The recently introduced concept of photonic doping in epsilon-near-zero media enables the tailoring and control of the effective magnetic response over broad regions of the parameter space, by resorting to a limited number of arbitrarily placed, nonmagnetic doping particles. Here, we theoretically extend this idea to non-Hermitian scenarios with either doping particles or host media characterized by tailored distributions of gain and loss. This considerably enlarges the attainable effective permeability parameter space, granting access to the entire complex plane. In this extended vision, losses are not considered as second-order, detrimental effects, and their interplay with gain is instrumental to enabling several intriguing effects of potential interest in reconfigurable nanophotonics and optical sensing, whose practical implementation is deferred to future studies.In solid-state physics, doping is a pivotal concept that allows controlling and engineering of the macroscopic electronic and optical properties of materials such as semiconductors by judiciously introducing small concentrations of impurities. Recently, this concept has been translated to two-dimensional photonic scenarios in connection with host media characterized by vanishingly small relative permittivity (epsilon near zero), showing that it is possible to obtain broadly tunable effective magnetic responses by introducing a single, nonmagnetic doping particle at an arbitrary position. So far, this phenomenon has been studied mostly for lossless configurations. In principle, the inevitable presence of material losses can be compensated via optical gain. However, taking inspiration from quantum (e.g., parity-time) symmetries that are eliciting growing attention in the emerging fields of non-Hermitian optics and photonics, this suggests considering more general gain-loss interactions. Here, we theoretically show that the photonic doping concept can be extended to non-Hermitian scenarios characterized by tailored distributions of gain and loss in either the doping particles or the host medium. In these scenarios, the effective permeability can be modeled as a complex-valued quantity (with the imaginary part accounting for the gain or loss), which can be tailored over broad regions of the complex plane. This enables a variety of unconventional optical responses and waveguiding mechanisms, which can be, in principle, reconfigured by varying the optical gain (e.g., via optical pumping). We envision several possible applications of this concept, including reconfigurable nanophotonics platforms and optical sensing, which motivate further studies for their experimental validation.

The recently proposed digital coding metasurfaces make it possible to control electromagnetic (EM) waves in real time, and allow the implementation of many different functionalities in a programmable way. However, current configurations are only space-encoded, and do not exploit the temporal dimension. Here, we propose a general theory of space-time modulated digital coding metasurfaces to obtain simultaneous manipulations of EM waves in both space and frequency domains, i.e., to control the propagation direction and harmonic power distribution simultaneously. As proof-of-principle application examples, we consider harmonic beam steering, beam shaping, and scattering-signature control. For validation, we realize a prototype controlled by a field-programmable gate array, which implements the harmonic beam steering via an optimized space-time coding sequence. Numerical and experimental results, in good agreement, demonstrate good performance of the proposed approach, with potential applications to diverse fields such as wireless communications, cognitive radars, adaptive beamforming, holographic imaging.

We introduce the concept of metamaterial analog computing, based on suitably designed metamaterial blocks that can perform mathematical operations (such as spatial differentiation, integration, or convolution) on the profile of an impinging wave as it propagates through these blocks. Two approaches are presented to achieve such functionality: (i) subwavelength structured metascreens combined with graded-index waveguides and (ii) multilayered slabs designed to achieve a desired spatial Green’s function. Both techniques offer the possibility of miniaturized, potentially integrable, wave-based computing systems that are thinner than conventional lens-based optical signal and data processors by several orders of magnitude.