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arXiv · 1612.08718

Two-dimensional wave propagation without anomalous dispersion

Carl M. Bender·Francisco J. Rodriguez·Sarben Sarkar·Anatoly V. Zayats
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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.

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Carl M. Bender, Francisco J. Rodriguez, Sarben Sarkar, Anatoly V. Zayats. 2016-12-27. Two-dimensional wave propagation without anomalous dispersion. https://doi.org/10.1103/physrevlett.119.114301

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