**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# Approximate Cloaking via Transformation Optics for Electromagnetic Waves

Abstract

Cloaking via transformation optics was introduced by Pendry, Schurig, and Smith for the Maxwell system and Leonhardt in the geometric optics setting. They used a singular change of variables which blows up a point into a cloaked region. The same transformation had been used by Greenleaf, Lassas, and Uhlmann in an inverse context. This singular structure implies difficulties not only in practice but also in analysis. To avoid using the singular structure, regularized schemes have been proposed. One of them was suggested by Kohn, Shen, Vogelius, and Weinstein for which they used a transformation which blows up a small ball instead of a point into the cloaked region. In this thesis, we study the approximate cloaking via transformation optics for electromagnetic waves in both the time harmonic regime and time regime. In the time-harmonic regime, the cloaking device only consists of a layer constructed by the mapping technique, no (damping) lossy-layer is required. Due to the fact that nolossy layer is required, resonance might appear. The analysis is therefore delicate and the phenomena are complex. In particular, we show that the energy can blow up inside the cloaked region in the resonant case and/whereas cloaking is achieved in both non-resonant and resonant cases. Moreover, the degree of visibility depends on the compatibility of the source inside the cloaked region and the system. These facts are new and distinct from known mathematical results in the literature. In the time regime, the cloaking device also consists of a fixed lossy layer. Our approach is based on estimates on the degree of visibility in the frequency domain for all frequency in which the frequency dependence is explicit. The difficulty and the novelty in the analysis are in the low and high frequency regimes. To this end, we implement the variational technique in low frequency and the multiplier and duality techniques in high frequency domain. The first part of the thesis is inspired by the work of Nguyen and the second part by the work of Nguyen and Vogelius on the wave equation.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related MOOCs (32)

Related concepts (45)

Related publications (57)

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Applications

Learn about plasma applications from nuclear fusion powering the sun, to making integrated circuits, to generating electricity.

Resonance

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system.

Frequency domain

In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal.

Academic degree

An academic degree is a qualification awarded to a student upon successful completion of a course of study in higher education, usually at a college or university. These institutions often offer degrees at various levels, usually divided into undergraduate and postgraduate degrees. The most common undergraduate degree is the bachelor's degree, although some educational systems offer lower level undergraduate degrees such as associate and foundation degrees. Common postgraduate degrees include master's degrees and doctorates.

Laurent Villard, Stephan Brunner, Alberto Bottino, Moahan Murugappan

We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

Karim Achouri, Jean-Yves Duboz

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...

The technique referred as ray approximation treats wave propagation in a heterogeneous medium at the infinitely small wavelength limit. This classic simplification allows useful approximate analytical results to be obtained in cases where complete descript ...

2022