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Recent studies on non-Hermitian optical systems having exceptional points (EPs) have revealed a host of unique characteristics associated with these singularities, including unidirectional invisibility, chiral mode switching and laser self-termination, to mention just a few examples. The vast majority of these works focused either on passive systems or active structures where the EPs were accessed below the lasing threshold, i.e. when the system description is inherently linear. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed and tracked above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning will impede the formation of an EP, here we demonstrate that this same detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the nonlinear EP in the lasing regime. Furthermore, unlike linear non-Hermitian systems, we find that the spectral location of EPs above laser threshold varies as a function of total pump power and can therefore be continuously tracked. Our work is a first step towards the realization of lasing EPs in more complex laser geometries, and enabling the enhancement of photonic local density of states through non-Hermitian symmetries combined with nonlinear interactions in coupled laser arrays.

We demonstrate the universality of Rayleigh-Jeans distribution in nonlinear multimoded optical systems, regardless of the type of nonlinearity or the existence of wave mixing.

The realization of higher-order exceptional points (HOEPs) can lead to orders of magnitude enhancement in light-matter interactions beyond the current fundamental limits. Unfortunately, implementing HOEPs in the existing schemes is a rather difficult task, due to the complexity and sensitivity to fabrication imperfections. Here we introduce a hierarchical approach for engineering photonic structures having HOEPs that are easier to build and more resilient to experimental uncertainties. We demonstrate our technique by an example that involves parity-time (PT) symmetric optical microring resonators with chiral coupling among the internal optical modes of each resonator. Interestingly, we find that the uniform coupling profile is not required to achieve HOEPs in this system -- a feature that implies the emergence of HOEPs from disorder and provides resilience against some fabrication errors. Our results are confirmed by using full-wave simulations based on Maxwell's equation in realistic optical material systems.

We investigate spontaneous emission from a quantum emitter located within the mode volume of a microring resonator that features chiral exceptional points. We show that this configuration offers enough degrees of freedom to exhibit a full control to either enhance or suppress the emission process. Particularly, we demonstrate that the Purcell factor can be enhanced by a factor of two beyond its value in an identical microring operating at a diabolic point. Our conclusions, which are derived using a non-Hermitian Hamiltonian formalism, are confirmed by employing full-wave simulations of realistic photonic structures and materials. Our results offer a straightforward route to improve the performance of single photon sources using current photonics technology without the need for building optical resonators with ultrahigh quality factors or nanoscale volumes.

Light trapping and radiation process from linear reciprocal photonic resonators is one of the fundamental processes in optical science and engineering. Recently, the concept of coherent virtual absorption (CVA) of light was introduced and investigated for planar and cylindrical optical structures. The key feature of CVA is that by engineering the time-dependence of the excitation waveform, one can temporarily store all the input energy into the optical structure without any leakage. Here we further explore this novel concept in integrated photonic setups made of microring resonators. By using coupled-mode theory (CMT), we derive an analytical expression for CVA in this platform. This in turn allows us to make the connection with the notion of coherent perfect absorption (CPA) as well as extending our analysis to active resonators (having optical gain). We next provide a physical insight into this process by using a simple model made of cascaded beam splitters. Importantly, we confirm our results using a full-wave analysis of realistic material systems. Finally, we discuss the limitation on the CVA process due to waveform mismatch and nonlinear effects.

The finite gain-bandwidth product is a fundamental figure of merit that restricts the operation of standard optical amplifiers. In microcavity setups, this becomes a serious problem due to the narrow bandwidth of the device. Here we introduce a new design paradigm based on exceptional points, that relaxes this limitation and allows for building a new generation of optical amplifiers that exhibits better gain-bandwidth scaling relations. Importantly, our results can be extended to other physical systems such as acoustics and microwaves.

