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Updated: Dec 8, 2025
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
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Random Möbius maps: Distribution of reflection in non-Hermitian one-dimensional disordered systems.
Theodoros G Tsironis1, Aris L Moustakas1
1Department of Physics, National Kapodistrian University of Athens, Athens 15784, Greece.
Physical Review. E
|September 18, 2020
Summary
This study analyzes wave reflection in random materials, finding conditions for perfect absorption and characterizing wave penetration using random Möbius transformations.
Area of Science:
- Wave physics
- Statistical mechanics
- Condensed matter theory
Background:
- Understanding wave propagation in disordered media is crucial for various applications.
- Random chains of scatterers present complex behaviors that are challenging to model.
- The reflection coefficient and absorption properties are key parameters in characterizing wave-matter interactions.
Purpose of the Study:
- To investigate the statistical properties of the reflection coefficient in random chains of lossy scatterers.
- To determine the conditions for coherent perfect absorption.
- To analyze wave penetration depth and the nature of the reflection coefficient's distribution tails.
Main Methods:
- Utilizing properties of random Möbius transformations to model the system.
- Explicitly determining the support of the reflection coefficient's distribution.
- Calculating the Lyapunov exponent to quantify wave penetration.
Main Results:
- The study explicitly determines the support of the reflection coefficient's distribution.
- Conditions for coherent perfect absorption are established.
- Lifshits-like tails at the distribution boundaries are identified and evaluated.
- The Lyapunov exponent provides the extent of wave penetration into the medium.
Conclusions:
- The research provides a theoretical framework for understanding wave phenomena in disordered, lossy media.
- The findings offer insights into coherent perfect absorption and wave penetration.
- Results are validated through comparison with numerical simulations.
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