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An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces
T Antonakakis1, R V Craster2, S Guenneau3
1Department of Mathematics , Imperial College London , London SW7 2AZ, UK ; European Organization for Nuclear Research, CERN 1211, Geneva 23, Switzerland.
Proceedings. Mathematical, Physical, and Engineering Sciences
|January 9, 2014
Summary
A new surface equation models microstructured surfaces, accurately describing Rayleigh-Bloch waves and similar phenomena. This model extends to gratings and explains localized defect states in varied structures.
Area of Science:
- Physics
- Materials Science
- Surface Science
Background:
- Microstructured surfaces exhibit unique wave phenomena, such as Rayleigh-Bloch waves.
- Existing models may not fully capture the behavior of waves on complex microstructures.
Purpose of the Study:
- To develop an effective surface equation for modeling microstructured surfaces.
- To accurately reproduce and explain wave phenomena like Rayleigh-Bloch waves.
Main Methods:
- Derivation of an effective surface equation.
- Analysis of wave propagation on periodic and non-periodic microstructures.
- Comparison with numerical simulations.
Main Results:
- The derived equations accurately model Rayleigh-Bloch waves and spoof surface plasmon polaritons.
- The theory successfully extends to wave propagation along gratings.
- Localized defect states emerge in non-periodic structures and are explained by the theory.
Conclusions:
- The developed surface equation provides an effective tool for understanding microstructured surfaces.
- The model offers insights into wave phenomena in both periodic and non-periodic systems.
- This work advances the study of surface waves in engineered materials.
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