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In this paper, a novel microwave photonic filter (MPF) based on a single longitudinal mode Brillouin laser achieved by parity time (PT) symmetry mode selection is proposed, and its unparalleled ultra-narrow bandwidth as low as to sub-kHz together with simple and agile tuning performance is experimentally verified. The Brillouin fiber laser ring resonator is cascaded with a PT symmetric system to achieve this MPF. Wherein, the Brillouin laser resonator is excited by a 5 km single mode fiber to generate Brillouin gain, and the PT symmetric system is configured with Polarization Beam Splitter (PBS) and polarization controller (PC) to achieve PT symmetry. Thanks to the significant enhancement of the gain difference between the main mode and the edge mode when the polarization state PT symmetry system breaks, a single mode oscillating Brillouin laser is generated. Through the selective amplification of sideband modulated signals by ultra-narrow linewidth Brillouin single mode laser gain, the MPF with ultra-narrow single passband performance is obtained. By simply tuning the central wavelength of the stimulated Brillouin scattering (SBS) pumped laser to adjust the Brillouin oscillation frequency, the gain position of the Brillouin laser can be shifted, thereby achieving flexible tunability. The experimental results indicate that the MPF proposed in this paper achieves a single pass band narrow to 72 Hz and the side mode rejection ratio of more than 18 dB, with a center frequency tuning range of 0–20 GHz in the testing range of vector network analysis, which means that the MPF possesses ultra high spectral resolution and enormous potential application value in the domain of ultra fine microwave spectrum filtering such as radar imaging and electronic countermeasures.

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\cal PT$-) and anti-$\cal PT$-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). On the other, topological and localization transitions in non-Hermitian systems reveal new phenomena, e.g., the non-Hermitian skin effect and the absence of conventional bulk-boundary correspondence. The great majority of previous studies exclusively focus on non-Hermitian Hamiltonians, whose realization requires an {\it a priori} fine-tuned extended lattices to exhibit topological and localization transition phenomena.In this work, we show how the non-Hermitian localization phenomena can naturally emerge in the synthetic field moments space of zero-dimensional bosonic systems, e.g., in anti-$\cal PT$ and $\cal PT$-symmetric quantum dimers. This offers an opportunity to simulate localization transitions in low-dimensional systems, without the need to construct complex arrays of, e.g., coupled cavities or waveguides. Indeed, the field moment equations of motion can describe an equivalent (quasi-)particle moving in a one-dimensional (1D) synthetic lattice. This synthetic field moments space can exhibit a nontrivial localization phenomena, such as non-Hermitian skin effect, induced by the presence of highly-degenerate EPs. We demonstrate our findings on the example of an anti-$\cal PT$-symmetric two-mode system, whose higher-order field moments eigenspace is emulated by a synthetic 1D non-Hermitian Hamiltonian having a Sylvester matrix shape. Our results can be directly verified in state-of-the-art optical setups, such as superconducting circuits and toroidal resonators, by measuring photon moments or correlation functions., 18 pages

Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectra theory on the prototypical non-Hermitian SSH (NHSSH) lattice. Topological modes are robust with respect to chiral perturbations and sensitive to parity-time (PT) symmetry preserving perturbations. In fact, the chiral symmetry exactly at the exceptional point leads to the suppression of its sensitivity, corresponding to a lower order exceptional point. However, counterintuitively, they are most sensitive with respect to unstructured perturbations, leaving the fingerprint of the pertinent higher order exceptional (HEP) point., Comment: 6 pages, 4 figures

The concept of topology is universally observed in various physical objects when the objects can be described by geometric structures. Although a representative example is the knotted geometry of wavefunctions in reciprocal space for quantum Hall family and topological insulators, topological states have also been defined for other physical quantities, such as topologically distinct Fermi surfaces and enhanced lattice degrees of freedom in hyperbolic geometry. Here, we investigate a different class of topological states – topological geometry of dynamical state trajectories – in non-Hermitian and nonlinear optical dynamics, revealing topologically protected oscillation quenching mechanisms determined by parity–time (PT) symmetry. For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death. We then show that these PT-symmetric quenching mechanisms lead to immunity against temporal perturbations, enabling the applications of topologically protected laser modulation and rectification. The observed connection between the topological geometry of dynamical states, oscillation quenching phenomena in dynamical systems theory, and PT symmetry provides a powerful toolkit for noise-immune signal processing.

The exceptional points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors, which are associated with remarkable dynamical properties. These EPs can be generated experimentally in open quantum systems, evolving under a Lindblad equation, by postselecting on trajectories that present no quantum jumps, such that the dynamics is ruled by a NHH. Interestingly, changing the way the information used for postselection is collected leads to different unravelings, i.e., different set of trajectories, which average to the same Lindblad equation, but are associated with a different NHH. Here, we exploit this mechanism to create and control EPs solely by changing the measurement we postselect on. Our scheme is based on a realistic homodyne reading of the emitted leaking photons with a weak-intensity laser (a process that we call beta-dyne), which we show generates a tunable NHH, that can exhibit EPs even though the system does have any in the absence of the laser. We consider a few illustrative examples pointing out the dramatic effects that different postselections can have on the spectral features of the NHH, paving the road towards engineering of EPs in simple quantum systems.

The new paradigm of parity-time symmetry in quantum mechanics has readily been applied in the field of optics with numerous demonstrations of exotic properties in photonic systems. In this work, we report on the implementation of single frequency electrically injected distributed feedback (DFB) laser diodes based on parity-time symmetric dual gratings in a standard ridge waveguide configuration. We demonstrate enhanced modal discrimination for these devices as compared with index or gain coupled ones, fabricated in the same technology run. Optical transmission probing experiments further show asymmetric amplification in the light propagation confirming the parity-time symmetry signature of unidirectional light behavior. Another asset of these complex coupled devices is further highlighted in terms of robustness to optical feedback.

