Optical pulse frequency conversion inside transformation-optical metamaterials

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 fields 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 infinite 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 finite 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 finite frequency converter is, for example, not affected by introducing the saw tooth evolution of the material parameters. Finally, we studied the effect 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