ABSTRACT
In artificially engineered materials (also known as metamaterials),
fascinating phenomena such as a negative index of refraction and
a negative modulus can emerge and defy our common intuition.
Such responses of metamaterials are strongly dictated by their
engineered internal structures. As conventional media owe their
properties to the average response from an ensemble of atoms and
molecules, in metamaterials, each structural unit plays the role of
an atom. This emergent nature provides researchers with great
flexibility in tailoring the material’s response to the external fields
and waves of interest. Many significant advances in this rapidly
moving field have been made utilizing transformation optics (TO)
theory. In a dauntingly large phase space of material parameters
and their arrangement, the TO formalism provides a clear-cut recipe
that is based on the idea of representing the spatial manipulation
of a phenomenon of interest with a coordinate transformation.
While tying such a geometrical interpretation to required mate-
rial parameters through linear algebraic operations, this concept
provides a systematic approach for designing a single functionality
in a given physical domain. In this chapter, we describe recent
developments in our attempt to extend the TO formalism beyond a
single functionality to independently manipulate multiple physical
phenomena simultaneously. Through the example of designing a
multifunctional shell that behaves as an electrical invisibility cloak
and a thermal concentrator, we describe a step towards a framework
that can be called transformation multiphysics [1].