We propose a scheme to realize a parity-time (PT) symmetric nonlinear system in a coherent atomic gas via electromagnetically induced transparency. We show that it is possible to construct an optical potential with PT symmetry due to the interplay among the Kerr nonlinearity stemmed from the atom-photon interaction, the linear potential induced by a far-detuned Stark laser field, and the optical gain originated from an incoherent pumping. Since the real part of the PT-symmetric potential depends only on the intensity of the probe field, the potential is nonlinear and its PT-symmetric properties are determined by the input laser intensity of the probe field. Moreover, we obtain the fundamental soliton solutions of the system and attain their stability region in the system parameter space. The dependence of the exceptional point (EP) location on the soliton maximum amplitude is also illustrated. The research results reported here open a new avenue for understanding the unique properties of PT symmetry of a nonlinear system. They are also promising for designing novel optical devices applicable in optical information processing and transmission.

Exceptional points (EPs), singularities of non-Hermitian physics where complex spectral resonances degenerate, are one of the most exotic features of nonequilibrium open systems with unique properties. For instance, the emission rate of quantum emitters placed near resonators with EPs is enhanced (compared to the free-space emission rate) by a factor that scales quadratically with the resonance quality factor. Here, we verify the theory of spontaneous emission at EPs by measuring photoluminescence from photonic-crystal slabs that are embedded with a high-quantum-yield active material. While our experimental results verify the theoretically predicted enhancement, they also highlight the practical limitations on the enhancement due to material loss. Our designed structures can be used in applications that require enhanced and controlled emission, such as quantum sensing and imaging. Published version This work was partly funded by the French National Research Agency (ANR) under the Project POPEYE (Project No. ANR-17-CE24-0020) and the IDEXLYON from Universite de Lyon, Scientific Breakthrough project TORE within the Programme Investissements d Avenir (Project No. ANR-19-IDEX-0005) . It is also supported by the Auvergne-Rhne-Alpes region in the framework of PAI2020 and the Vingroup Innovation Foundation (VINIF) annual research grant program under Project No. VINIF.2021.DA00169. Q. X. gratefully acknowledges the funding support from National Natural Science Foundation of China (Grant No. 12020101003) and a Tsinghua University start-up grant.

The reverse space-time nonlocal complex modified Kortewewg–de Vries (mKdV) equation is investigated by using the consistent tanh expansion (CTE) method. According to the CTE method, a nonauto-Bäcklund transformation theorem of nonlocal complex mKdV is obtained. The interactions between one kink soliton and other different nonlinear excitations are constructed via the nonauto-Bäcklund transformation theorem. By selecting cnoidal periodic waves, the interaction between one kink soliton and the cnoidal periodic waves is derived. The specific Jacobi function-type solution and graphs of its analysis are provided in this paper.

In this manuscript, we experimentally demonstrate a parity-time-symmetric optoelectronic oscillator (OEO) with polarization multiplexed channels. We obtained a microwave single-mode oscillation at 9.5 GHz with phase noise values of −116.2 and −122.3 dBc Hz−1 at 10 kHz offset frequencies, and side mode suppression values below −68 and −75 dBc Hz−1, by utilizing a 1 km long and 5 km long single mode fiber delay lines, respectively. Our experimental results suggest that parity-time-symmetric OEOs with polarization multiplexed channels are simple and cost-efficient alternatives to their more complex counterparts.

We study the scattering properties of the partially coherent vector beams with the deterministic media having the classic symmetric and parity-time (PT) symmetric scattering potential functions. The closed-form expressions for the intensity and polarization matrix of the far-zone scattered field are obtained, under first-order Born approximation, when the partially coherent vector beams are taken to be radially polarized and the deterministic media are assumed as the four-point scatterers. We demonstrate both analytically and numerically that the far-zone scattered field becomes noncentrosymmetric and the directionality appears in the scattering pattern when the scattering potential function is switched from classic symmetry to PT symmetry. We show the effect of spatial coherence of the incident partially coherent vector beam on the directionality in scattering. We find that by turning the symmetry property of the spatial coherence function of the incident beam, i.e., into PT symmetry, the directionality in the far-zone scattering can be suppressed or enhanced, depending on the joint effect from the symmetry of the scattering potential and the symmetry of the spatial coherence. Our findings may be useful in the application of dynamic control of the directionality in light scattering.

In the field of modern optical communication systems and photoelectric detection, new components with complex functions and excellent performance are urgently needed. In this paper, a graphene-based parity–time (PT) symmetry structure is proposed, which is achieved by preparing the graphene layer on the top of a PT-symmetry photonic crystal. The transfer matrix method was used to calculate the absorptance of graphene, and a unique amplified absorption effect was found. Meanwhile, the peak value and wavelength position of the absorption can be modulated via the applied electric field. The results show that by adjusting the negative square-wave electric field from −3.5 × 10−5 to −13.5 × 10−5 V/nm (or the positive square-wave electric field from 2 × 10−5 to 11 × 10−5 V/nm), the proposed structure can achieve in-phase (or out-phase) enhanced absorption for the communication wavelength 1550 nm, with the absorption of graphene from 17 to 28 dB (or 30 to 15 dB) corresponding to the square-wave modulation electric field change. The modulable absorption properties of graphene in the structure have potential in optoelectronic devices and optical communication systems.

In this paper, an analysis of gain properties of a single primitive cell of a one-dimensional photonic crystal with parity–time symmetry is demonstrated for the first time. The proposed simple model makes it possible to study the transmission and amplification properties of the investigated cell made of a wide range of optical materials, taking into account the refractive index of the surrounding medium. This analysis is carried out with the use of a transfer matrix method. The obtained characteristics allow indicating the optimal size of the studied structure providing wave amplification, i.e., a transmittance greater than unity. In this case, the increase in the wave intensity in the gain layer exceeds its decrease in the loss layer. This effect is illustrated with the distributions of the electromagnetic field of waves propagating inside the cell.

A noticeable challenge for a multi-load wireless power transfer system is to achieve stable power transfer under a dynamic change in coupling conditions. It was proposed that the parity–time symmetric wireless power transfer (PT-WPT) system can achieve stable output efficiency for a single receiver when tuned at the purely real eigenfrequency. However, in the case of higher order, PT symmetric systems usually cannot maintain the real eigenfrequency. To address the issue, a high-order PT-WPT model was established using coupled mode theory (CMT) theory in this paper, and the eigenfrequency of the multi-load PT-WPT system was analyzed. Here, we propose that, theoretically, the system can work at the purely real eigenfrequency by impedance matching. The transfer efficiency of the multi-load PT-WPT system when the system works at the real eigenfrequency was analyzed. The results of the numerical simulation show that the multi load PT-WPT system can maintain stable output efficiency under a dynamic change in coupling conditions. In the long run, our work provides a new possibility for the stable transmission of the multi-load wireless power transfer system.

