Effect of eigenmodes on the optical transmission through one-dimensional random media

Area of Science:

• Condensed matter physics
• Optics
• Wave phenomena

Background:

• Photonic crystals exhibit unique wave propagation properties.
• Understanding transitions to disordered media is crucial for material science.
• The Kronig-Penney model is a foundational concept for periodic potentials.

Purpose of the Study:

• To investigate the transition from finite photonic crystals to random dielectric media.
• To assess the applicability of the Kronig-Penney model for finite-sized crystals.
• To analyze the spatial characteristics of eigenmodes in increasingly irregular photonic structures.

Main Methods:

• Employing the transfer matrix method.
• Utilizing numerical solutions to the one-dimensional wave equation derived from Maxwell's equations.

Main Results:

• The study examines the validity of the Kronig-Penney model in finite systems.
• Analysis of eigenmode spatial structure reveals changes with increasing irregularity.
• Characterization of the transition dynamics between ordered and disordered dielectric media.

Conclusions:

• The Kronig-Penney model's validity is evaluated for finite photonic crystals.
• The spatial structure of eigenmodes provides insight into the transition to randomness.
• This research contributes to understanding wave behavior in structured and disordered dielectric materials.