Homogenization of three-dimensional metamaterial objects and validation by a fast surface-integral equation solver

Area of Science:

• Electromagnetics and Materials Science
• Computational Physics

Background:

• Metamaterial objects composed of periodic arrays present challenges in modeling wave interactions.
• Homogenization models offer a simplified approach but require validation for complex structures.

Purpose of the Study:

• To develop and validate a homogenization model for wave interaction with finite 3D metamaterial objects.
• To assess the accuracy of modeling periodic sphere arrays as homogeneous objects.

Main Methods:

• Application of a homogenization model based on a dipolar inclusion model.
• Incorporation of weak spatial dispersion and dynamic array coupling.
• Validation using full-wave numerical simulations with a fast surface-integral equation solver.

Main Results:

• The homogenization model accurately describes wave interaction with metamaterial objects.
• The model holds for densely packed arrays when spatial dispersion and array coupling are considered.
• Simulations show good agreement between large sphere arrays and equivalent homogeneous objects, even near the arrays.

Conclusions:

• The proposed homogenization model provides a reliable method for analyzing wave scattering from finite metamaterial objects.
• The transition from discrete sphere arrays to homogeneous objects is accurately quantified.
• The model's validity extends to large-scale structures, offering computational efficiency.