Manipulation of lasing modes in a circular-side octagonal microcavity laser with a spatially distributed current injection

We propose and demonstrate a circular-side octagonal microcavity (COM) semiconductor laser with a spatially distributed current injection for manipulating the lasing modes. There are two types of high-quality-factor whispering-gallery (WG) modes with distinct field patterns in a COM: the four-bounced quadrilateral modes and the eight-bounced octagonal modes. By designing two separated p-electrodes, the COM laser is divided into two regions that are pumped independently to select specific modes for lasing. The two types of WG modes lase simultaneously when the two regions are injected with equivalent currents. Degeneracy removal of the quadrilateral modes is observed in both simulation and experiment when the two regions are injected with inequivalent currents. The quadrilateral modes are suppressed when one of the two regions is un-injected or biased with a negative current, and single-octagonal-mode lasing is realized. The results show that the lasing modes can be efficiently manipulated with the spatially distributed current injection considering the distinct field patterns of different WG modes in the microcavities, which can promote the practical application of the microcavity lasers.

Active Mode Switching in Plasmonic Microlasers by Spatial Control of Optical Gain

The pursuit of miniaturized optical sources for on-chip applications has led to the development of surface plasmon polariton lasers (plasmonic lasers). While applications in spectroscopy and information technology would greatly benefit from the facile and active tuning of the output wavelength from such devices, this topic remains underexplored. Here, we demonstrate optically controlled switching between predefined wavelengths within a plasmonic microlaser. After fabricating Fabry-Pérot plasmonic cavities that consist of two curved block reflectors on an ultrasmooth flat Ag surface, we deposit a thin film of CdSe/Cd_xZn_1-xS/ZnS colloidal core/shell/shell nanoplatelets (NPLs) as the gain medium. Our cavity geometry allows the spatial and energetic separation of transverse modes. By spatially modulating the gain profile within this device, we demonstrate active selection and switching between four transverse modes within a single plasmonic laser. The fast buildup and decay of the plasmonic modes promises picosecond switching times, given sufficiently rapid changes in the structured illumination.

Tunable single-mode laser on thin film lithium niobate

The erbium-doped lithium niobate on insulator (LNOI) laser plays an important role in the complete photonic integrated circuits (PICs). Here, we demonstrate an integrated tunable whispering gallery single-mode laser (WGSML) by making use of a coupled microdisk and microring on LNOI. A 974 nm single-mode pump light can have an excellent resonance in the designed microdisk, which is beneficial to the whispering gallery mode (WGM) laser generation. The WGSML at 1560.40 nm with a maximum 31.4 dB side mode suppression ratio (SMSR) has been achieved. By regulating the temperature, the output power of the WGSML increases, and the central wavelength can be changed from 1560.30 to 1560.40 nm. Furthermore, 1560.60 and 1565.00 nm WGSMLs have been achieved by changing the coupling gap width between the microdisk and microring. We can also use the electro-optic effect of LNOI to obtain more accurate adjustable WGSMLs in further research.

Toward Microlasers with Artificial Structure Based on Single-Crystal Ultrathin Perovskite Films

A perovskite microlaser is potentially valuable for integrated photonics due to its excellent properties. The artificial microlasers were mostly made on polycrystalline films. Though a perovskite single crystal has significantly improved properties in comparison with its polycrystalline counterpart, an artificial microlaser based on single-crystal perovskite has been much less explored due to the difficulty in producing an ultrathin-single-crystal (UTSC) film. Here we show a device processing based on a perovskite UTSC film, confirming the high performance of the UTSC device with a quality factor of 1250. The single-crystal device shows 4.5 times the quality factor and 8 times the radiation intensity in comparison with its polycrystalline counterpart. The experiment first proved that hybrid perovskite microlasers with a subwavelength fine structure can be processed by focused ion beams (FIB). In addition, a wavelength-tunable distributed feedback (DFB) laser is demonstrated, with a tuning range of ∼4.6 nm. The research provides an easily applicable approach for perovskite photonic devices with excellent performance.