Wireless sensors based on micromachined tunable resonators are important in a variety of applications, ranging from medical diagnosis to industrial and environmental monitoring. The sensitivity of these devices is, however, often limited by their low quality (Q) factor. Here, we introduce the concept of isospectral party–time–reciprocal scaling (PTX) symmetry and show that it can be used to build a new family of radiofrequency wireless microsensors exhibiting ultrasensitive responses and ultrahigh resolution, which are well beyond the limitations of conventional passive sensors. We show theoretically, and demonstrate experimentally using microelectromechanical-based wireless pressure sensors, that PTX-symmetric electronic systems share the same eigenfrequencies as their parity–time (PT)-symmetric counterparts, but crucially have different circuit profiles and eigenmodes. This simplifies the electronic circuit design and enables further enhancements to the extrinsic Q-factor of the sensors.

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices., 20 page, 5 figures

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Higher-order topological states that are robust against certain classes of disorder and pinned to lattice corners are now observed in photonics platforms.

Nearly one century after the birth of quantum mechanics, parity–time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity–time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously. General concepts and recent developments of parity–time symmetry in classical photonics are reviewed.

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement-specifically, a ternary, parity-time-symmetric photonic laser molecule-with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

Significant efforts have been dedicated to engineering optical systems with predefined, excitation-dependent light absorption. An important concept along this line is that of exceptional points which allow for engineering directional light absorbing schemes. Current systems, however, do not lend themselves to easy design criterion or robust experimental realization. Here we demonstrate that an optical microring resonator coupled to a waveguide terminated with a mirror supports a chiral exceptional surface that can be used as a platform for tailoring directional light absorption in a straightforward fashion. We further demonstrate that this configuration can be used to implement a unidirectional coherent perfect absorber with controllable differential loss by tuning only a single parameter.

Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge-a feature that was exploited for several applications. Here, we theoretically introduce and experimentally demonstrate a new class of parity-time symmetric systems [implemented using radio frequency (rf) circuits] that combine EPs with another type of mathematical singularity associated with the poles of complex functions. These nearly divergent exceptional points can exhibit an unprecedentedly large eigenvalue bifurcation beyond those obtained by standard EPs. Our results pave the way for building a new generation of telemetering and sensing devices with superior performance.

Non-Hermitian exceptional points (EPs) represent a special type of degeneracy where not only the eigenvalues coalesce, but also the eigenstates tend to collapse on each other. Recent studies have shown that in the presence of an EP, light-matter interactions are profoundly modified, leading to a host of novel optical phenomena ranging from enhanced sensitivity to chiral light transport. As of now, however, in order to stabilize a system at the vicinity of an exceptional point, its related parameters must be carefully tuned and/or continuously controlled. To overcome this limitation, here we introduce a new family of broadband exceptional points based on unidirectional coupling, implemented by incorporating an Sshaped waveguide in a microring cavity. In active settings, the resulting unidirectionality exhibits unprecedented resilience to perturbations, thus providing a robust and tunable approach for directly generating beams with distinct orbital angular momentum (OAM). This work could open up new possibilities for manipulating OAM degrees of freedom in applications pertaining to telecommunications and quantum computing, while at the same time may expand the notions of non-Hermiticity in the orbital angular momentum space.

Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Current research efforts focus only on systems supporting isolated EPs characterized by increased sensitivity to external perturbations, which makes them potential candidates for building next generation optical sensors. On the downside, this feature is also the Achilles heel of these devices: they are very sensitive to fabrication errors and experimental uncertainties. To overcome this problem, we introduce a new design concept for implementing photonic EPs that combine the robustness required for practical use together with their hallmark sensitivity. Particularly, our proposed structure exhibits a hypersurface of Jordan EPs embedded in a larger space, and having the following peculiar features: (1) A large class of undesired perturbations shift the operating point along the exceptional surface (ES), thus, leaving the system at another EP which explains the robustness; (2) Perturbations due to back reflection or backscattering force the operating point out of the ES, leading to enhanced sensitivity. Importantly, our proposed geometry is relatively easy to implement using standard photonics components and the design concept can be extended to other physical platforms such as microwave or acoustics.

