Complex-coordinate non-Hermitian transformation optics


Transformation optics (TO) is conventionally based on real-valued coordinate transformations and, therefore, cannot naturally handle metamaterials featuring gain and/or losses. Motivated by the growing interest in non-Hermitian optical scenarios featuring spatial modulation of gain and loss, and building upon our previous studies, we explore here possible extensions of the TO framework relying on complex-valued coordinate transformations. We show that such extensions can be naturally combined with well-established powerful tools and formalisms in electromagnetics and optics, based on the ‘complexification’ of spatial and spectral quantities. This enables us to deal with rather general non-Hermitian optical scenarios, while retaining the attractive characteristics of conventional (real-valued) TO in terms of physically incisive modeling and geometry-driven intuitive design. As representative examples, we illustrate the manipulation of beam-like wave-objects (modeled in terms of ‘complex source points’) as well as radiating states (’leaky waves’, modeled in terms of complex-valued propagation constants). Our analytical results, validated against full-wave numerical simulations, provide useful insight into the wave propagation in non-Hermitian scenarios, and may indicate new directions in the synthesis of active optical devices and antennas.

Journal of Optics 18(4), 044027