Proceedings Article | 1 May 2012
KEYWORDS: Metamaterials, Maxwell's equations, Electromagnetism, Dielectrics, Free space optics, Frequency conversion, Geometrical optics, Electromagnetic radiation, Electroluminescent displays, 3D modeling
Based on the analogy between the Maxwell equations in complex metamaterials and the free-space Maxwell
equations on the background of an arbitrary metric, transformation optics allows for the design of metamaterial
devices using a geometrical perspective. This intuitive geometrical approach has already generated various novel
applications within the elds of invisibility cloaking, electromagnetic beam manipulation, optical information
storage, and imaging. Nevertheless, the framework of transformation optics is not limited to three-dimensional
transformations and can be extended to four-dimensional metrics, which allow for the implementation of metrics
that occur in general relativistic or cosmological models. This enables, for example, the implementation of black
hole phenomena and space-time cloaks inside dielectrics with exotic material parameters. In this contribution,
we present a time-dependent metamaterial device that mimics the cosmological redshift. Theoretically, the
transformation-optical analogy requires an innite medium with a permittivity and a permeability that vary
monotonically as a function of time. We demonstrate that the cosmological frequency shift can also be reproduced
in more realistic devices, considering the fact that practical devices have a nite extent and bound material
parameters. Indeed, our recent numerical results indicate that it is possible to alter the frequency of optical
pulses in a medium with solely a modulated permittivity. Furthermore, it is shown that the overall frequency
shift does not depend on the actual variation of the permittivity. The performance of a nite frequency converter
is, for example, not aected by introducing the saw tooth evolution of the material parameters. Finally, we studied
the eect of the introduction of realistic metamaterial losses and, surprisingly, we found a very high robustness
with respect to this parameter. These results open up the possibility to fabricate this frequency converting device
with currently available metamaterials [V. Ginis, P. Tassin, B. Craps, and I. Veretennico, Opt. Express 18,
5350{5355 (2010)1].