Work statistics in non-Hermitian evolutions with Hermitian endpoints

Non-Hermitian systems with specific forms of Hamiltonians can exhibit novel phenomena. However, it is difficult to study their quantum thermodynamical properties. In particular, the calculation of work statistics can be challenging in non-Hermitian systems due to the change of state norm. To tackle this problem, we modify the two-point measurement method in Hermitian systems. The modified method can be applied to non-Hermitian systems which are Hermitian before and after the evolution. In Hermitian systems, our method is equivalent to the two-point measurement method. When the system is non-Hermitian, our results represent a projection of the statistics in a larger Hermitian system. As an example, we calculate the work statistics in a non-Hermitian Su-Schrieffer-Heeger model. Our results reveal several differences between the work statistics in non-Hermitian systems and the one in Hermitian systems.

Continuous tuning of unidirectional emission wavelength by bending a notched-elliptical polymer microdisk

An approach of continuously tunable unidirectional emission through bending a notched-elliptical polymer microdisk is proposed. The characteristics of the bending-dependent action are carefully analyzed, and the resonance wavelength for unidirectional emission can be tuned continuously through bending the device. Such a whispering-gallery-mode microresonator enables unidirectional emission with ultra-low divergence, of which the emission efficiency and Q factor are stabilized, demonstrating the whole structure is robust and relatively insensitive within a certain bending angle range. A maximum resonance wavelength shift of ∼100 nm and Q factor of 1500 can be achieved with the total size of the microdisk less than 10 μm. This kind of microresonator is promising for applications in multilevel integrated photonics circuits and may open the door to new functionalities of resonator devices, from sensing to optical amplification.

Photonic analog of Mollow triplet with on-chip photon-pair generation in dressed modes

Making analogy with atomic physics is a powerful tool for photonic technology, witnessed by the recent development in topological photonics and non-Hermitian photonics based on parity-time symmetry. The Mollow triplet is a prominent atomic effect with both fundamental and technological importance. Here we demonstrate the analog of the Mollow triplet with quantum photonic systems. Photonic entanglement is generated with spontaneous nonlinear processes in dressed photonic modes, which are introduced through coherent multimode coupling. We further demonstrate the possibility of the photonic system to realize different configurations of dressed states, leading to modification of the Mollow triplet. Our work would enable the investigation of complex atomic processes and the realization of unique quantum functionalities based on photonic systems.

Coherent perfect absorption at an exceptional point

[Figure: see text].

Plasmonic topological metasurface by encircling an exceptional point

[Figure: see text].

Configurable Phase Transitions in a Topological Thermal Material

Diffusive nature of thermal transportation fundamentally restricts topological characteristics due to the absence of a sufficient parametric space with complex dimensionalities. Here, we create an orthogonal advection space with two advective pairs to reveal the unexplored topological transitions in thermal material. We demonstrate four types of configurable thermal phases, including the nontrivial dynamic-equilibrium distribution, nonchiral steplike π-phase transition, and another two trivial profiles related to the anti-parity-time symmetry nature. Our findings provide a recipe for realizing a topologically robust thermal system under arbitrary perturbations.

Direct Measurement of Topological Properties of an Exceptional Parabola

Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a discriminant number (DN) or the eigenvector holonomy that generates a Berry phase. The multiplicity of topological invariants also makes non-Hermitian topology richer than its Hermitian counterpart. Here, we study a parabola-shaped trajectory formed by EPs with both theory and acoustic experiments. By obtaining both the DNs and Berry phases through the measurement of eigenvalues and eigenfunctions, we show that the EP trajectory endows the parameter space with a nontrivial fundamental group. Our findings not only shed light on exotic non-Hermitian topology but also provide a route for the experimental characterization of non-Hermitian topological invariants.

Observation of exceptional points in helically structured thin films

Exceptional points (EPs) in the polarization space were observed in reflection on helically structured thin films. These films have form anisotropy at the nanoscale introduced through dynamic control of crystalline growth geometry by changing the orientation of the substrate with respect to the impinging vapor. They are simpler alternatives to metasurfaces, because they can be produced at low cost using conventional thin-film deposition techniques. The EPs were experimentally confirmed by eigenstate swapping on a closed circuit surrounding them and were predicted by numerical calculations. Reflective surfaces operating at an EP could be used to make ultrasensitive sensors.

