Negative Index Materials: Some Mathematical Perspectives
- 2 Downloads
Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.
KeywordsSuperlensing Cloaking Finite speed propagation Complementary media Negative index metamaterials.
Mathematics Subject Classification (2010)35B34 35B35 35J05 35Q60.
This paper is an extended version of the lecture given by the author at VIASM annual meeting in 2017 at Vietnam Institute for Advanced Study in Mathematics. The author warmly thanks the institute for the hospitality.
- 12.Evans, L.C.: Partial Differential Equations Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (1998)Google Scholar
- 29.Nguyen, H.-M.: Superlensing using complementary media and reflecting complementary media for electromagnetic waves. Adv. Nonlinear Anal. to appear, https://doi.org/10.1515/anona-2017-0146
- 30.Nguyen, H.-M.: Cloaking via anomalous localized resonance for doubly complementary media in the finite frequency regime. J. Anal. Math. to appear, arXiv:https://arxiv.org/abs/1511.08053
- 31.Nguyen, H.-M.: Cloaking using complementary media for electromagnetic waves. ESAIM Control Optim. Calc. Var., to appear, https://doi.org/10.1051/cocv/2017078
- 34.Nguyen, H.-M., Vinoles, V.: Electromagnetic wave propagation in dispersive metamaterials. submitted, arXiv:https://arxiv.org/abs/1710.08648