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