Mie scattering by an anisotropic object. Part II. Arbitrary-shaped object: differential theory

Area of Science:

• Electromagnetism
• Computational Physics
• Materials Science

Background:

• Electromagnetic diffraction is crucial for understanding wave interactions with matter.
• Anisotropic materials present unique challenges due to their directional electromagnetic properties.
• Existing diffraction theories often struggle with arbitrary shapes and anisotropic properties.

Purpose of the Study:

• To develop a comprehensive differential theory for electromagnetic diffraction.
• To handle arbitrary-shaped bodies and anisotropic materials.
• To provide a robust numerical method for solving complex diffraction problems.

Main Methods:

• Expansion of electromagnetic fields using vector spherical harmonics.
• Reduction of Maxwell's equations in spherical coordinates to a first-order differential set.
• Application of fast numerical factorization for permittivity discontinuities.
• Utilizing a shooting method combined with the S-matrix propagation algorithm for boundary-value problems.

Main Results:

• A novel differential theory for diffraction by arbitrary anisotropic bodies is established.
• The method effectively links electric field and electric induction vectors.
• The diffraction problem is successfully reduced to a solvable boundary-value problem.
• The S-matrix propagation algorithm is formulated using field components.

Conclusions:

• The developed theory offers a powerful tool for analyzing electromagnetic diffraction.
• The numerical approach provides accurate solutions for complex scattering scenarios.
• This work advances the understanding of wave phenomena in anisotropic media.