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Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave

J Flores Méndez^1,2, A C Piñón Reyes¹, M Moreno Moreno³

¹Departamento de Ingeniería, Benemérita Universidad Autónoma de Puebla-Ciudad Universitaria, Blvd. Valsequillo y Esquina, Av. San Claudio s/n, Col. San Manuel, C.P. 72570 Puebla, Pue, Mexico.

Materials (Basel, Switzerland)

|March 28, 2020

Summary

This study proposes a new homogenization theory for photonic crystals, extending beyond long wavelengths. It provides simplified effective tensors for 1D photonic crystals, useful for designing metamaterials.

Area of Science:

Condensed Matter Physics
Electromagnetism
Materials Science

Background:

Homogenization theories typically apply to long wavelengths, limiting their use for phenomena near the Brillouin zone edge.
Understanding effective electromagnetic properties of periodic structures is crucial for designing advanced optical materials.

Purpose of the Study:

To develop a homogenization theory valid for wavelengths approaching the Brillouin zone edge.
To derive explicit expressions for effective bianisotropic response tensors in photonic crystals.
To analyze the behavior of effective tensors in 1D photonic crystals with magnetic inclusions.

Main Methods:

Applying homogenization theory to Maxwell's equations for periodic media.
Utilizing Fourier formalism to derive explicit expressions for effective tensors.
Numerical calculations to analyze the dependence of effective tensors on inclusion filling fraction.

Main Results:

Explicit expressions for effective permittivity, permeability, and crossed magneto-electric tensors were obtained for photonic crystals.
Simplified expressions were derived for 1D photonic crystals, including cases with magnetic inclusions.
Numerical analysis revealed the dependence of effective tensors on the filling fraction of magnetic inclusions.

Conclusions:

The proposed theory extends homogenization beyond the long-wavelength limit.
The derived formulas are useful for designing anisotropic optical metamaterials.
Results show good agreement with Rytov's effective medium approach.

Keywords:

effective parameters homogenization theory metamaterial photonic crystal

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Erratum: Flores, J., et al. Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory. Materials 2020, 13, 1475.

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