To realize the design of a medical sensor with excellent comprehensive performance indexes, herein, a plasma concentration sensing model satisfying the Parity-Time (PT) symmetric condition is proposed. In this paper, the transfer matrix method was used to simulate the transmittance spectrum of the structure, according to the amplification effect on defect mode transmission and various detection performance indexes of the structure. We numerically optimized the parameters of the structure, such as the number of PT-symmetry unit cell N, the sample layer thickness dD as well as the macroscopic Lorentz oscillation intensity α in the PT-symmetry unit cell. The calculation results demonstrate that when the sample concentration changes from 0 g/L to 50 g/L, the wavelength of defect peak shifts from 1538 nm to 1561 nm, and the average quality factor, sensitivity, average figure of merit, average detection limit and average resolution of the structure can reach 78,564, 0.4409 nm/(g/L) (or 227.05 nm/RIU), 11,515 RIU−1, 5.1 × 10−6 RIU and 0.038 g/L, respectively. Not only the sensitivity and resolution of the PT-symmetry structure are better than that of the similar sensors, but it also has excellent comprehensive detection performance, which indicates that the developed sensor can be used in high-precision biomedical detection devices.

Originating from the non-Hermitian quantum mechanics, the parity-time (PT) symmetry has been extensively explored to ensure a stable single-mode oscillation for optoelectronic oscillators (OEOs), while avoiding additional extremely challenging ultrahigh-Q filters. Enabled by the emerging photonics integrated circuit (PIC) technology, we report the tunable PT-symmetric OEO by using an integrated mode-locked laser, as a striking advance to reduce the footprint of OEOs. Stable single-mode oscillating signal at 24.5 GHz has been generated with a phase noise of-108 dBc/Hz @ 10 kHz frequency offset. In particular, a tunable frequency range from 24 to 25 GHz is achieved by manipulating the injection currents into the well-designed on-chip linear laser cavity. This work exhibits a breakthrough in conceptual integrated microwave photonic devices, and also accelerates the real-world applications of fundamental physical theory of PT symmetry to information industry.

International audience; The new paradigm of parity-time symmetry in quantum mechanics has readily been applied in the field of optics with numerous demonstrations of exotic properties in photonic systems. In this work we report on the implementation of single frequency electrically injected DFB lasers based on Parity-Time symmetric dual gratings in a standard ridge waveguide configuration. We demonstrate enhanced modal discrimination for these devices as compared with index or gain coupled ones, fabricated in the same technology run. Optical transmission probing experiments further show asymmetric amplification in the light propagation confirming the Parity-Time symmetry signature of unidirectional light behavior. Another asset of these complex coupled devices is further highlighted in terms of robustness to optical feedback.

International audience; A generic model of two dissimilar antenna-type resonators coupled both via near-field and farfield and embedded in active gain and/or loss medium is considered. Conditions required for hitting the superscattering regime corresponding to the threshold of lasing emission operation are established. It is shown that modulation of the medium gain and losses level within realistic parameters is an efficient approach for implementation of tunability. This two-antenna setup can serve as an inspiration for the implementation of high-contrast tunable metasurfaces.

In this thesis, the electromagnetic wave propagation is studied in nonstationary-medium scenarios. The electromagnetic fields under material time-modulation are shown to conserve their momentum but not their energy. The mathematical foundations and analysis to treat wave propagation in time-Floquet media are given additionally to the related parametric amplification phenomena, which are mapped to the stability analysis of the corresponding hypergeometric equations. Assuming a time-variation of permittivity, permeability and conductivity the appropriate time-domain solutions are derived, based on an observation of the fields in the past. The formulation of a time-transitioning state matrix connects the unusual energy transitions of electromagnetic fields in time-varying media with the exceptional point theory, a theory strongly connected with parity-time symmetry. Consequently, the state-matrix approach of this thesis allows the analysis of the electromagnetic waves in terms of parity and time-reversal symmetries and signify parity-time symmetric wave-states without the presence of a spatially symmetric distribution of gain and loss, or any inhomogeneities and material periodicity. The parametric amplification phenomena of time-Floquet media and more precisely those that generate a Mathieu equation at the first momentum gap are theoretically studied and numerically compared with simulations using FDTD and connected with the parity-time scattering conventional characteristics. In the last part of this thesis, studies regarding resonant acoustic and electromagnetic systems are exhibited. The theoretical foundation to treat both acoustic and electromagnetic resonant phenomena is given based on the coupled mode theory and the appropriate Hilbert space. Two examples of interest are shown leveraging the time-dynamics of a temporal resonant system. The first example is related to the design of an artificial resonant acoustic lattice with the appropriate time-modulation leading to an effective zero index of refraction. The second example is related to resonant systems with temporal coupling and the possibility to induce nonreciprocal gain by leveraging the frequency conversion occurring in parametric systems. This thesis enriches the literature and the theoretical bases for dynamical wave systems and provides an insight on the broad capabilities of time-varying systems in electromagnetics, optics and acoustics. It may be used as a guidance to realize wave devices that amplify and actively filter wave signals for many future applications in lasing, sensing, signal amplifying, energy transferring and imaging.

In the multi-load wireless power transfer (WPT) system, the output power and transfer efficiency will drop significantly with the change of distance between transmitter and receiver. Power distribution among multiple loads is also a major challenge. In order to solve these problems, a novel multi-load WPT system based on parity–time symmetry (PT-WPT) is proposed in this paper. Firstly, the multi-load PT-WPT system is modeled based on the circuit model. Then, the transmission characteristics of the multi-load PT-WPT system are analyzed. It is found that constant output power with constant transfer efficiency can be maintained against the variation of coupling coefficient, and the power distribution relationship among loads is only related to the coupling coefficient. Further, power distribution under different coupling situations is analyzed in detail to meet different power demands. Finally, taking a dual-load PT-WPT system as an example, the system parameters are designed and the circuit simulation is carried out. The simulation results are consistent with the theoretical analysis, which shows that PT symmetry can be applied to the multi-load WPT system to achieve constant output power, constant transfer efficiency, and power distribution simultaneously.