Suppression and revival of single-cavity lasing induced by polarization-dependent loss

For most photonics devices and systems, loss is desperately averted, since it will increase the power consumption and degrade the performance. However, in some non-Hermitian systems, loss can induce a modal gain when the parity-time symmetry is broken, which offers a new way to manipulate the lasing of active cavities. Here we experimentally observe the counterintuitive phenomenon in a single laser cavity assisted by the polarization-dependent loss. A parity-time symmetric system is constituted by the two orthogonally polarized photonic loops in a single laser cavity, which can guarantee the consistency of two coupling loops. The measured output power of the cavity depends on the cross-polarization loss, which reveals virtually opposite relationships before and after the critical point. It provides a novel, to the best of our knowledge, understanding of polarization loss and shows great potential for lasing manipulation in a single cavity with polarization control.

Approaches to tuning the exceptional point of PT-symmetric double ridge stripe lasers

Electrically injected Parity-time (PT)-symmetric double ridge stripe semiconductor lasers lasing at 980 nm range are designed and measured. The spontaneous PT-symmetric breaking point or exceptional point (EP) of the laser is tuned below or above the lasing threshold by means of varying the coupling constant or the mirror loss. The linewidth of the optical spectrum of the PT-symmetric laser is narrowed, compared with that of traditional single ridge (SR) laser and double ridge (DR) laser. Furthermore, the far field pattern of the PT-symmetric laser with EP below the lasing threshold is compared with that of the PT-symmetric laser with EP above the lasing threshold experimentally. It is found that when the laser start to lase, the former is single-lobed while the latter is double-lobed. when the current continues to increase, the former develops into double lobe directly while the latter first develops into single lobe and then double lobe again.

Observation of Non-Bloch Parity-Time Symmetry and Exceptional Points

Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in nonunitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These "non-Bloch exceptional points" originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized PT-symmetry framework, and reveals the intriguing interplay between PT symmetry and non-Hermitian skin effect.

Single-mode characteristic of a supermode microcavity Raman laser

Microlasers in near-degenerate supermodes lay the cornerstone for studies of non-Hermitian physics, novel light sources, and advanced sensors. Recent experiments of the stimulated scattering in supermode microcavities reported beating phenomena, interpreted as dual-mode lasing, which, however, contradicts their single-mode nature due to the clamped pump field. Here, we investigate the supermode Raman laser in a whispering-gallery microcavity and demonstrate experimentally its single-mode lasing behavior with a side-mode suppression ratio (SMSR) up to 37 dB, despite the emergence of near-degenerate supermodes by the backscattering between counterpropagating waves. Moreover, the beating signal is recognized as the transient interference during the switching process between the two supermode lasers. Self-injection is exploited to manipulate the lasing supermodes, where the SMSR is further improved by 15 dB and the laser linewidth is below 100 Hz.

Nonlinear-dissipation-induced nonreciprocal exceptional points

Exceptional points (EPs) have revealed a lot of fundamental physics and promise many important applications. The effect of system nonlinearity on the property of EPs is yet to be well studied. Here, we propose an optical system with nonlinear dissipation to achieve a nonreciprocal EP. Our system consists of a linear whispering-gallery-mode microresonator (WGMR) coupling to a WGMR with nonlinear dissipation. In our system, the condition of EP appearance is dependent on the field intensity in the nonlinear WGMR. Due to the chirality of intracavity field intensity, the EPs and the transmission of the system can be nonreciprocal. Our work may pave the way to exploit nonreciprocal EP for optical information processing.

Designing plasmonic exceptional points by transformation optics

Exceptional points (EPs) have been shown to be useful in bringing about sensitive optical properties based on non-Hermitian physics. For example, they have been applied in plasmonics to realize nano-sensing with extreme sensitivity. While the exceptional points are conventionally constructed by considering parity-time symmetric or anti-parity-time symmetric media, we theoretically demonstrate the possibility of generating a series of non-Hermitian systems by transforming a seed system with conventional parity-time symmetry within the transformation optics framework. The transformed systems do not possess PT-symmetry with a conventional parity operator after a spatial operation, i.e. hidden from conventional sense, but are equipped with exceptional points and phase transitions, hinting an alternative method to design non-Hermitian plasmonic systems with sensitive spectra or eigenmodes.

Non-Hermitian semi-Dirac semi-metals

Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points (EPs) originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems.

