Mathematical Theories for Metamaterials

Habib Ammari, ETH Zurich, Switzerland, Bryn Davies, University of Warwick, Coventry, United Kingdom, and Erik Orvehed Hiltunen, University of Oslo, Norway

Part 1. Finite systems of subwavelength resonators; Subwavelength resonances; Exceptional points in non-Hermitian systems of subwavelength resonators; Effective medium theory for finite systems of weakly interacting subwavelength resonators; Part 2. Periodic systems of subwavelength resonators; Hermitian systems of subwavelength resonators; Non-Hermitian systems of subwavelength resonators; Part 3. Convergence results for large finite systems of subwavelength resonators; Spectral convergence of defect modes; Convergence to the essential spectrum and band structure; Concluding remarks and open problems; Appendix A. Some basic results; Appendix B. Layer potential techniques; Appendix C. Some technical results and proofs; Bibliography; Index