Recent years have seen a tremendous progress in the theory and experimental implementations of non-Hermitian photonics, including all-lossy optical systems as well as parity-time symmetric systems consisting of both optical loss and gain. This progress has led to a host of new intriguing results in the physics of light–matter interactions with promising potential applications in optical sciences and engineering. In this comment, we present a brief perspective on the developments in this field and discuss possible future research directions that can benefit from the notion of non-Hermitian engineering. The concept of non-Hermitian parity-time reversal symmetry in optics has given rise to a vast amount of research aimed at exploring some of the exotic features displayed by photonics systems. The authors present a brief account of the state-of-the-art on non-Hermitian photonics and provide their perspective on the topic.

The development of on-chip optical isolators for integrated photonic circuits has been actively pursued for several decades now, especially since the advent of optical-fiber telecommunication. This article reports the experimental realization, practical implementation, and performance of a $t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ $e\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}e\ensuremath{-}s\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}e$ $i\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r$, based on the Su-Shrieffer-Heeger model in the optical regime. Such isolators have been predicted to deliver superior isolation ratios (up to -50 dB at telecom wavelengths), due to the existence of a topological edge state in the forward propagation direction, and its destruction in the reverse direction via the magneto-optical nonreciprocal phase-shift effect.

Supersymmetric transformations aim to relate boson and fermions, two different species of particles, and their interactions. In quantum mechanics, the mathematical framework of SUSY can be used to design isospectral potentials. By virtue of the isomorphism between Schrodinger and wave equations, one can use such transformations for designing novel optical systems. In this talk, we review the recent developments in the general area of supersymmetric optics and photonics. We will also discuss the possibility of generating high brightness coherent light in supersymmetric laser arrays.

Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However, present quasi one dimensional (1D) designs, such as the Su–Schrieffer–Heeger and Rice–Mele models, support only a limited number of nontrivial phases due to restrictions on dispersion band engineering. Here, a flexible topological photonic lattice on a silicon photonic platform is experimentally demonstrated that realizes multiple topologically nontrivial dispersion bands. By suitably setting the couplings between the 1D waveguides, different lattices can exhibit the transition between multiple different topological phases and allow the independent realization of the corresponding edge states. Heterodyne measurements clearly reveal the ultrafast transport dynamics of the edge states in different phases at a femtosecond scale, validating the designed topological features. The study equips topological models with enriched edge dynamics and considerably expands the scope to engineer unique topological features into photonic, acoustic, and atomic systems.

Stability through symmetry A common route to get more light out of a laser system is to couple multiple lasers to form an array. However, instabilities owing to cross-talk and interference between different modes of individual cavities is generally detrimental to performance and could ultimately be damaging to the laser cavities. Hokmabadi et al. applied notions derived from supersymmetry, a theory developed in high-energy physics to describe the make-up and properties of particles, to design a stable array of semiconductor lasers (see the Perspective by Kottos). Based on symmetry arguments, the method is scalable and could provide a practical platform to design and develop complex photonic systems. Science , this issue p. 623 ; see also p. 586

We present a novel design for on-chip integrated saturable absorbers and optical limiters based on the so-called Jx lattice, and demonstrate its practical feasibility in realistic material platforms such as femtosecond laser-written waveguide arrays.

Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of ∼ 9 d B for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ( ∼ 600 n m ). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventional silicon-photonics-based four-wave mixing process.

An introduction is provided to the feature issue of Optical Materials Express on Photonic Topological Materials.

“Invited” was added to two reviews in this feature issue [Opt. Mater. Express 11(4), 1119 (2021)10.1364/OME.414890] and [Opt. Mater. Express 11(4), 1292 (2021)10.1364/OME.417392].

Chiral exceptional points (CEPs) have been shown to emerge in traveling wave resonators via asymmetric back scattering from two or more nano-scatterers. Here, we provide a new perspective on the formation of CEPs based on the coupled oscillator model. Our approach provides an intuitive understanding for the modal coalescence that signals the emergence of CEPs, and emphasizes the role played by dissipation throughout this process. In doing so, our model also unveils an otherwise unexplored connection between CEPs and other types of exceptional points associated with parity-time symmetric photonic arrangements. In addition, our model also explains qualitative results observed in recent experimental work involving CEPs. Importantly, the tight-binding nature of our approach allows us to extend the notion of CEP to discrete photonics setups that consist coupled resonator and waveguide arrays, thus opening new avenues for exploring the exotic features of CEPs in conjunction with other interesting physical effects such as nonlinearities and topological protections., 7 pages, 2 figures

