A non-asymptotic homogenization theory for periodic electromagnetic structures

Area of Science:

• Electromagnetism
• Materials Science
• Computational Physics

Background:

• Electromagnetic periodic composites require accurate modeling for advanced applications.
• Traditional homogenization methods may lack precision, especially near boundaries.
• Understanding material behavior at multiple scales is crucial.

Purpose of the Study:

• To develop a robust homogenization theory for electromagnetic periodic composites.
• To introduce a quantifiable error indicator for homogenization accuracy.
• To enable the definition of position-dependent material parameters.

Main Methods:

• Treating homogenization as a two-scale problem.
• Approximating electromagnetic fields using eigenmodes that satisfy Maxwell's equations and boundary conditions.
• Developing an error indicator to characterize homogenization accuracy.

Main Results:

• A novel homogenization methodology for electromagnetic periodic composites.
• An error indicator that quantifies the accuracy of the homogenization process.
• The ability to define bulk and position-dependent material parameters.

Conclusions:

• The proposed theory provides a more accurate and versatile approach to homogenizing electromagnetic periodic composites.
• The error indicator allows for a clear understanding of the trade-off between accuracy and applicability.
• This method facilitates the design of composites with tailored properties, even near physical boundaries.