We extend the transformation-optics paradigm to a complex spatial coordinate domain, in order to deal with electromagnetic metamaterials characterized by balanced loss and gain, giving special emphasis to parity-time (PT ) symmetric metamaterials. We apply this general theory to complex-source-point radiation and anisotropic transmission resonances, illustrating the capability and potentials of our approach in terms of systematic design, analytical modeling and physical insights into complex-coordinate wave-objects and resonant states.PACS numbers: 42.25. Bs, 11.30.Er Balanced loss-gain artificial materials have elicited a growing attention in optics and photonics, mostly inspired by the emerging parity-time (PT ) symmetry concept, which was originally introduced in connection with quantum physics [1] (see [2] for a comprehensive review). Against the traditional axioms in quantum mechanics, Bender and co-workers [2] proved that even nonHermitian Hamiltonians may exhibit entirely real energy eigenspectra, as long as they commute with the combined PT -operator and share the same eigenstates. This implies, as a necessary condition on the quantum potential, V (−r) = V * (r), with r denoting a vector position and * complex conjugation.In view of the formal analogies between Schrödinger and paraxial Helmholtz equations, the above concepts and conditions may be straightforwardly translated to scalar optics and photonics scenarios, with complexvalued refractive-index profiles n(−r) = n * (r) playing the role of the quantum potential. Such symmetry condition cannot be found in natural materials, but it may be engineered within current metamaterial technology, with a judicious spatial modulation of optical gain and losses (either along or across the propagation direction). Besides providing convenient experimental testbeds for PTsymmetry-induced quantum-field effects that are still a subject of debate, PT -symmetric metamaterials constitute per se a very intriguing paradigm, as the complex interplay between losses and gain may give rise to a wealth of anomalous, and otherwise unattainable, light-matter interaction effects that extend far beyond the rather intuitive loss (over)compensation effects [3] In this Letter, we show that the transformation optics (TO) framework [19,20] may be extended, via complex analytic continuation of the spatial coordinates, in order to deal with PT -symmetric metamaterials. This extension brings along the powerful TO "bag of tools," already applied successfully to a wide variety of fieldmanipulating metamaterials [21], in terms of systematic design, analytical modeling and valuable physical insights. Our approach may be related to recent efforts in applying the coordinate-transformation methods to quantum mechanics in order to generate classes of exactly-solvable PT -symmetric potentials (see, e.g., [22,23] and references therein).For simplicity, we start considering an auxiliary vacuum space with Cartesian coordinates r ′ ≡ (x ′ , y ′ , z ′ ), where time-harmonic [exp(−iωt)] electric (J ...

We show that obliquely-incident, transversely-magnetic-polarized plane waves can be totally transmitted (with zero reflection) through epsilon-near-zero (ENZ) bi-layers characterized by balanced loss and gain with parity-time (PT ) symmetry. This tunneling phenomenon is mediated by the excitation of a surface-wave localized at the interface separating the loss and gain regions. We determine the parameter configurations for which the phenomenon may occur and, in particular, the relationship between the incidence direction and the electrical thickness. We show that, below a critical threshold of gain and loss, there always exists a tunneling angle which, for moderately thick (wavelength-sized) structures, approaches a critical value dictated by the surface-wave phasematching condition. We also investigate the unidirectional character of the tunneling phenomenon, as well as the possible onset of spontaneous symmetry breaking, typical of PT -symmetric systems. Our results constitute an interesting example of a PT -symmetry-induced tunneling phenomenon, and may open up intriguing venues in the applications of ENZ materials featuring loss and gain.

Inspired by the parity-time symmetry concept, we show that a judicious spatial modulation of gain and loss in epsilon-near-zero metamaterials can induce the propagation of exponentiallybound interface modes characterized by zero attenuation. With specific reference to a bi-layer configuration, via analytical studies and parameterization of the dispersion equation, we show that this waveguiding mechanism can be sustained in the presence of moderate gain/loss levels, and it becomes leaky (i.e., radiative) below a gain/loss threshold. Moreover, we explore a possible rodbased metamaterial implementation, based on realistic material constituents, which captures the essential features of the waveguiding mechanism, in good agreement with our theoretical predictions. Our results may open up new possibilities for the design of optical devices and reconfigurable nanophotonics platforms.

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.

Sensing schemes based on Rayleigh anomalies (RAs) in metal nanogratings exhibit an impressive bulk refractive-index sensitivity determined solely by the grating period. However, the surface sensitivity (which is a key figure of merit for label-free chemical and biological sensing) needs to be carefully investigated to assess the actual applicability of this technological platform. In this paper, we explore the sensitivity of RAs in metal nanogratings when local refractive-index changes are considered. Our studies reveal that the surface sensitivity deteriorates up to two orders of magnitude by comparison with the corresponding bulk value; interestingly, this residual sensitivity is not attributable to the wavelength shift of the RAs, which are completely insensitive to local refractive-index changes, but rather to a strictly connected plasmonic effect. Our analysis for increasing overlay thickness reveals an ultimate surface sensitivity that approaches the RA bulk value, which turns out to be the upper-limit of grating-assisted surface-plasmon-polariton sensitivities.