Hyperbolic Plasmons Propagate through a Nodal Metal

Metals are canonical plasmonic media at infrared and optical wavelengths allowing one to guide and manipulate light at sub-diffractional length scales. A special form of optical waveguiding is offered by highly anisotropic crystals revealing different signs of the dielectric function along orthogonal directions. These latter types of media are classified as hyperbolic and many crystalline insulators, semiconductors and artificial metal-based metamaterials belong to that class. Layered anisotropic metals are also anticipated to support hyperbolic waveguiding. Yet this behavior remains elusive primarily because interband processes introduce extreme losses and arrest light propagation. Here, we report on the observation of propagating hyperbolic waves in a prototypical layered nodal-line semimetal ZrSiSe. The unique electronic structure with touching energy bands at nodal points/lines suppresses losses and enables a hyperbolic regime at the telecommunications frequencies. The observed waveguiding in metallic ZrSiSe is a product of polaritonic hybridization between near-infrared light and long-lived nodal-line plasmons. By mapping the energy-momentum dispersion of the nodal-line hyperbolic modes in ZrSiSe we inquired into the role of additional screening associated with the surface states.

Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

ASYMPTOTIC METHOD FOR APPROXIMATION OF RESONANT INTERACTION OF NONLINEAR MULTIDIMENSIONAL HYPERBOLIC WAVES

A method of averaging along characteristics of weakly nonlinear hyperbolic systems, which was presented in earlier works of the author for one dimensional waves, is generalized for some cases of multidimensional wave problems. In this work we consider such systems and discuss a way to use the internal averaging along characteristics for new problems of asymptotical integration.