We theoretically and numerically demonstrate that the spontaneous parity-time (PT) symmetry breaking phase transition can be realized respectively by using two independent tuning ways in a tri-layered metamaterial that consists of periodic array of metal-semiconductor Schottky junctions. The existence conditions of PT symmetry and its phase transition are obtained by using a theoretical model based on the coupled mode theory. A hot-electron photodetection based on the same tri-layered metamaterial is proposed, which can directly show the spontaneous PT symmetry breaking phase transition in photocurrent and possesses dynamical tunability and switchability. This work extends the concept of PT symmetry into the hot-electron photodetection, enriches the functionality of the metamaterial and the hot-electron device, and has varieties of potential and important applications in optoelectronics, photodetection, photovoltaics, and photocatalytics.

Integrated optical filters based on microring resonators play a critical role in many applications, ranging from wavelength division multiplexing and switching to channel routing. Bandwidth tunable filters are capable of meeting the on-demand flexible operations in complex situations, due to their advantages of scalability, multi-functionality, and being energy-saving. Recent studies have investigated how parity-time (PT) symmetry coupled-resonant systems can be applied to the bandwidth-tunable filters. However, due to the trade-off between the bandwidth-tunable contrast ratio and insertion loss of the system, the bandwidth-tunable contrast ratio of this method is severely limited. Here, the bandwidth-tunable contrast ratio is defined as the maximum bandwidth divided by the minimum bandwidth. In this work, we show that a high bandwidth-tunable contrast ratio and low insertion loss of the system can be achieved simultaneously by increasing the coupling strength between the input port and the resonant. Theoretical analysis under different coupling states reveals that the low insertion loss can be obtained when the system initially operates at the over-coupling condition. A high bandwidth-tunable contrast ratio PT-symmetry band-pass filter with moderate insertion loss is shown on the Silicon platform. Our scheme provides an effective method to reduce the insertion loss of on-chip tunable filters, which is also applicable to the high-order cascaded microring systems.

Effect of optical loss, presented in a superstructure grating with a complex refractive index profile, on the mode coupling is studied in a two-mode silicon-on-insulator waveguide. In this scheme, both our theory and experimental results indicate that the optical loss not only provides optical absorption of a targeted output mode and thus the corresponding modal coupling loss, but also induces a broken parity-time symmetry phase that strongly prohibits power coupling from the incident mode to the output mode. As a result, the latter can give rise to a much-enhanced modal coupling loss of the targeted output mode. Under a reasonable device length about 37 μm, the enhancement factor can be as high as ~20 dB in simulation and ~17 dB in experiment. This paper may offer a different way to exploit the role of optical loss in boosting modal coupling loss that can directly translate to power extinction ratio. It thus may find potential applications in novel intensity modulator designs.

We report on the lasing action in weakly modulated parity-time (PT) symmetric lattices. At the exceptional point in PT-symmetric lattices, the amplitude and phase of unidirectionally scattered waves are independently and flexibly determined by the PT modulations, thus, providing a distinctive route to construct a lasing mode in finite systems with weakly modulated structures. It is revealed that the resonant feedback mechanism plays a crucial role in building up the lasing action. Our finding would enrich the singularity dynamics in the weakly modulated PT systems.

Defect modes of defective parity-time symmetry in one-dimensional fractional Schrödinger equation are theoretically investigated. Both positive and negative defect modes are extremely sensitive to the defect strength and amplitude of periodic potential. Their eigenvalues increase almost linearly with the defect strength and continuously jump among neighboring gaps in the entire defect strength domain. There exists a phase transition point where two adjacent defect mode curves merge into a single one. Below which the eigenvalues are real, and their profiles have the same symmetry as the parity-time symmetric potential. Above the transition point, the defect modes give rise to complex eigenvalues, and the above symmetric property is destroyed. The transition point also grows linearly with the defect strength. As defect strength increases, much more positive defect mode branches merge together and more phase transition points appear in each gap. However, only one phase transition point exists for negative defect modes, and moves into the higher gaps.

In standard quantum theory, the Hamiltonian describing a physical system is assumed to be Hermitian in order to guarantee the energy spectrum to be real and the time evolution to be unitary. In recent years, it was recognized that non-Hermitian Hamiltonians with parity-time ($ \mathcal PT $) symmetry can exhibit entirely real spectra, raising the possibility for extending the quantum theory to complex domain and hence stimulated growing interest in recent years. Many proposals have been presented for realizing $ \mathcal PT $-symmetric Hamiltonians in various physical systems. Among them $ \mathcal PT $-symmetric coherent atomic gases are special and possess many unique advantages, including the possibility to obtain authentic $ \mathcal PT $-symmetric refractive indexes (which have balanced gain and loss in the whole space), the capability to actively control and precisely manipulate system parameters in situ, and the feasibility to acquire large Kerr nonlinearity based on the resonance character between light and atoms. In this article, we review various schemes for the realization of $ \mathcal PT $ symmetry with coherent atomic gases, elucidate their interesting properties and promising applications. In particular, the non-linear optical effect in the $ \mathcal PT $-symmetric atomic gases are described, which may be served as useful building blocks for developing novel photonic devices with active light control at very low power level.

In this paper, we provide a comprehensive review of unidirectional reflectionless light propagation in photonic devices at exceptional points (EPs). EPs, which are branch point singularities of the spectrum, associated with the coalescence of both eigenvalues and corresponding eigenstates, lead to interesting phenomena, such as level repulsion and crossing, bifurcation, chaos, and phase transitions in open quantum systems described by non-Hermitian Hamiltonians. Recently, it was shown that judiciously designed photonic synthetic matters could mimic the complex non-Hermitian Hamiltonians in quantum mechanics and realize unidirectional reflection at optical EPs. Unidirectional reflectionlessness is of great interest for optical invisibility. Achieving unidirectional reflectionless light propagation could also be potentially important for developing optical devices, such as optical network analyzers. Here, we discuss unidirectional reflectionlessness at EPs in both parity-time (PT)-symmetric and non-PT-symmetric optical systems. We also provide an outlook on possible future directions in this field.

