This special issue is dedicated to the emerging field of non-Hermitian photonics of complex media, with emphasis on PT-symmetric optical structures. In particular, the papers highlight the variety of applications being considered and the ways in which non-Hermitian optics can improve their performance.

The effect of material dispersion on the optical properties of one-dimensional non-Hermitian scattering systems is investigated in detail. In particular, multilayer heterostructures with gain and loss (parity-time symmetric or not) are examined by taking into account the dispersion of each layer. The exceptional points and phase transitions are characterized based on the spectrum of the corresponding scattering matrix. We demonstrate that an on-average lossy heterostructure can amplify an incident plane wave in the frequency range associated with the emission frequency of the layer with gain.

Integrated nonlinear waveguide structures enable generation of quantum entangled photons. We describe theoretically the effects of spatially inhomogeneous loss on the creation of photon pairs through spontaneous parametric down-conversion in quadratically nonlinear directional couplers, where photons experience effective parity-time (PT) symmetric potential due to the presence of optical loss in one of the waveguides. We show that for losses below the PT-breaking threshold, the quantum photon states can be flexibly tuned similarly to conservative couplers, whereas for stronger losses, the correlations between two waveguide modes are suppressed. We also formulate a quantum-classical correspondence with sum-frequency generation for fast evaluation of device performance. These results can be applied for the design of quantum plasmonic circuits.

In this work, we first discuss systematically three general approaches to construct a non-Hermitian flat band, defined by its dispersionless real part. These approaches resort to, respectively, spontaneous restoration of non-Hermitian particle-hole symmetry, a persisting flat band from the underlying Hermitian system, and a compact Wannier function that is an eigenstate of the entire system. For the last approach in particular, we show the simplest lattice structure where it can be applied, and we further identify a special case of such a flat band where every point in the Brillouin zone is an exceptional point of order 3. A localized excitation in this “EP3 flat band” can display either a conserved power, quadratic power increase, or even quartic power increase, depending on whether the localized eigenstate or one of the two generalized eigenvectors is initially excited. Nevertheless, the asymptotic wave function in the long time limit is always given by the eigenstate, in this case, the compact Wannier function or its superposition in two or more unit cells.

We propose a parity-time (PT) symmetric fiber laser composed of two coupled ring cavities with gains and losses, which operates both in PT-symmetric and symmetry-broken regimes depending on the static phase shifts. We perform analytical and numerical analysis by the transfer matrix method taking into account gain saturation and predict laser bistability in the PT-symmetric regime in contrast to a symmetry-broken single-mode operation. In the PT-broken regime, the generation power counterintuitively increases with an increase of the cavity losses.

We present a study of single nanoparticle detection using parity-time (PT) symmetric whispering-gallery mode (WGM) resonators. Our theoretical model and numerical simulations show that, with balanced gain and loss, the PT-symmetric WGM nanoparticle sensor, tailored to operate at PT phase transition points (also called exceptional points), exhibits significant enhancement in frequency splitting when compared with a single WGM nanoparticle sensor subject to the same perturbation. The presence of gain in the PT-symmetric system leads to narrower linewidth, which helps to resolve smaller changes in frequency splitting and improve the detection limit of nanoparticle sensing. Furthermore, we also provide a general method for detecting multiple nanoparticles entering the mode volume of a PT-symmetric WGM sensor one by one. Our study shows the feasibility of PT-symmetric WGM resonators for ultrasensitive single nanoparticle and biomolecule sensing.

We study light propagation through cyclic arrays, composed by copies of a given PT-symmetric dimer, using a group theoretical approach and finite element modeling. The theoretical mode-coupling analysis suggests the use of these devices as output port replicators where the dynamics is controlled by the impinging light field. This is confirmed in good agreement with finite element propagation in an experimentally feasible necklace of passive PT-symmetric dimers constructed from lossy and lossless waveguides.

Parity–time (PT) symmetry has been demonstrated in the frame of classic optics. Its applications in laser science have resulted in unconventional control and manipulation of resonant modes. PT-symmetric periodic circular Bragg lasers were previously proposed. Analyses with a transfer-matrix method have shown their superior properties of reduced threshold and enhanced modal discrimination between the radial modes. However, the properties of the azimuthal modes were not analyzed, which restricts further development of circular Bragg lasers. Here, we adopt the coupled-mode theory to design and analyze chirped circular Bragg lasers with radial PT symmetry. The new structures possess more versatile modal control with further enhanced modal discrimination between the azimuthal modes. We also analyze azimuthally modulated circular Bragg lasers with radial PT symmetry, which are shown to achieve even higher modal discrimination.

Non-Hermitian characteristics accompany any photonic device incorporating spatial domains of gain and loss. In this work, a one-dimensional beam-forming array playing the role of the active part is disturbed from the scattering losses produced by an obstacle in its vicinity. It is found that the placement of the radiating elements leading to perfect beam shaping is practically not affected by the presence of that jammer. A trial-and-error inverse technique of identifying the features of the obstacle is presented based on the difference between the beam target pattern and the actual one. Such a difference is an analytic function of the position, size, and texture of the object, empowering the designer to find the feeding fields for the lasers giving a perfect beam forming. In this way, an optimal beam-shaping equilibrium is re-established by effectively cloaking the object and nullifying its jamming effect.

Over the past decade, parity-time (PT)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the PT-symmetry-breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the PT transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam-propagation-method analysis. Our results pave a robust way toward studying the interplay between passive PT transitions and quantum effects in dissipative photonic configurations.