Semi-phenomenological effective permittivity approach to metallic periodic structures

Area of Science:

• Optics and Photonics
• Materials Science
• Electromagnetism

Background:

• The theory of effective permittivity is crucial for understanding periodic structures.
• Existing models have limitations for metal-dielectric structures, particularly when feature sizes approach the metal skin depth in optical frequencies.

Purpose of the Study:

• To develop a corrected theory for effective permittivity in one- and two-dimensional periodic metal-dielectric structures.
• To provide analytical expressions for effective permittivity and reflection coefficients that are more accurate for visible and near-infrared applications.

Main Methods:

• A phenomenological correction to static formulae based on realistic electric field behavior within metal features.
• Derivation of analytical expressions for effective permittivity and reflection coefficients.
• Comparison of analytical results with numerical simulations using the Fourier modal method.

Main Results:

• The proposed phenomenological correction yields analytical formulae for effective permittivity that agree well with numerical results.
• Improved analytical formulae for the reflection coefficient are obtained by considering impedance approximation at boundaries.
• The relationship between averaged field ratios and metamaterial parameters is clarified.

Conclusions:

• The corrected effective permittivity theory is valid for metal-dielectric periodic structures where electric fields are not homogeneous.
• The analytical models offer a more accurate and accessible approach compared to purely numerical methods for certain optical regimes.
• This work enhances the understanding and design of metamaterials and periodic optical structures.