Non-Hermitian singularities are ubiquitous in non-conservative open systems. Owing to their peculiar topology, they can remotely induce observable effects when encircled by closed trajectories in the parameter space. To date, a general formalism for describing this process beyond simple cases is still lacking. Here we develop a general approach for treating this problem by utilizing the power of permutation operators and representation theory. This in turn allows us to reveal a surprising result that has so far escaped attention: loops that enclose the same singularities in the parameter space starting from the same point and traveling in the same direction, do not necessarily share the same end outcome. Interestingly, we find that this equivalence can be formally established only by invoking the topological notion of homotopy. Our findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics., A general description of observable effects induced by non-Hermitian singularities is complex. Here, Zhong et al. develop such a formalism, showing that loops around the same exceptional point starting from the same point in the same direction do not need to have the same outcome.

We show that the theoretical framework linking exceptional points (EPs) to phase transitions in parity-time (PT) symmetric Hamiltonians is incomplete. Particularly, we demonstrate that the application of the squaring operator to a Jx PT lattice dramatically alter the topology of its Riemann surface, eventually resulting in a system that can cross an EP without undergoing a symmetry breaking. We elucidate on these rather surprising results by invoking the notion of phase diagrams in higher dimensional parameter space. Within this perspective, the canonical PT symmetry breaking paradigm arises only along certainprojections of the Riemann surface in the parameter space.

A multimode, chaotic, and broadband emission is an undesired characteristic of laser arrays which is an adverse effect of supermodes in coupled waveguides. Employing optical supersymmetry, we experimentally demonstrate single mode lasing in arrays of supersymmetric lasers where a superpatner array eliminates undesired lasing modes.

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time ($\mathcal{PT}$) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other physical systems as well.

We introduce a new design concept for non-Hermitian photonic that combine robustness with sensitivity and demonstrate its utility for sensing applications.

We investigate the extreme dynamics of non-Hermitian photonic systems near higher order exceptional points (EP) and we show that the maximum possible power amplification follows a power-law dependence on the order of the EP.

We theoretically investigate the problem of localization control of few-photon states in driven-dissipative parity-symmetric photonic molecules. We show that a quantum feedback loop can utilize the information of the spontaneously-emitted photons from each cavity to induce asymmetric photon population in the system, while maintaining a balanced pump that respects parity symmetry. To better understand the system's behaviour, we characterize the degree of asymmetry as a function of the coupling between the two optical cavities. Contrary to intuitive expectations, we find that in some regimes the coupling can enhance the population asymmetry. We also show that these results are robust against experimental imperfections and limitations such as detection efficiency., Comment: 16 pages with appendices, 5 figures

Multimode emission adversely affects phased-locked laser arrays resulting in chaotic behaviors. Utilizing optical supersymmetry, we experimentally demonstrate a single mode laser array where a superpartner array eliminates undesired higher order transverse modes.

The introduction of parity-time (PT) symmetry in optics and photonics has initiated intense activities exploring the exotic properties of these structures, eventually leading to the more general notion of non-Hermitian photonics. Efforts to understand the behavior of these systems have revealed a host of distinct features originating from the unusual character of their eigenspectra and eigenstates. These include for example, spontaneous symmetry breaking, bandgap merging, laser self-termination, unidirectional invisibility, and ultra-sensitivity to external perturbations. A central notion pertinent to all these effects is the concept of exceptional points (EPs). Also known as branch points, EPs are non-Hermitian spectral singularities that arise when two (or more) eigenvalues and their corresponding eigenstates become identical. While exceptional points of order two have been studied thoroughly at both the theoretical and experimental level, higher order EPs are attracting attention only recently. Here we discuss a systematic approach based on a recursive bosonic quantization scheme for generating discrete photonic networks that exhibit exceptional points of any arbitrary order. We also discuss the spectral properties and the extreme dynamics near these singularities as well as their physical implementation in various photonic platforms.

In vivo sensors can be interrogated using a wireless system locked to an exceptional point, providing a sensitivity beyond the capabilities of standard wireless readout schemes.

