High-frequency homogenization for checkerboard structures: defect modes, ultrarefraction, and all-angle negative...

Area of Science:

• Physics
• Materials Science
• Optics

Background:

• Photonic crystals exhibit counterintuitive properties like all-angle negative refraction (AANR) and ultrarefraction, linked to anomalous dispersion.
• Conventional homogenization methods fail at high frequencies due to limitations with microstructural length scales relative to wavelength.

Purpose of the Study:

• To explore an asymptotic approach for understanding anomalous dispersion in photonic crystals.
• To apply high-frequency homogenization (HFH) theory to model checkerboard media and predict unique optical phenomena.

Main Methods:

• Developed and applied high-frequency homogenization (HFH) theory to generate macroscale effective partial differential equations.
• Embedded microscale information through averaged quantities within the HFH framework.
• Utilized finite element analysis for numerical illustration on finite-size checkerboard models.

Main Results:

• HFH theory provides analytical predictions for ultrarefraction, localized defect mode decay, and all-angle negative refraction (AANR) frequencies.
• Effective medium with HFH-derived refractive index accurately describes ultrarefraction.
• Demonstrated HFH's capability to model high-frequency phenomena where conventional theories fail.
• Investigated light confinement in finite-size checkerboards acting as open resonators under AANR conditions.

Conclusions:

• High-frequency homogenization (HFH) offers a robust theoretical framework for analyzing complex photonic crystal behaviors.
• HFH enables accurate analytical and numerical predictions of phenomena like AANR and ultrarefraction.
• The study highlights the limitations of conventional methods and the power of HFH for advanced optical applications.