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Polyadic Cantor superlattices with variable lacunarity
Optics Letters
|February 1, 1997
Summary
This study analyzes wave reflection and transmission in fractal superlattices, introducing lacunarity as a key factor. Novel computational methods efficiently model these complex structures for the first time.
Area of Science:
- Condensed matter physics
- Materials science
- Wave phenomena
Background:
- Fractal superlattices exhibit unique wave interaction properties.
- Understanding these properties is crucial for advanced material design.
- Previous studies have not fully explored the impact of structural disorder.
Purpose of the Study:
- To formulate and analytically solve the reflection and transmission properties of polyadic fractal superlattices.
- To characterize these properties concerning stage of growth, fractal dimension, and lacunarity.
- To introduce and investigate the effect of lacunarity on wave interactions with fractal structures.
Main Methods:
- Analytical formulation and solution of wave propagation.
- Characterization using parameters like stage of growth, fractal dimension, and lacunarity.
- Development of a novel doubly recursive computational technique.
Main Results:
- Reflection and transmission coefficients were derived for fractal superlattices.
- The study presents twist plots summarizing reflection data.
- The impact of lacunarity on wave interactions was quantified for the first time.
Conclusions:
- Lacunarity significantly influences wave reflection and transmission in fractal superlattices.
- The developed computational technique efficiently models complex Cantor superlattices.
- This research provides a new framework for understanding wave phenomena in disordered fractal materials.
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