Student contribution: In recent years, non-Hermitian degeneracies, also known as exceptional points (EPs), have emerged as a new paradigm for engineering the response of optical systems. This class of degeneracies represents points in parameter space where the eigenvalues and their corresponding eigenvectors simultaneously coalesce [1,2]. Among the large set of non-conservative photonic systems, parity-time (PT) symmetric arrangements are of particular interest since they provide an excellent platform to study the physics and properties of non-Hermitian degeneracies [3,4]. So far, the abrupt nature of the phase transitions at EPs has led to a number of new functionalities such as loss-induced transparency [5], unidirectional invisibility [6,7], and single mode lasing [8-11]. In addition, it has been suggested that the bifurcation properties associated with second-order exceptional points can be utilized to achieve enhanced sensitivity in micro-resonator arrangements [11]. Of interest is to use even higher-order exceptional points that in principle could further amplify the effect of perturbations. While such higher-order singularities have been theoretically studied in a number of recent works [13,14], their experimental realization in the optical domain has so far remained out of reach. In this paper, for the first time, we show the emergence of third order exceptional points in ternary parity-time-symmetric coupled resonator lasers by judiciously designing the gain/loss distribution and coupling strengths following a recursive bosonic quantization procedure. Subsequently, the nature of the third order exceptional point is confirmed through the cubic root response of this ternary system to external perturbations. Our work may pave the way towards the utilization of higher order exceptional points in designing ultrasensitive photonic arrangements. References [1] W. D. Heiss, J. of Phys. A: Mathematical and Theoretical 45, 444016 (2012). [2] N. Moiseyev, Non-Hermitian Quantum Mechanics. (Cambridge University Press, 2011). [3] K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 103904 (2008). [4] C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010). [5] A. Guo et al., Phys. Rev. Lett. 103, 093902 (2009). [6] B. Peng et al., Nat. Phys. 10, 394 (2015). [7] A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012). [7] M. Miri, P. Likamwa, D. N. Christodoulides, Opt. Lett. 37, 764 (2012) [8] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Science 346, 975 (2014). [9] L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang, Science 346, 972 (2014). [11] H. Hodaei et al., Laser & Photon. Rev. 10, 494 (2016). [12] J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014). [13] G. Demange, and E.-M. Graefe, J. Phys. Math. Theor. 45, 25303 (2012). [14] M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A .Szameit, D.N. Christodoulides, Phys. Rev. A 90, 053817 (2014).

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.

We investigate two important aspects of PT symmetric photonic molecule lasers, namely the robustness of their single longitudinal mode operation against instabilities triggered by spectral hole burning effects, and the possibility of more versatile mode selectivity. Our results, supported by numerically integrating the nonlinear rate equations and performing linear stability analysis, reveals the following: (1) In principle a second threshold exists after which single mode operation becomes unstable, signaling multimode oscillatory dynamics, (2) For a wide range of design parameters, single mode operation of PT lasers having relatively large free spectral range (FSR) can be robust even at higher gain values, (3) PT symmetric photonic molecule lasers are more robust than their counterpart structures made of single microresonators; and (4) Extending the concept of single longitudinal mode operation based on PT symmetry in millimeter long edge emitting lasers having smaller FSR can be challenging due to instabilities induced by nonlinear modal interactions. Finally we also present a possible strategy based on loss engineering to achieve more control over the mode selectivity by suppressing the mode that has the highest gain (i.e. lies under the peak of the gain spectrum curve) and switch the lasing action to another mode.

We introduce a new type of synthetic saturable absorber based on quantum-inspired Jx photonic arrays. We demonstrate that the interplay between optical Kerr nonlinearity, interference effects and non-Hermiticity through radiation loss leads to a nonlinear optical filtering response with two distinct regimes of small and large optical transmissions. More interestingly, we show that the boundary between these two regimes can be very sharp. The threshold optical intensity that marks this abrupt "phase transition" and its steepness can be engineered by varying the number of the guiding elements. The practical feasibility of these structures as well as their potential applications in laser systems and optical signal processing are also discussed.