Nonlocal transformation optics

TL;DR

This paper extends transformation optics to engineer nonlocal electromagnetic responses in artificial materials, providing a systematic framework for designing materials with tailored dispersion properties.

Contribution

It introduces a general method to derive constitutive blueprints for nonlocal transformation media using spectral domain analysis and geometrical interpretation.

Findings

Derived general constitutive blueprints for nonlocal media

Provided a geometrical interpretation via equi-frequency contour deformation

Demonstrated application to wave-splitting refraction scenario

Abstract

We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects, and provide a physically-incisive and powerful geometrical interpretation in terms of deformation of the equi-frequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.