The Open Collections website will be undergoing maintenance on Wednesday December 7th from 9pm to 11pm PST. The site may be temporarily unavailable during this time.

BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

On the Helmholtz equations with sign changing coefficients Nguyen, Hoai-Minh


This talk is devoted to various properties and applica- tions of the Helmholtz equations with sign changing coefficients. These equations are used to model negative index materials which are artifi- cial structures whose refractive index are negative over some frequency range. These materials were first investigated theoretically by Veselago in 1964 and their existence was confirmed experimentally by Shelby et al. in 2001. The study of these equations faces two difficulties. First the ellipticity and the compactness are lost in general due to the changing sign coefficients. Second, the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others as the loss (the viscosity) goes to 0, might occur. In this talk, I will present several remarkable properties of these equations and their applications such as cloaking and superlensing using complementary media and cloaking an object via anomalous localized resonance. Various conditions under which the equations are stable are also presented. Some useful tech- niques dealing with these equations such as reflecting and removing localized singularity techniques are mentioned.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International