Complex-coordinate non-Hermitian transformation optics

Abstract

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.

Parity-time symmetry meets photonics: A new twist in non-Hermitian optics

“…The concept of PT symmetry in dielectric optical media has inspired new design criteria in other optical media such as in plasmonic, metamaterial and epsilonnear-to-zero structures. Ongoing research in this area can be found in [26][27][28][29][30][103][104][105]. Since the technological realization of such structures is more challenging than PTsymmetric dielectric media, experiments and device applications in this area are still to come.…”

“…Earlier studies showed, for example, that asymmetric transport, anomalous diffraction and unidirectional invisibility can be realized in complex crystals at p-1 arXiv:1802.05025v1 [physics.optics] 14 Feb 2018 the PT symmetry breaking transition, where lattice bands start to merge [13,[18][19][20][21][22][23][24][25][26]. Invisibility, cloaking, non-Hermitian metamaterials and metasurfaces, based on PT symmetry concepts, were subsequently suggested [26][27][28][29][30]. PT symmetry has inspired the idea of a laser-absorber device [31][32][33], i.e.…”

Launching and controlling Gaussian beams from point sources via planar transformation media

“…A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to nonsymmetric complex coordinate transformations as put forth in [6] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed outside the slab as well [6].…”

Transformation Optics: From Classic Theory and Applications to its New Branches

“…In addition to the above aspects, TO has many other applications, such as calculating the optical force, designing gratings, designing spontaneous emissions, reverse ray tracings, designing perfect matched layers in numerical simulations, etc. In recent years, more and more new branches are emerging from TO, such as TO with graphene, TO with photonic crystals, TO with meta‐surfaces, TO with Fourier optics, TO for lossy media by complex coordinate transformations, etc. Such a coordinate transformation method that can link physical quantities in two spaces will lead the trends in future optical design and multiphysical fields design …”

“…branches are emerging from TO, such as TO with graphene, [238] TO with photonic crystals, [239] TO with meta-surfaces, [240] TO with Fourier optics, [241,242] TO for lossy media by complex coordinate transformations, [243][244][245] etc. Such a coordinate transformation method that can link physical quantities in two spaces will lead the trends in future optical design and multiphysical fields design.…”