Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations. This technique enables a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence, providing a powerful and intuitive design tool for the control of EM fields on all length scales. With the unprecedented design flexibility offered by transformation optics (TO), researchers have demonstrated a host of interesting devices, such as invisibility cloaks, field concentrators, and optical illusion devices. Recently, the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena, where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena, such as nonlocal effects, Casimir interactions, and compact dimensions. We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.
While typically designed to manipulate classical light, metamaterials have many potential applications for quantum optics as well. We argue why a quantum optical effective-medium theory is needed. We present such a theory for layered metamaterials that is valid for light propagation in all spatial directions, thereby generalizing earlier work for one-dimensional propagation. In contrast to classical effective-medium theory there is an additional effective parameter that describes quantum noise. Our results for metamaterials are based on a rather general Lagrangian theory for the quantum electrodynamics of media with both loss and gain. In the second part of this paper, we present a new application of transformation optics whereby local spontaneous-emission rates of quantum emitters can be designed. This follows from an analysis how electromagnetic Green functions trans- form under coordinate transformations. Spontaneous-emission rates can be either enhanced or suppressed using invisibility cloaks or gradient index lenses. Furthermore, the anisotropic material profile of the cloak enables the directional control of spontaneous emission.
Nonmagnetic cloak offers a feasible way to achieve invisibility at optical frequencies using materials with only electric
responses. In this letter, we suggest an approximation of the ideal nonmagnetic cloak and quantitatively study its
electromagnetic characteristics using a full-wave scattering theory. It is demonstrated that the forward scattering of the
impedance matched cloak increases dramatically as the thickness of the cloak decreases. Nevertheless, it is still possible
to effectively reduce the total scattering cross section with a very thin cloak whose impedance is not matched to the
surrounding material at the outer boundary. Our analysis also provides the flexibility of reducing the scattering in an
arbitrary direction.
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