Non-Reciprocal and Topological Wave Phenomena at the Sub-Wavelength Scale

The utilization of subwavelength resonators, such as small electric dipoles, plasmonic resonators, or objects made of materials with a high dielectric constant, has enabled the manipulation of electromagnetic fields down to the subwavelength regime with synthetic electromagnetic materials built from dense arrangements of such resonant inclusions [1]. Guiding [2] and focusing [3] of electromagnetic energy at the deep subwavelength scale has been demonstrated for electromagnetic waves in metamaterials, by exploiting a combination of two physical effects: multiple scattering and Fano interferences. These two effects together lead to interesting, strongly spatially dispersive effects in deeply subwavelength volumes, for instance negative refraction [4]. In this talk, we will discuss the possibility to extend the reach of subwavelength wave phenomena to include two interesting phenomena: (i) non-reciprocal behavior and (ii) topological effects. In terms of subwavelength non-reciprocity, we will see that by breaking time-reversal symmetry in locally-resonant metamaterials, it is possible to induce large non-reciprocal behavior between two points separated by a deep subwavelength distance, which may result in new possibilities to control backscattering in ultracompact electromagnetic systems. We will then focus on demonstrating several examples in which subwavelength spatial dispersion directly controls the topology of a system, and will discuss how to induce topological phase transitions to build subwavelength topological insulators supporting subwavelength symmetry-protected edges or corner states [5,6]. 1. K. N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2006. 2. F. Lemoult, N. Kaina, M. Fink, and G. Lerosey, “Wave propagation control at the deep subwavelength scale in metamaterials,” Nat. Phys., vol. 9, no. 1, pp. 55–60, 2013. 3. N. Kaina, F. Lemoult, M. Fink, and G. Lerosey, “Ultra small mode volume defect cavities in spatially ordered and disordered metamaterials,” Appl. Phys. Lett., vol. 102, no. 14, 2013. 4. N. Kaina, F. Lemoult, M. Fink, and G. Lerosey, “Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials,” Nature, vol. 525, pp. 77-81, 2015. 5. L.-H. Wu and X. Hu, “Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material,” Phys. Rev. Lett., vol. 114, no. 22, p. 223901, 2015. 6. S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun., vol. 8, no. May, p. 16023, 2017.