Field approach in the transformation optics concept

Abstract

An alternative, field-based formulation of transformation optics is proposed. Field transformations are expressed in the language of boundary conditions for the electromagnetic fields facilitated through the introduction of generalized potential functions. It is shown that the field-based approach is equivalent to the conventional coordinate-transformation approach but is preferable when looking for specific field distribution. A set of example devices such as invisibility cloaks, concentrators, rotators, and transformation optics lenses capable of creating light beams with predetermined field distribution (e.g., Gaussian and sinusoidal) is studied to validate the effectiveness of the field-based formulation. As for the boundary conditions for the cloaked region the absence of the normal component of the Poynting vector is justified. In the frames of the field-based approach the physical reasons behind infinite components (singularities) of the material parameters of transformation optics devices are straightforwardly revealed.