Two cases of spatial transformations

Here, we give an overview of our work on two topics related to the theme of spatial transformations in wave theory, namely the concepts of transformation electronics and 'digital' metamaterials. In the first topic, we show that the notion of transformation optics can be extended to other physical phenomena such as tailoring the effective mass of charged carriers, e.g. electrons, in specially designed semiconductor superlattices. We discuss how the combination of thin layers of electronic materials with different effective mass of electrons may lead to bulk composite structures in which the effective mass of electrons may exhibit extreme anisotropy. For the second case, we show that any desired electromagnetic permittivity can, in principle, be engineered with proper combinations of two deeply subwavelength building blocks with relative permittivity values whose real parts have opposite signs. Owing to the presence of a plasmonic resonance between the two building blocks with oppositely signed dielectric constants, the achieved effective relative permittivity for the bulk composite may have values outside the range defined by the two permittivity values of the building blocks. We discuss some of the salient features of these two spatial transformation phenomena.