Abstract: Our goal is to advance the development of wave-guiding subwavelength crystals (i.e. high-contrast metamaterials) by developing designs whose properties are stable with respect to geometric imperfections. Using layer-potential formulations and asymptotic techniques, we have studied the topological properties of chains of resonator dimers and seen that stable edge modes exist at the interfaces of topological indices. We will also examine more recent work which builds on this by proving results which describe how edge mode frequencies cross the subwavelength band gap when dislocations are introduced to the initial periodic array. We study infinite chains of resonators, using the method of fictitious sources, and conduct a stability analysis through numerical experiments on the corresponding truncated finite structure. This approach gives an intuitive insight into the mechanisms that underpin the existence of robust localized edge modes in topological crystals and reveals an analytic way to fine tune their properties.
Dr Bryn Davies is a Research Associate in the Department of Mathematics at Imperial College London. His research concerns the analysis of wave propagation in complex media. He uses integral methods and asymptotic techniques to study problems from the fields of topological insulators, subwavelength waveguides, enhanced sensing and bio-inspired metamaterials. The talk will discuss results developed in collaboration with Habib Ammari, Erik Orvehed Hiltunen and Sanghyeon Yu.
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