We present new edge-emitting laser configurations to improve the laser performance with a double benefit, light localization into a bright narrow beam emission and the suppression of spatiotemporal dynamics. The proposal is based on the management of the transverse light flow inside the laser cavity through non-Hermitian potentials. We impose pump and refractive index modulations to generate a local PT-symmetric configuration with a central symmetry axis. Such configuration induces the accumulation in axis of light generated in the whole active layer. The exploration of the modulation parameters shows a significant improvement of the intensity concentration, stability and brightness of the emitted beam.

In this article, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We assume a time-variation of permittivity, permeability, and conductivity, and derive the appropriate time-domain solutions based on the causality state at a past observation time. We formulate a time-transitioning state matrix and connect the unusual energy transitions of electromagnetic fields in time-varying media with the exceptional point theory. This state-matrix approach allows us to analyze further the electromagnetic waves in terms of parity and time-reversal symmetries and signify parity-time symmetric wave-states without the presence of a spatially symmetric distribution of gain and loss, or any inhomogeneities and material periodicity. This article provides a useful arsenal to study electromagnetic wave phenomena under time-varying media and points out novel physical insights connecting the resulting energy transitions and electromagnetic modes with exceptional point physics and operator symmetries.

It is well known that different optical techniques can be used to measure angular velocities. Interferometric Optical Gyroscopes (IFOGs) and Ring Laser Gyroscopes (RLG) exploit the Sagnac effect and are the preferred solutions for tactile grade applications. However, in the Sagnac effect the measured output is directly proportional to the gyroscope sizes. So, the miniaturization and the integration of optical gyroscopes is still a challenge in optoelectronics research. In this paper different approaches based on parity-time and anti-parity-time symmetry are explained and compared as highly performance solutions for the integration of optical gyroscopes. The sensitivity of the rotation-induced frequency-splitting (broadening) can be several orders of magnitude higher than the classical Sagnac splitting achieved with a single ring gyroscope occupying the same surface. We will show that anti-parity-time-symmetric solutions represent a better choice for angular velocity sensing.

To achieve ultrafast neuromorphic signal processing, the realization of photonic equivalents to neuronal functions has been challenged. In article number 1900771, Namkyoo Park and co‐workers present a neuromorphic photonic system ruled by parity‐time symmetry as a building block for light‐based neural signal processing. Inspired by neuronal ion channels, saturable photonic channels using coupled resonators are developed to achieve multifaceted neuromorphic functionalities such as quenching and firing.

International audience; The principle of Parity-Time symmetric optics is exploited for realization of electrically injected single frequency DFB lasers based on industry-adopted design and fabrication approaches. Experimental evidence is provided for “unidirectional” gain discrimination mechanism induced by the complex refractive index Bragg grating. This is expected to enhance lasers’ resistance to parasitic optical feedback. The experimental results showing an apparent correlation between the gratings real-to-imaginary phase shift and the laser feedback resistance are corroborating theoretical prediction.

International audience; We present a approach aimed at generalizing Parity-Time symmetry to mesoscopic ensembles of coupled oscillators with gain and loss, with inspiration from graph-theoretic tools. We globally minimize the imaginary part of the eigenvalues for small gain/loss and describe how couplingsadopt some topologies. We also discuss recent results on distributed-feedback laser diodes operating at 1550 nm and having both real and imaginary index modulation. We notably study their resistance to optical feedback.

International audience; The impact of imbalance in waveguides propagation constants among Parity-Time symmetric coupled waveguides and/or of a complex-valued coupling coefficient is assessed. The narrow tolerance found implies that attempts to tightly control waveguides parameters appear as elusive because of fabrication technology limitations, calling for more feasible mitigation avenues. It is shown that a grating-assisted Parity-Time symmetric coupler design restores both technologically robust binary switching operation and exceptional point. In addition the proposed design is compatible with birefringence compensation techniques providing polarization-independent operation as well as coupling and/or gain-loss profile modulation techniques that extend the control of switching operation in the Parity-Time symmetric phase. Using wavelength as an additional tuning parameter near exceptional points opens promising avenues for manipulating the trajectory on Riemann sheets in topological photonics applications.

Parity-time (PT) symmetric systems based on bal- anced distributions of gain and loss have attracted significant attention in wave physics, enabling the possibility of compen- sating material losses in photonic systems, and of inducing ex- ceptional scattering phenomena, offering new possibilities for wave manipulation. A successful transition of these theoretical concepts to devices and practical applications requires a sufficient level of control over the frequency dispersion of the involved gain and loss elements, in order to engineer a PT-symmetric system that is stable and practical. Here, we show that such a degree of control can be achieved for acoustic waves, and obtain stable PT-symmetric acoustic systems that can manipulate sound in un- precedented ways. We describe the theory, design and potentials of PT-based negative refraction and phase compensation devices in free-space, induced by a pair of PT-symmetric acoustic metasur- faces engineered from active electro-acoustic resonators. Our study proves that acoustic systems represent an ideal platform to apply the unique scattering phenomena associated with PT-symmetric systems operated at exceptional points. We envision applications in acoustic imaging, furtive sensing, and noise control, and extension of these concepts to electromagnetics, optics, and nanophotonic systems

