Two-dimensional wave propagation without anomalous dispersion

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.

References in corpus (3)

• Broad-band acoustic hyperbolic metamaterial
• Green function for hyperbolic media
• Generation of unipolar pulses in a circular Raman-active medium excited by few-cycle optical pulses

Cited by in corpus (4)

• Experimental observation of effective gravity and two times physics in ferrofluid-based hyperbolic metamaterials
• Hyperbolic Metamaterials and Massive Klein-Gordon Equation in 2+1 Dimensional de Sitter Spacetime
• Anomalous Dispersion in Gravity Theories
• Wake-Tail Effects in Two-Dimensional Wave Refocusing