Dynamically Encircling an Exceptional Point in a Real Quantum System

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our Letter reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.

Controlled single-mode emission in quantum dot micro-lasers

In this paper, we demonstrate an efficient and easy fabrication method for whispering-gallery-mode (WGM) manipulation and report the first electrically driven single-mode quantum dot micro-ring (QDMR) lasers. Using self-assembled InAs/InAlGaAs QD active layers with deeply etched azimuthal gratings, continuous-wave (CW) lasing with controllable single-mode emission wavelengths covering 1300 nm to 1370 nm has been achieved. A record-high side-mode-suppression-ratio (SMSR) value of 49 dB is obtained. These QDMR lasers exhibit excellent single-mode lasing stabilities over the current and temperature tuning range with a thermal tunability of 0.092 nm/°C. The concept is applicable to other wavelength bands depending on the gain spectrum, demonstrating a feasible solution in realizing energy-efficient and densely integrated photonic building blocks.

Active mode selection by defects in lithium niobate on insulator microdisks

Whispering gallery mode (WGM) optical microcavities are important building blocks in photonic integrated circuits. Operation of such cavities on specific lower- or higher- order transverse modes has much interest in application perspectives. Here, we demonstrate active mode selection by introducing defects in lithium niobate on insulator microdisks. A focused ion beam is applied to precisely inscribe nano slits into the perimeter of the microdisk. The transmission spectra can be significantly thinned out without severe quality factor degradation. Either fundamental or high-order transverse WGMs can be retained by properly designing the size and location of the defects. The approach may have promising applications in single-mode lasing and nonlinear optics.

Tuning of Two-Dimensional Plasmon-Exciton Coupling in Full Parameter Space: A Polaritonic Non-Hermitian System

Non-Hermitian photonic systems with gains and/or losses have recently emerged as a powerful approach for topology-protected optical transport and novel device applications. To date, most of these systems employ coupled optical systems of diffraction-limited dielectric waveguides or microcavities, which exchange energy spatially or temporally. Here, we introduce a diffraction-unlimited approach using a plasmon-exciton coupling (polariton) system with tunable plasmonic resonance (energy and line width) and coupling strength. By designing a chirped silver nanogroove cavity array and coupling a single tungsten disulfide monolayer with a large contrast in resonance line width, we show the tuning capability through energy level anticrossing and plasmon-exciton hybridization (line width crossover), as well as spontaneous symmetry breaking across the exceptional point at zero detuning. This two-dimensional hybrid material system can be applied as a scalable and integratable platform for non-Hermitian photonics, featuring seamless integration of two-dimensional materials, broadband tuning, and operation at room temperature.

Single-mode lasing of CsPbBr3 perovskite NWs enabled by the Vernier effect

Inorganic lead halide perovskite (CsPbX3, X = Cl, Br, I) NWs (NWs) have been employed in lasers due to their intriguing attributes of tunable wavelength, low threshold, superior stability, and easy preparation. However, current CsPbX3 NW lasers usually work in a multi-mode modal, impeding their practical applications in optical communication due to the associated false signaling. In this work, high-performance single-mode lasing has been demonstrated by designing and fabricating coupled cavities in the high-quality single-crystal CsPbBr3 NWs via the focused ion beam (FIB) milling approach. The single-mode laser shows a threshold of 20.1 μJ cm-2 and a high quality factor of ∼2800 profiting from the Vernier effect, as demonstrated by the experiments and finite-different time-domain (FDTD) simulations. These results demonstrate the promising potentials of the CsPbX3 NW lasers in optical communication and integrated optoelectronic devices.

Topological mode switching in modulated structures with dynamic encircling of an exceptional point

Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with time-driven elasticity and viscosity. Topological mode switching with robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour of topological mode switching.

