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| Negative Index Materials and Their Applications: Recent Mathematics Progress |
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Citation： |
Hoai-Minh NGUYEN.Negative Index Materials and Their Applications: Recent Mathematics Progress[J].Chinese Annals of Mathematics B,2017,38(2):601~628 |
| Page view： 614
Net amount： 699 |
Authors： |
Hoai-Minh NGUYEN; |
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| Abstract： |
Negative index materials are artificial structures whose refractive
index has negative value over some frequency range. These materials
were first investigated theoretically by Veselago in 1946 and were
confirmed experimentally by Shelby, Smith, and Schultz in 2001.
Mathematically, the study of negative index materials faces two
difficulties. Firstly, the equations describing the phenomenon have
sign changing coefficients, hence the ellipticity and the
compactness are lost in general. Secondly, the localized resonance,
i.e., the field explodes in some regions and remains bounded in some
others as the loss goes to 0, might appear. In this survey, the
author discusses recent mathematics progress in understanding
properties of negative index materials and their applications. The
topics are reflecting complementary media, superlensing and
cloaking by using complementary media, cloaking a source via
anomalous localized resonance, the limiting absorption principle and
the well-posedness of the Helmholtz equation with sign changing
coefficients. |
Keywords： |
Negative index materials, Localized resonance, Cloaking,Superlensing |
Classification： |
35B34, 35B35, 35B40, 35J05, 78A25 |
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