Generalized transformation optics from triple spacetime metamaterials

Abstract

In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the excitation tensor (displacement field and magnetic field), resp. In this way, several limitations of standard transformation media can be overcome. In particular it is possible to provide a geometric interpretation of non-reciprocal as well as indefinite materials. We show that these transformations can be complemented by a continuous version of electric-magnetic duality and comment on the relation to the complementary approach of field-transforming metamaterials.Comment: 11 pages, 3 figures, v2: typos, new figures, REVTeX, v3: typos, new example added, final versio

Doubly skew: A new class of non-birefringent media

“…Therefore, G = (Q + Q T )/2 can be interpreted as the optical metric of Q-media, which agrees with their interpretation in transformation optics [2], [6]. To our knowledge no systematic study of further classes of non-birefringent media exists.…”

“…1 In some equations we use component notation in conjunction with the Einstein summation convention [8], [3], [6]. In these equations a summation over repeated indices is assumed.…”

“…All media of this type are non-birefringent, respect the Post constraint [3] and have propagating solutions for any frequency ω. Transformation media are a subclass of the class of Q-media [4], [5], described by a generic 4 × 4 matrix and geometrically interpretable as an extension of transformation optics [6]. All Q-media are non-birefringent and most standard examples of linear, non-birefringent media are found as the special cases.…”

The variational principle in transformation optics engineering and some applications

“…We will use this last approach in the next section. Expressions similar to (2.29) were obtained in [12] starting from Maxwell's equations instead of from a variational principle. It is worth mentioning that there is an erroneous extra factor of 1 2 in the expression for X µνρσ in [12].…”

Design and implementation of photonic metamaterials

“…95 We must bear in mind that virtual space (stage 2) could be the result of a coordinate transformation from virtual space in other coordinate system (stage 1). Extension to the case in which virtual space is non-empty is simple.…”