Parity-time symmetric frequency-tunable optoelectronic oscillator based on a Si3N4 microdisk resonator

The optoelectronic oscillator (OEO) generates low-phase noise and high-frequency microwave signals thanks to a high Q-factor cavity with long and low-loss fiber delay. Traditionally, for the desired mode selection from the ultradense cavity modes, a narrowband electrical filter is needed, whose frequency tuning is very limited. On the other hand, for a tunable OEO offered by a microwave photonic filter (MPF), a paradox existed between the large number of cavity modes and the wide MPF bandwidth. Here, we achieve a tunable OEO using the mode-selection mechanism of parity-time symmetry, which overcomes the paradox. A high Q-factor silicon nitride microdisk resonator (Si₃N₄ MDR) is introduced to achieve frequency filtering and tuning. Moreover, the experimental results reveal that the tunable OEO generates a signal range from 3 GHz to 20 GHz with a phase noise about -120dBc/Hz at a 10 kHz offset frequency.

Experimental Determination of PT-Symmetric Exceptional Points in a Single Trapped Ion

Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.

Controlling wave fronts with tunable disordered non-Hermitian multilayers

Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices.

Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre

The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has recently drawn a great deal of attention. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. So far, these principles have been implemented at the expense of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of single-mode telecommunication fibre, using a setup consisting of off-the-shelf components. Two propagating signals are amplified and coupled through stimulated Brillouin scattering, enabling exquisite control over the interaction-governing non-Hermitian parameters. Singular response to small-scale variations and topological features arising around the exceptional point are experimentally demonstrated with large precision, enabling robustly enhanced response to changes in Brillouin frequency shift.

Extraordinary wave modes in purely imaginary metamaterials beyond the critical angle

When waves are incident from a high-index medium to a low one, total reflection occurs commonly for the incidence beyond the critical angle. However, this common sense is broken by a purely imaginary metamaterial (PIM), which also supports a real refraction index yet with pure loss and gain elements in their permittivity and permeability. We find that even beyond the critical angle of a lower-index PIM slab, some extraordinary wave modes including laser, anti-laser, perfect attenuator and perfect amplifier can appear. The general conditions of these wave modes are theoretically given out and the underlying mechanisms are revealed. Also, we study the influence of incident polarizations, geometric thickness and the parameters of the PIM slab on these extraordinary wave modes, with more wave propagation behaviors discovered.

Single-Mode Semiconductor Nanowire Lasers With Coupled Cavities

Semiconductor nanowires are one of the most fascinating topics over the past few decades. As miniaturized coherent light sources, semiconductor nanowires have been attracting tremendous attention in recent years for scientific and technological interest as potential ultra-compact, low cost, high efficiency, and low power consumption. Among different types of lasers, one-dimensional nanowires are of great interest as a promising material for next-generation nanophotonics and nanoelectronics applications due to their unique optical and electrical properties. Semiconductor nanowire lasers with single-mode output are vital in a variety of practical applications ranging from signal processing, spectroscopy, displays, optical sensing, on-chip communications, and biological studies. This article reviews the basic technology and research progress of single-mode semiconductor nanowire lasers. Afterward, the key methods and development of the different types of coupling to achieved single-mode laser output are elaborated. Finally, the challenges faced by each scheme are summarized.

Knots and Non-Hermitian Bloch Bands

Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian (NH) Hamiltonians with separable bands. A Z_{2} knot invariant, the global biorthogonal Berry phase Q as the sum of the Wilson loop eigenphases, is proved to be equal to the permutation parity of the NH bands. We show the transition between two phases characterized by distinct knots occur through exceptional points and come in two types. We further develop an algorithm to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and propose a scheme to probe the knot structure via quantum quench. The theory and algorithm are demonstrated by model Hamiltonians that feature, for example, the Hopf link, the trefoil knot, the figure-8 knot, and the Whitehead link.

Recent advances in nanocavities and their applications

High quality factor and small mode volume in nanocavities enable the demonstration of efficient nanophotonic devices with low power consumption, strong nonlinearity, and high modulation speed, due to the strong light-matter interaction. In this review, we focus on recent state-of-the-art nanocavities and their applications. We introduce single nanocavities including semiconductor nanowires, plasmonic cavities, and nanostructures based on quasi-bound states in the continuum (quasi-BIC), for laser, photovoltaic, and nonlinear applications. In addition, nanocavity arrays with unique feedback mechanisms, including BIC cavities, parity-time symmetry coupled cavities, and photonic topological cavities, are introduced for laser applications. These various cavity designs and underlying physics in single and array nanocavities are useful for the practical implementation of promising nanophotonic devices.

