal scatterers.
• Successfully integrated FEC with VPW formulation for accurate electromagnetic scattering characterization.
• Developed and provided an open-source code for reproducing the numerical results.

Conclusions:

• The hybrid FEC-VPW method is a powerful and accurate technique for characterizing electromagnetic scattering of individual particles.
• The explicit recurrence relations enhance computational efficiency.
• The open-source code facilitates further research and application in the field.