The development of photonics during the pastdecades, enabled by the advent of nanofabricationtechnologies, witnessed the appearance of new types ofartificial materials such as photonic crystals,metamaterials, plasmonic circuits, and more recently the socalled “PT symmetry” structures. The characteristic featureof this new type of artificial structures is that though theyare described by non-Hermitian Hamiltonians theireigenvalues can still be real. In optics, several physicalphenomena are known to obey equations that are formallyequivalent to that of Hamiltonians in quantum mechanics.During this work, we investigated the design, fabricationand characterization of complex-coupled DFB lasers, withthe intent to apply Parity-Time (PT) symmetry to apractical device. The mode selectivity inside the cavity isbrought by the combination of a gain-coupled and indexcoupledBragg grating, under the form of respectively acorrugated waveguide and a metallic absorbing surfacegrating.Through the simulation of the mode evolution insideconventional DFB lasers and complexe-coupled DFBlasers using Ables matrix method, the advantages ofefficient mode filtering while keeping a low thresholdcurrent was observed. The specific phase shift of a quarterperiod, matching the PT-symmetric configuration, is foundto show highly asymmetric mode selection, with unidirectionalamplification in reflection.Index, gain and complex-coupled DFB lasers with differentphase shifts between loss and index grating profiles werefabricated, using photonics integrated circuits fabricationbuilding blocks: electron beam lithography and inducedcoupled plasma dry etching to name but a few.The characterization of the fabricated lasers shows areduction in threshold compared to equivalent third ordergain-coupled DFB lasers, and improved monomodeoperation and yield compared to third order index-coupledDFB lasers.Real and imaginary parts of the index modulation as wellas reflection spectral response was investigated by externaloptical probing of the laser cavities.The resistance of the CC DFB lasers to external opticalfeedback was studied. If results show an apparentcorrelation between the gratings phase shift and thefeedback resistance, but no significant improvement wasfound with regards to IC DFB lasers.This first milestone on the application of PT-symmetry tothe design and fabrication of DFB lasers provide interestingprospects on the improvement of existing technologies.This work reinforces the interest of this concept for thedesign of feedback tolerant DFB lasers, and theirintegration in an all PT-symmetric laser-modulator system.; Le développement des systèmes photoniques aucours des dernières décennies, rendu possible parl’évolution des technologies de nanofabrication, a vul’apparition de nouveaux matériaux synthétiques tels queles cristaux photoniques, les métamatériaux, les plasmonsde surface, et plus récemment les structures dites « àsymétrie Parité-Temps ». La caractéristique de ces derniersmatériaux synthétiques est que bien qu’ils soient décrits parun Hamiltonien non-Hermitien, leurs valeurs proprespeuvent toutefois être réelles. En optique plusieursphénomènes physiques sont connus pour la ressemblancedes équations les décrivant, avec l’expression de ce typed’Hamiltonien en mécanique quantique. C’est le cas deséquations de modes couplés dans les lasers DFB.Ce travail de thèse a porté sur la conception, fabrication etétude de lasers DFB à couplage complexe, dans l’optiqued’appliquer le principe de symétrie Parité Temps (PT) à uncomposant fonctionnel. Ces lasers sont combinent un réseaupar l’indice et par les pertes, avec un déphasage spécifique.La simulation des modes dans la cavité, effectuée parméthode matricielle de Ables, a dévoilé l’avantageuxfiltrage apporté par les lasers DFB à couplage complexe, engardant un seuil faible. Le cas spécifique d’un déphasaged’un quart de période entre les deux réseaux, correspondantà une condition de symétrie PT, induit des effetsunidirectionnels d’amplification en réflexion.Des lasers DFB à couplage par l’indice, par les pertes et àcouplage complexe avec différentes phases entre les réseauxont été fabriqués selon les techniques courantes deréalisation de circuits photonique intégrés : lithographieélectronique et gravure ICP notamment.Les mesures de caractéristiques courant /puissancemontrent une diminution du courant de seuil des lasers àcouplage complexe en comparaison de leur équivalent àcouplage par les pertes, et un comportement monomodeplus robuste et plus systématique en comparaison de leuréquivalent à couplage par l’indice.Les variations d’indice réelle et imaginaire dans les cavitésont été mesurés à l’aide d’un laser externe.La résistance au retour optique de nos lasers a également étéétudiée. Les résultats montrent une corrélation entre latolérance au retour optique et le déphasage des réseauxd’indice et de pertes, sans montrer d’améliorationsignificative de cette résistance par rapport aux lasers DFBà couplage par l’indice.Ce premier « véhicule test » sur l’application de la symétriePT aux lasers à contre réaction répartie a permis d’obtenirdes perspectives encourageantes quant à l’amélioration desperformances des technologies existantes. Ce travailconforte l’intérêt de ce concept pour la conception de lasersDFB tolérant au feedback et leur intégration dans unsystème laser-modulateur fonctionnant sur la même base.

