Two-dimensional wave propagation without anomalous dispersion

TL;DR

This paper demonstrates that in a space with two time dimensions, wave shape changes due to dispersion are avoided, enabling new wave control methods in anisotropic metamaterials with negative permittivity.

Contribution

It introduces a theoretical framework showing wave propagation without anomalous dispersion in a two-time-dimensional space, realized via anisotropic metamaterials.

Findings

Wave shape remains stable in two-time-dimensional space.

Metamaterials can simulate multiple time dimensions.

Potential applications in ultrashort pulse shaping.

Abstract

In two space dimensions and one time dimension a wave changes its shape even in the absence of a dispersive medium. However, this anomalous dispersive behavior in empty two-dimensional space does not occur if the wave dynamics is described by a linear homogeneous wave equation in two space dimensions and {\it two} time dimensions. Wave propagation in such a space can be realized in a three-dimensional anisotropic metamaterial in which one of the space dimensions has a negative permittivity and thus serves as an effective second time dimension. These results lead to a fundamental understanding and new approaches to ultrashort pulse shaping in nanostructures and metamaterials.