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 Negative index materials: properties and applications

Hoai-Minh Nguyen (EPFL, Switzerland)

Location:  Hill 705
Date & time: Friday, 15 November 2019 at 4:00PM - 5:00PM

Abstract:  Negative-index metamaterials are engineered structures whose refractive index has a negative value over some frequency range. Their existence was postulated by Veselago in 1964 and confirmed experimentally by Shelby, Smith, and Schultz in 2001. Negative-index metamaterial research has been a very active topic of investigation not only because of potentially interesting applications but also because of challenges in understanding their surprising properties. From a mathematical point of view, the subtlety and the challenges in the study of negative-index metamaterials are from the sign-changing coefficients in the modeling equations, hence the ellipticity and the compactness are lost in general. Moreover, localized resonance, i.e., a phenomenon for which the field explodes in some regions and remains bounded in some others as the loss (the damping/viscosity coefficient) goes to 0, might occur. In this talk, I discuss superlensing and cloaking applications of negative-index metamaterials, and the stability of associated fields in the frequency domain. Mathematical ideas/techniques/tools used to analyse these phenomena are mentioned. These involves deriving/analysing Cauchy's problems, applying/establising three-sphere inequalities (with partial data), and introducing the removing localized singularity technique. 

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