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2024 | Book

Introduction and Preliminaries Read chapter Read first chapter

Spectral Theory of Localized Resonances and Applications

Authors: Youjun Deng, Hongyu Liu

Publisher: Springer Nature Singapore

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book is devoted to the spectral theory of localized resonances including surface plasmon/polariton resonances, atypical resonances, anomalous localized resonances and interior transmission resonances. Those resonance phenomena arise in different physical contexts, but share similar features. They form the fundamental basis for many cutting-edge technologies and applications including invisibility cloaking and super-resolution imaging. The book presents a systematic and comprehensive treatment on these resonance phenomena and the associated applications in a unified manner from a mathematical and spectral perspective, covering acoustic, electromagnetic and elastic wave scattering.
The book can serve as a handy reference book for researchers in this field and it can also serve as a textbook or an inspiring source for postgraduate students who are interested in entering this field.

Table of Contents

Frontmatter
Chapter 1. Introduction and Preliminaries
Abstract
Surface plasmon resonance is the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material stimulated by incident light. It is a type of surface wave, guided along the interface in much the same way that light can be guided by an optical fiber. Similar resonance phenomenon occurs at the interface of negative and positive elastic materials and is referred to as the surface polariton resonance.
Youjun Deng, Hongyu Liu
Chapter 2. Mathematical Theory of Plasmon/Polariton Resonances in Quasi-Static Regime
Abstract
In this chapter, we consider the surface plasmon resonance for electro-magnetic scattering governed by the Maxwell system and the surface polariton resonance for elastic scattering governed by the Lamé system. As mentioned earlier, we consider the two resonance phenomena in the quasi-static regime, i.e. the size of the metamaterial structures are smaller than the operating wavelength.
Youjun Deng, Hongyu Liu
Chapter 3. Anomalous Localized Resonances and Their Cloaking Effect
Abstract
In this chapter, we present the spectral analysis of anomalous localized resonances (ALRs) in elastostatics and electrostatics.
Youjun Deng, Hongyu Liu
Chapter 4. Localized Resonances for Anisotropic Geometry
Abstract
In Chaps. 2 and 3, we consider localized resonances associated with nanoparticles. In this chapter, we consider plasmon resonances associated with nanorods. Nanorods possess high aspect ratios and present an anisotropic geometric setup. We shall follow the treatment in [59, 65]. The results in this chapter provides a quantitative understanding of the curvature effect of the material structure on the localized resonance.
Youjun Deng, Hongyu Liu
Chapter 5. Localized Resonances Beyond the Quasi-Static Approximation
Abstract
Based on the results in Chaps. 2–4, it is natural to consider the plasmon and polariton resonances beyond the quasi-static approximation. This can be obtained via considering the spectral properties of the layer potential operators introduced in the previous chapters with frequencies attached to integral kernels. This makes the spectral analysis much radically more challenging. In fact, the relevant layer potential operators are no longer self-adjoint in any function space and many classical spectral tools, say e.g. diagonalization, do not apply. Nevertheless, one still can manage to establish the resonance conditions which couple the geometric and medium parameters of the material structure as well as the frequency in a highly intricate and delicate manner. It turns out that the resonant fields possess distinct properties with some of them similar to the quasi-static resonances and some different.
Youjun Deng, Hongyu Liu
Chapter 6. Interior Transmission Resonance
Abstract
In this chapter, we consider the interior transmission eigenvalue problem. Our focus is on justifying that the transmission eigenfunctions form a certain interior resonant modes. In fact, the results in this chapter show that the transmission eigenfunctions generically oscillate at frequencies much higher than the operating frequency, which is a typical resonance behaviour. Moreover, the high oscillation tend to localize on the boundary of the underlying the domain.
Youjun Deng, Hongyu Liu
Backmatter
Metadata
Title
Spectral Theory of Localized Resonances and Applications
Authors
Youjun Deng
Hongyu Liu
Copyright Year
2024
Publisher
Springer Nature Singapore
Electronic ISBN
978-981-9962-44-0
Print ISBN
978-981-9962-43-3
DOI
https://doi.org/10.1007/978-981-99-6244-0

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