One-Way Zero Reflection in an Insulator-Metal-Insulator Structure Using the Transfer Matrix Method

We numerically demonstrate one-way zero reflection using the transfer matrix method. Using simulations, we adjusted the thickness of SiO2 layers in a simple SiO2-Au-SiO2 layer structure. We found two solutions, 47 nm-10 nm-32 nm and 71 nm-10 nm-60 nm, which are the thicknesses for one-way zero reflection at a wavelength of 560 nm. We confirmed it with reflection spectra, where reflectance is zero for forwardly incident light and 2.5% for backwardly incident light at the wavelength 560 nm, and thickness 47 nm-10 nm-32 nm.

Experimental Investigation of Quantum PT-Enhanced Sensor

PT-symmetric theory is developed to extend quantum mechanics to a complex region, but it wins its great success first in classical systems, for example, optical waveguides and electric circuits, etc., because there are so many counterintuitive phenomena and striking applications, including unidirectional light transport, PT-enhanced sensors (one kind of exceptional-point-based sensor), and wireless power transfer. However, these phenomena and applications are mostly based on the ability to approach a PT-symmetric broken region, which makes it difficult to transfer them to the quantum regime, since the broken quantum PT-symmetric system has not been constructed effectively, until recently several methods have been raised. Here, we construct a quantum PT-symmetric system assisted by weak measurement, which can effectively transit from the unbroken region to the broken region. The full energy spectrum including the real and imaginary parts is directly measured using weak values. Furthermore, based on the ability of approaching a broken region, we for the first time translate the previously mentioned PT-enhanced sensor into the quantum version, and investigate its various features that are associated to the optimal conditions for sensitivity enhancement. In this experiment, we obtain an enhancement of 8.856 times over the conventional Hermitian sensor. Moreover, by separately detecting the real and imaginary parts of energy splitting, we can derive the additional information of the direction of perturbations. Our work paves the way of leading classical interesting PT phenomena and applications to their quantum counterparts. More generally, since the PT system is a subset of non-Hermitian systems, our work will be also helpful in the studies of general exception point in the quantum regime.

Recent Progress in Nanolaser Technology

Nanolasers are key elements in the implementation of optical integrated circuits owing to their low lasing thresholds, high energy efficiencies, and high modulation speeds. With the development of semiconductor wafer growth and nanofabrication techniques, various types of wavelength-scale and subwavelength-scale nanolasers have been proposed. For example, photonic crystal lasers and plasmonic lasers based on the feedback mechanisms of the photonic bandgap and surface plasmon polaritons, respectively, have been successfully demonstrated. More recently, nanolasers employing new mechanisms of light confinement, including parity-time symmetry lasers, photonic topological insulator lasers, and bound states in the continuum lasers, have been developed. Here, the operational mechanisms, optical characterizations, and practical applications of these nanolasers based on recent research results are outlined. Their scientific and engineering challenges are also discussed.

Mode control through anti-Hermitian coupling in regular-polygonal microcavities with non-uniform gain and loss

We theoretically and numerically study optical modes in regular-polygonal microcavities with non-uniform gain and loss, where high quality (Q) whispering-gallery-like modes typically appear as superscar states. High Q superscar modes can be described by the propagating plane waves in an effective rectangle formed by unfolding the periodic orbits and exhibit regular and predictable spatial field distributions and transverse-mode spectra. With non-uniform gain and loss, anti-Hermitian coupling between the transverse modes with close frequencies occurs according to the mode coupling theory, which results in novel mode properties such as modified mode spectra and field patterns, and the appearance of exceptional points. Numerical simulation results are in good agreement with the theoretical analyses, and such analyses are also suitable for other kinds of high Q microcavities with non-uniform gain and loss. These results will be highly useful for studying non-Hermitian physics in optical microcavities and advancing the practical applications of microcavity devices.

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of [Formula: see text] symmetry

We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ([Formula: see text]) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time ([Formula: see text]) symmetry. We observe that [Formula: see text]-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing [Formula: see text]-symmetric Hamiltonians. We believe that our results on the [Formula: see text]-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the [Formula: see text]-symmetric systems.

