Two-dimensional wave propagation without anomalous dispersion
  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. 
Carl M. Bender, Francisco J. Rodriguez, Sarben Sarkar and Anatoly V.   Zayats
cond-mat.mes-hall physics.class-ph