A 3D spatial spectral integral equation method for electromagnetic scattering from finite objects in a layered medium

Area of Science:

• Electromagnetics
• Computational Physics
• Applied Mathematics

Background:

• Integral equation methods are crucial for solving electromagnetic scattering problems.
• Existing 2D formulations require extension for complex 3D scenarios.
• Dielectric objects in stratified media present unique computational challenges.

Purpose of the Study:

• To generalize a 2D spatial spectral volume integral equation to a 3D formulation.
• To develop an efficient computational method for electromagnetic scattering from dielectric objects in stratified media.
• To analyze the computational scaling and accuracy of the proposed 3D method.

Main Methods:

• Formulation of a 3D spatial spectral integral equation in the spectral domain using a complex integration manifold.
• Representation of Green function, contrast current density, and scattered electric field.
• Reformulation of field-material interactions in the spatial domain via a normal-vector field approach obeying Li factorization rules.

Main Results:

• The proposed 3D method demonstrates a computational time scaling of $$ with the number of unknowns.
• Numerical results show the method's efficiency and accuracy.
• Comparison with a finite element method (FEM) reference validates the accuracy for three numerical examples.

Conclusions:

• The generalized 3D spatial spectral integral equation provides an efficient and accurate approach for electromagnetic scattering.
• The method's favorable computational scaling makes it suitable for complex scattering problems.
• This formulation advances the capability to simulate electromagnetic wave interactions with dielectric objects in stratified environments.