Steering magnonic dynamics and permeability at exceptional points in a parity-time symmetric waveguide

Tuning the magneto optical response and magnetic dynamics are key elements in designing magnetic metamaterials and devices. This theoretical study uncovers a highly effective way of controlling the magnetic permeability via shaping the magnonic properties of coupled magnetic waveguides separated by a nonmagnetic spacer with strong spin–orbit interaction (SOI). We demonstrate how a spacer charge current leads to enhancement of magnetic damping in one waveguide and a decrease in the other, constituting a bias-controlled magnetic parity–time (PT) symmetric system at the verge of the exceptional point where magnetic gains/losses are balanced. We find phenomena inherent to PT-symmetric systems and SOI-driven interfacial structures, including field-controlled magnon power oscillations, nonreciprocal propagation, magnon trapping and enhancement as well as an increased sensitivity to perturbations and abrupt spin reversal. The results point to a new route for designing magnonic waveguides and microstructures with enhanced magnetic response.

The ability to guide and control magnons is central to their potential in future information processing. Here, using a combination of computations and analytical approaches, the authors propose a magnonic waveguide with a unique gain and loss mechanism.

Hamiltonian Hopping for Efficient Chiral Mode Switching in Encircling Exceptional Points

Dynamically encircling exceptional points (EPs) can lead to chiral mode switching as the system parameters are varied along a path that encircles EP. However, conventional encircling protocols result in low transmittance due to path-dependent losses. Here, we present a paradigm to encircle EPs that includes fast Hamiltonian variations on the parameter boundaries, termed Hamiltonian hopping, enabling ultrahigh-efficiency chiral mode switching. This protocol avoids path-dependent loss and allows us to experimentally demonstrate nearly 90% efficiency at 1550 nm in the clockwise direction, overcoming a long-standing challenge of non-Hermitian optical systems and powering up new opportunities for EP physics.

Breaking Anti-PT Symmetry by Spinning a Resonator

Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time (PT) operations, can have entirely real or imaginary eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and topological energy transfer. A merit of anti-PT systems is free of gain, but in recent efforts on making anti-PT devices, nonlinearity is still required. Here, counterintuitively, we show how to achieve anti-PT symmetry and its spontaneous breaking in a linear device by spinning a lossy resonator. Compared with a Hermitian spinning device, significantly enhanced optical isolation and ultrasensitive nanoparticle sensing are achievable in the anti-PT-broken phase. In a broader view, our work provides a new tool to study anti-PT physics, with such a wide range of applications as anti-PT lasers, anti-PT gyroscopes, and anti-PT topological photonics or optomechanics.

Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers

We present a systematic analysis of the stationary regimes of nonlinear parity-time (PT) symmetric laser composed of two coupled fiber cavities. We find that power-dependent nonlinear phase shifters broaden regions of existence of both PT-symmetric and PT-broken modes, and can facilitate transitions between modes of different types. We show the existence of non-stationary regimes and demonstrate an ambiguity of the transition process for some of the unstable states. We also identify the presence of higher-order stationary modes, which return to the initial state periodically after a certain number of round-trips.

Transfer Characteristics of the Nonlinear Parity-Time-Symmetric Wireless Power Transfer System at Detuning

The nonlinear parity-time-symmetric wireless power transfer (NPTS-WPT) system is more robust against transfer distance than the traditional WPT system. Current studies mainly focus on the situation in which the transmitter (Tx) and the receiver (Rx) are completely matched. Our study focuses on the transfer characteristics of the NPTS-WPT system under detuning between the Tx and the Rx. First, the mathematical model of the detuned system is established, and then the model is solved using Shengjin’s formula. Then, the exact analytical solutions for the operating frequency, the amplification factor of the operational amplifier (OP Amp) and the transfer efficiency at detuning are obtained. It was noted, for the first time, that even though the Tx and the Rx were completely matched, a frequency jump could occur when the distance between the Tx and Rx coils slowly changed. Our study found that when the degree of detuning of the system changed, the operating frequency of the system could jump. By investigating the amplification factor of the OP Amp, the reason for the frequency jump when the system was detuned was explained. Our study also revealed that detuning did not imply a decreased transfer efficiency, and the over-detuning can improve the transfer efficiency sometimes. Finally, an experimental system was constructed, and the correctness of the theory was validated using the experimental system.