The development of photonics during the pastdecades, enabled by the advent of nanofabricationtechnologies, witnessed the appearance of new types ofartificial materials such as photonic crystals,metamaterials, plasmonic circuits, and more recently the socalled “PT symmetry” structures. The characteristic featureof this new type of artificial structures is that though theyare described by non-Hermitian Hamiltonians theireigenvalues can still be real. In optics, several physicalphenomena are known to obey equations that are formallyequivalent to that of Hamiltonians in quantum mechanics.During this work, we investigated the design, fabricationand characterization of complex-coupled DFB lasers, withthe intent to apply Parity-Time (PT) symmetry to apractical device. The mode selectivity inside the cavity isbrought by the combination of a gain-coupled and indexcoupledBragg grating, under the form of respectively acorrugated waveguide and a metallic absorbing surfacegrating.Through the simulation of the mode evolution insideconventional DFB lasers and complexe-coupled DFBlasers using Ables matrix method, the advantages ofefficient mode filtering while keeping a low thresholdcurrent was observed. The specific phase shift of a quarterperiod, matching the PT-symmetric configuration, is foundto show highly asymmetric mode selection, with unidirectionalamplification in reflection.Index, gain and complex-coupled DFB lasers with differentphase shifts between loss and index grating profiles werefabricated, using photonics integrated circuits fabricationbuilding blocks: electron beam lithography and inducedcoupled plasma dry etching to name but a few.The characterization of the fabricated lasers shows areduction in threshold compared to equivalent third ordergain-coupled DFB lasers, and improved monomodeoperation and yield compared to third order index-coupledDFB lasers.Real and imaginary parts of the index modulation as wellas reflection spectral response was investigated by externaloptical probing of the laser cavities.The resistance of the CC DFB lasers to external opticalfeedback was studied. If results show an apparentcorrelation between the gratings phase shift and thefeedback resistance, but no significant improvement wasfound with regards to IC DFB lasers.This first milestone on the application of PT-symmetry tothe design and fabrication of DFB lasers provide interestingprospects on the improvement of existing technologies.This work reinforces the interest of this concept for thedesign of feedback tolerant DFB lasers, and theirintegration in an all PT-symmetric laser-modulator system.; Le développement des systèmes photoniques aucours des dernières décennies, rendu possible parl’évolution des technologies de nanofabrication, a vul’apparition de nouveaux matériaux synthétiques tels queles cristaux photoniques, les métamatériaux, les plasmonsde surface, et plus récemment les structures dites « àsymétrie Parité-Temps ». La caractéristique de ces derniersmatériaux synthétiques est que bien qu’ils soient décrits parun Hamiltonien non-Hermitien, leurs valeurs proprespeuvent toutefois être réelles. En optique plusieursphénomènes physiques sont connus pour la ressemblancedes équations les décrivant, avec l’expression de ce typed’Hamiltonien en mécanique quantique. C’est le cas deséquations de modes couplés dans les lasers DFB.Ce travail de thèse a porté sur la conception, fabrication etétude de lasers DFB à couplage complexe, dans l’optiqued’appliquer le principe de symétrie Parité Temps (PT) à uncomposant fonctionnel. Ces lasers sont combinent un réseaupar l’indice et par les pertes, avec un déphasage spécifique.La simulation des modes dans la cavité, effectuée parméthode matricielle de Ables, a dévoilé l’avantageuxfiltrage apporté par les lasers DFB à couplage complexe, engardant un seuil faible. Le cas spécifique d’un déphasaged’un quart de période entre les deux réseaux, correspondantà une condition de symétrie PT, induit des effetsunidirectionnels d’amplification en réflexion.Des lasers DFB à couplage par l’indice, par les pertes et àcouplage complexe avec différentes phases entre les réseauxont été fabriqués selon les techniques courantes deréalisation de circuits photonique intégrés : lithographieélectronique et gravure ICP notamment.Les mesures de caractéristiques courant /puissancemontrent une diminution du courant de seuil des lasers àcouplage complexe en comparaison de leur équivalent àcouplage par les pertes, et un comportement monomodeplus robuste et plus systématique en comparaison de leuréquivalent à couplage par l’indice.Les variations d’indice réelle et imaginaire dans les cavitésont été mesurés à l’aide d’un laser externe.La résistance au retour optique de nos lasers a également étéétudiée. Les résultats montrent une corrélation entre latolérance au retour optique et le déphasage des réseauxd’indice et de pertes, sans montrer d’améliorationsignificative de cette résistance par rapport aux lasers DFBà couplage par l’indice.Ce premier « véhicule test » sur l’application de la symétriePT aux lasers à contre réaction répartie a permis d’obtenirdes perspectives encourageantes quant à l’amélioration desperformances des technologies existantes. Ce travailconforte l’intérêt de ce concept pour la conception de lasersDFB tolérant au feedback et leur intégration dans unsystème laser-modulateur fonctionnant sur la même base.

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The aim is to design the appropriate photonic structures, with targeted geometrical characteristics and periodic properties, to precisely modify the dynamics of light propagation. The study was based theoretically and numerically on the paraxial equation of electromagnetism and the approximate relations of the tight-binding model. In particular, through the description of the discrete model defined by the modes of the individual waveguides in the lattice, we reach an appropriate equivalence with the Dirac equation, which describes the dynamics of the fundamental relativistic free-space particles. In addition, through the appropriate modification of the properties of the individual waveguides, an attempt was made to break the basic symmetries of the quantum model and attain equivalence with a generalized form of the Dirac equation. This leads to the appearance of non-trivial phenomena such as the Dirac type II cones in the dispersion diagram. The structures designed for this purpose demonstrated great adaptability, and proved themselves very flexible in their ability to control all effective coupling terms in the discrete model and by extension all free variables of the generalised quantum model. Various phenomena are studied, both in continuous and infinite lattices as well as in terminated structures where the existence of edge modes is identified. The properties of these modes are extensively investigated and two notable effects are investigated, the ability to control the extend of the modes in the first Brillouin zone and the magnitude of dispersion for the Type-II case. The main objective of the final chapter is the incorporation of secondary characteristics through the theories of topology and PT symmetry. Through the appropriate splitting of the respective symmetries, both spatially in the propagation axis and temporally, phenomena such as zero damping in loss/gain structures and the appearance of unidirectional edge states emerge.

Fraunhofer light diffraction across a thin two-dimensional lattice of cold atoms subject to transverse hybrid modulations of two standing-wave crossed pump fields is seen to yield lopsided patterns of various degrees of symmetry. We show that one can fully restrain the diffraction of a weak incident probe to two diagonal or adjacent quadrants or even just to a single quadrant, depending on the phases of two standing-wave pumps and on the probe detuning. Different diffraction symmetries with respect to the axes or diagonals of the diffraction plane quadrants are interpreted here in terms of different out-of-phase interplay of absorption and dispersion periodic distributions, resulting from different combinations of Hermitian, $\mathcal{PT}$-symmetric, and non-Hermitian modulations.

Non-Hermitian quantum mechanics with parity-time (PT) symmetry is presently gaining great interest, especially within the fields of photonics and optics. Here, we give a brief overview of low-dimensional semiconductor nanodevices using the example of a quantum dot with input and output leads, which are mimicked by imaginary potentials for gain and loss, and how wave functions, particle flow, coalescence of levels and associated breaking of PT symmetry may be analysed within such a framework. Special attention is given to the presence of exceptional points and symmetry breaking. Related features for musical string instruments and 'wolf-notes' are outlined briefly with suggestions for further experiments.

The cascade of resonant topological structures with $\mathcal{PT}$-symmetry breaking is shown to emit laser light with a frequency-comb spectrum. We consider optically active topological Aubry-Andr\'e-Harper lattices supporting edge-modes at regularly spaced frequencies. When the amplified resonances in the $\mathcal{PT}$-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables to engineer the spectral features for specific applications. The robustness of the topological protection makes the system very well suited for a novel generation of compact frequency comb emitters for spectroscopy, metrology, and quantum information., Comment: 6 pages, 6 figures

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications. Here, we bridge this gap and present an experimental investigation of an active topological photonic system, demonstrating a topological hybrid silicon microlaser array respecting the charge-conjugation symmetry. The created new symmetry features favour the lasing of a protected zero mode, where robust single-mode laser action in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid implemented on a silicon-on-insulator substrate, and is thereby readily suitable for integrated silicon photonics with applications in optical communication and computing., Topological effects, first observed in condensed matter physics, are now also studied in optical systems, extending the scope to active topological devices. Here, Zhao et al. combine topological physics with non-Hermitian photonics, demonstrating a topological microlaser on a silicon platform.

