Frequency conversion by exploiting time in transformation optics

The fundamental framework of transformation optics describes how coordinate transformations on electromagnetic fields can be physically realized through complex material parameters. This approach includes the possibility of transforming time as well as space, but the applications of such transformations remain relatively unexplored. Here we analyze the material properties and wave effects of a one-dimensional spatially varying time transformation. This transformation results in relatively simple electromagnetic material parameters defined by isotropic dielectric constants with a time-varying magnetoelectric coupling constant. We show that the resulting wave and field behavior in this medium is what is expected from the transformation, namely that an input frequency is scaled to a new and arbitrary output frequency defined by the overall magnitude of the time transformation. While the parameters required to realize such a medium are complex, we describe how the needed time-varying magnetoelectric coupling is feasible using an externally tunable electromagnetic metamaterials approach.