Polarimetric parity-time symmetry in a photonic system

Parity-time (PT) symmetry has attracted intensive research interest in recent years. PT symmetry is conventionally implemented between two spatially distributed subspaces with identical localized eigenfrequencies and complementary gain and loss coefficients. The implementation is complicated. In this paper, we propose and demonstrate that PT symmetry can be implemented between two subspaces in a single spatial unit based on optical polarimetric diversity. By controlling the polarization states of light in the single spatial unit, the localized eigenfrequencies, gain, loss, and coupling coefficients of two polarimetric loops can be tuned, leading to PT symmetry breaking. As a demonstration, a fiber ring laser based on this concept supporting stable and single-mode lasing without using an ultranarrow bandpass filter is implemented.

Spectral singularities and asymmetric light scattering in PT-symmetric 2D nanoantenna arrays

The intriguing physics of non-Hermitian systems satisfying parity-time (PT) symmetry has spurred a surge of both theoretical and experimental research in interleaved gain-loss systems for novel photonic devices. In this work, we investigate vertically stacked GaInP PT-symmetric nanodisk resonators arranged in two-dimensional periodic lattice using full-wave numerical simulations and scattering matrix theory. The proposed dielectric metasurface supports lasing spectral singularities with asymmetric reflection and highly anisotropic far-field scattering patterns. It offers a much broader design parameter space to control wavelength, scattering direction, and efficiency of optical emission when compared to the predominantly one-dimentional (1D) or quasi-1D structures studied so far. The proposed system with Q-factor >10⁵ serves as a powerful platform for enhanced light-matter interaction by enabling extensive control of asymmetric light scattering, amplification, and unprecedented localization of electromagnetic fields.

Equal-intensity waves in non-Hermitian media

A novel type of waves is examined in the context of non-Hermitian photonics. We can identify a class of complex guided structures that support localized paraxial solutions whose intensity distribution is exactly the same as the intensity of a corresponding solution in homogeneous media (free or bulk space). In other words, intensity-wise the two solutions are identical and their phase is different by a factor exp[iθ(x,y)]. The non-Hermitian potential is determined by the phase θ, as well as the amplitude and phase of the bulk space solution that contributes to the imaginary and real part of the potential, respectively. That way we can connect the plane waves and Gaussian beams of free space to constant-intensity waves and what we call the equal-intensity waves (EI waves) in non-Hermitian media. Such a relation allows us to study three different physical problems: Propagating EI waves inside random media, interface lattice solitons, and moving solitons in photonic waveguide structures with free-space characteristics. The relation of EI waves to unidirectional invisibility and Bohmian photonics is also examined.

Tuneable red, green, and blue single-mode lasing in heterogeneously coupled organic spherical microcavities

Tuneable microlasers that span the full visible spectrum, particularly red, green, and blue (RGB) colors, are of crucial importance for various optical devices. However, RGB microlasers usually operate in multimode because the mode selection strategy cannot be applied to the entire visible spectrum simultaneously, which has severely restricted their applications in on-chip optical processing and communication. Here, an approach for the generation of tuneable multicolor single-mode lasers in heterogeneously coupled microresonators composed of distinct spherical microcavities is proposed. With each microcavity serving as both a whispering-gallery-mode (WGM) resonator and a modulator for the other microcavities, a single-mode laser has been achieved. The colors of the single-mode lasers can be freely designed by changing the optical gain in coupled cavities owing to the flexibility of the organic materials. Benefiting from the excellent compatibility, distinct color-emissive microspheres can be integrated to form a heterogeneously coupled system, where tuneable RGB single-mode lasing is realized owing to the capability for optical coupling between multiple resonators. Our findings provide a comprehensive understanding of the lasing modulation that might lead to innovation in structure designs for photonic integration.

Pseudochirality: A Manifestation of Noether's Theorem in Non-Hermitian Systems

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry that we term pseudochirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics. Using this observation, we reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We further elaborate the disparate implications of pseudochirality induced constant of motion: It signals the pair excitation of a generalized "particle" and the corresponding "hole" but vanishes universally when the pseudochiral operator is antisymmetric. This disparity, when manifested in a non-Hermitian topological lattice with the Landau gauge, depends on whether the lattice size is even or odd. We further discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudochirality can be used as an indicator of whether a pure chiral edge state is excited.