Wave Propagation in One-Dimensional Time-Modulated Subwavelength Metamaterials
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Date
2025
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Doctoral Thesis
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Abstract
This dissertation investigates the properties of wave propagation through one-dimensional, time-modulated subwavelength metamaterials from a mathematical perspective. These systems are composed of strongly contrasting resonators embedded in a background medium and exhibit rich physical behaviour due to subwavelength resonances and temporal modulation. We assume the material parameters to be periodic in time inside the resonators, which leads to the coupling of different frequency harmonics. Starting from first principles, we formulate the governing equations for time-dependent scattering and analyse the associated quasi-periodic solutions. We derive asymptotic formulas for scattered fields and quasifrequencies in the presence of temporal modulations, providing insight into phenomena such as non-reciprocal scattering and frequency conversion. An effective medium theory is developed to describe the macroscopic behaviour of these media in the subwavelength regime. Furthermore, we establish a generalised energy balance and Optical Theorem, accounting for the coupling between harmonics in time-modulated systems. The analysis culminates in a rigorous characterisation of wave localisation in space–time structured resonator chains. These results lay the groundwork for a deeper theoretical understanding of dynamic metamaterials and open up pathways for applications in wave control, photonic devices and acoustic systems.
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Examiner : Ammari, Habib
Examiner : Davies, Bryn
Examiner : Hiltunen, Erik Orvehed
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ETH Zurich
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Subject
Subwavelength physics, photonics, ODEs, Numerical Analysis
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09504 - Ammari, Habib / Ammari, Habib