In recent years, there has been considerable interest in the study of wave propagation in
nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led …

The goal of this paper is to advance the development of wave-guiding subwavelength
crystals by developing designs whose properties are stable with respect to imperfections in …

We survey functional analytic methods for studying subwavelength resonator systems. In
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …

We study energy propagation along line-defects (edges) in two dimensional continuous,
energy preserving periodic media. The unperturbed medium (bulk) is modeled by a …

The bulk-edge correspondence predicts that interfaces between topological insulators
support robust currents. We prove this principle for PDEs that are periodic away from an …

The aim of this paper is to provide a mathematical theory for understanding the mechanism
behind the double-negative refractive index phenomenon in bubbly fluids. The design of …

We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We
compute the bulk index of Bloch eigenbundles: it equals 2 or–2, with sign depending on …

We present the mathematical theory of one-dimensional infinitely periodic chains of
subwavelength resonators. We analyze both Hermitian and non-Hermitian systems …

Robustly manipulating waves on subwavelength scales can be achieved by, first, designing
a structure with a subwavelength band gap and, second, introducing a defect so that …

When sources of energy gain and loss are introduced to a wave scattering system, the
underlying mathematical formulation will be non-Hermitian. This paves the way for the …