Topological phases of electromagnetic waves in superlattices of negative- and positive- epsilon materials

Recently, a new topological invariant is proposed to classify electromagnetic waves in an isotropic medium with positive or negative permittivity and permeability, and various interface modes such as surface plasmons are interpreted as topological boundary modes [1]. We expect similar topological phases of electromagnetic waves even for metamaterials.
To this end, we consider the electromagnetic waves in a 1D multilayer consisting positive- and negative- epsilon layers, studied in [2]. Depending on the ratio of layer thicknesses and the values of the dielectric constants of the constituent layers, the spectra changes, and the dispersion opens a gap at the origin depending on the spatial average of the dielectric constant. We associate this with a change in the topological number proposed in [1]. In addition, we find that interface states appear at an interface between different topological phases as expected.

[1] K.Y. Bliokh, D. Leykam, M. Lein, F. Nori, Nat. Commun. 10, 580 (2019); [2] A.P. Vinogradov, A.V. Dorofeenko, I.A. Nechepurenko, Metamaterials 4, 181 (2010).