International audience; Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT symmetry of the Hamiltonians enables us to design configurations which perfectly absorb at multiple frequencies. Broadened and flat perfect absorption is predicted at the exceptional point of PT-symmetry breaking while, for a particular case, absorption is enhanced with the use of gain. The aforementioned phenomena are illustrated for acoustic scattering through Helmholtz resonators revealing how tailoring the non-Hermiticity of acoustic metamaterials leads to novel mechanisms for enhanced absorption.

We report on the numerical analysis of intensity dynamics of a pair of mutually coupled, single-mode semiconductor lasers that are operated in a configuration that leads to features reminiscent of parity&ndash, time symmetry. Starting from the rate equations for the intracavity electric fields of the two lasers and the rate equations for carrier inversions, we show how these equations reduce to a simple 2 &times, 2 effective Hamiltonian that is identical to that of a typical parity&ndash, time (PT)-symmetric dimer. After establishing that a pair of coupled semiconductor lasers could be PT-symmetric, we solve the full set of rate equations and show that despite complicating factors like gain saturation and nonlinearities, the rate equation model predicts intensity dynamics that are akin to those in a PT-symmetric system. The article describes some of the advantages of using semiconductor lasers to realize a PT-symmetric system and concludes with some possible directions for future work on this system.

As an elementary processor of neural networks, a neuron performs exotic dynamic functions, such as bifurcation, repetitive firing, and oscillation quenching. To achieve ultrafast neuromorphic signal processing, the realization of photonic equivalents to neuronal dynamic functions has attracted considerable attention. However, despite the nonconservative nature of neurons due to energy exchange between intra‐ and extra‐cellular regions through ion channels, the critical role of non‐Hermitian physics in the photonic analogy of a neuron has been neglected. Here, a neuromorphic non‐Hermitian photonic system ruled by parity‐time symmetry is presented. For a photonic platform that induces the competition between saturable gain and loss channels, dynamical phases are classified with respect to parity‐time symmetry and stability. In each phase, unique oscillation quenching functions and nonreciprocal oscillations of light fields are revealed as photonic equivalents of neuronal dynamic functions. The proposed photonic system for neuronal functionalities will become a fundamental building block for light‐based neural signal processing.

Nanoteknoloji; 1-100 nanometre mertebesinde olan yapıları inceleyen, çeşitli bilim ve mühendislik dallarını kapsayan bir disiplindir. Yapı boyutsal olarak küçüldükçe; yüzey/hacim oranı ve malzemenin kuantum etkileri artmakta ve dolayısıyla nanomalzemeler; alışılmadık fiziksel, kimyasal, biyolojik ve optik özellikler sergileyebilmektedir. Nanoteknoloji alanındaki çalışmaların amacı da; nanoboyutlu yapıların kullanılmasıyla fonksiyonel, verimli ve üstün özelliklere sahip cihazlar ve entegre devreler üretebilmektir. Suni nanoyapılardan olan, periyodik ve "Fotoniğin yarıiletkenleri" olarak da isimlendirilen Fotonik Kristaller (FK) ise; üstün optik özellikleri sayesinde nanoteknolojide yaygın olarak kullanılmaktadır. FK yapılarının simetrisinin düşürülmesi, alışılmadık optik özelliklerin gözlemlenmesini sağlamaktadır. FK tabanlı optik aygıtlara sıvı kristal infiltrasyonu ve bu hibrit yapıya harici voltaj uygulanması sayesinde; ayarlanabilir odak noktasına sahip optik lens, fotonik nanojet gibi fotonik entegre devrelerde önemli rolü olan aygıt tasarlamak mümkündür. Ayrıca Parite zaman simetri özelliği, FK yapılarında özellikle asimetrik ışık iletimi üzerine incelenen popüler konulardan biridir., Nanotechnology is a multi-disciplinary science and engineering deals with structures in 1-100 nanometer scale. Scaling the structure down provides to increase its surface/volume ratio and quantum effect and thus, nanostructures may exhibit extraordinary physical, chemical, biological and optical properties. The purpose of scientific studies in nanotechnology is to realize functional, efficient and outstanding featured devices and integrated circuits using nanostructures. Photonic Crystals from artificial nanostructures, also called periodic and "Semiconductors of photons" are widely used in nanotechnology due to their intriguing optical properties. Symmetry reduction in photonic crystals provides to observe intriguing optical properties. Liquid crystal infiltration into photonic crystal based optical devices and the external voltage excitation of such hybrid devices may provide the designs of tunable lenses and photonic nanojets. Furthermore, parity-time symmetry is another crucial effect especially studied about aymmetric light transmission in photonic crystal devices.

Coupled photonic systems satisfying parity-time symmetry (PTS) provide exibility to engineer the ow of light including non-reciprocal propagation, perfect laser-absorbers, and ultra-fast switching. Achieving the required index pro le for an optical system with ideal PTS, i.e. n(x) =n(-x)*, has proven to be difficult due to the challenge of controlling gain, loss and material dispersion simultaneously. Consequently, most research has focused on dilute or low gain optical systems where material dispersion is minimal. In this paper, we study a model system of coupled inorganic semiconductor waveguides with potentially high gain (>1,500 cm-1) and dispersion. Our analysis makes use of coupled mode theory's parameters to quantify smooth transitions between PTS phases under imperfect conditions. We find that the detrimental influence of gain-induced dispersion is counteracted and the key features of parity-time symmetric optical systems are recovered by working with non-identical waveguides and bias pumping of the optical waveguides. Our coupled mode theory results show excellent agreement with numerical solutions, proving the robustness of coupled mode theory in describing various degrees of imperfection in systems with PTS.

In optical experiments one-sided reflectionless (ORL) and coherent perfect absorption (CPA) are unusual scattering properties yet fascinating for their fundamental aspects and for their practical interest. Although these two concepts have so far remained separated from each other, we prove that the two phenomena are indeed strictly connected. We show that a CPA–ORL connection exists between pairs of points lying along lines close to each other in the 3D space-parameters of a realistic lossy atomic photonic crystal. The connection is expected to be a generic feature of wave scattering in non-Hermitian optical media encompassing, as a particular case, wave scattering in parity-time (PT) symmetric media.