Optical gradient forces in PT-symmetric coupled-waveguide structures

Optical gradient force in a parity-time (PT)-symmetric coupled-waveguide system is theoretically studied. We find that when the system evolves from PT-symmetric region to broken-PT-symmetric region, the normalized optical forces of the two eigenmodes decrease first and become the same when the exceptional point is reached. Besides, the optical force induced PT phase transition is demonstrated. It is worth noting that, when the system is in the broken-PT-symmetric region and the length of the waveguide is much longer than the propagation length of the lossy eigenmode, the total optical gradient force acting on the two waveguides will decrease with the decreasing of the gap. This work gives us a new understanding of integrated optomechanics by combining with PT symmetry.

Topological Band Theory for Non-Hermitian Hamiltonians

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Effect of PT symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and PT-symmetric potentials. PT symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the PT-symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of PT-symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

Unidirectional Wave Vector Manipulation in Two-Dimensional Space with an All Passive Acoustic Parity-Time-Symmetric Metamaterials Crystal

Exploring the concept of non-Hermitian Hamiltonians respecting parity-time symmetry with classical wave systems is of great interest as it enables the experimental investigation of parity-time-symmetric systems through the quantum-classical analogue. Here, we demonstrate unidirectional wave vector manipulation in two-dimensional space, with an all passive acoustic parity-time-symmetric metamaterials crystal. The metamaterials crystal is constructed through interleaving groove- and holey-structured acoustic metamaterials to provide an intrinsic parity-time-symmetric potential that is two-dimensionally extended and curved, which allows the flexible manipulation of unpaired wave vectors. At the transition point from the unbroken to broken parity-time symmetry phase, the unidirectional sound focusing effect (along with reflectionless acoustic transparency in the opposite direction) is experimentally realized over the spectrum. This demonstration confirms the capability of passive acoustic systems to carry the experimental studies on general parity-time symmetry physics and further reveals the unique functionalities enabled by the judiciously tailored unidirectional wave vectors in space.

Topological hybrid silicon microlasers

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.

Defect States Emerging from a Non-Hermitian Flatband of Photonic Zero Modes

We show the existence of a flatband consisting of photonic zero modes in a gain and loss modulated lattice system as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudospin under the influence of a complex-valued pseudomagnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength.

Cavity solitons in a microring dimer with gain and loss

We address a pair of vertically coupled microring resonators with gain and loss pumped by a single-frequency field. Coupling between microrings results in a twofold splitting of the single microring resonance that increases when gain and losses decrease, giving rise to two cavity soliton (CS) families. We show that the existence regions of CSs are tunable and that both CS families can be stable in the presence of an imbalance between gain and losses in the two microrings. These findings enable experimental realization of frequency combs in configurations with active microrings and contribute toward the realization of compact multisoliton comb sources.

Symmetry in optics and photonics: a group theory approach

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.

Single-mode ultraviolet whispering gallery mode lasing from a floating GaN microdisk

We fabricated a floating GaN microdisk supported by a silicon pillar through photolithography, dry-etching GaN, and isotropic wet-etching silicon methods. Single-mode ultraviolet whispering gallery mode (WGM) lasing was obtained from the floating GaN microdisk under optical pumping conditions at room temperature. The features of WGM lasing, i.e., the threshold, emission intensity, and lasing mode number, were characterized. A two-dimensional finite-difference time-domain simulation about the optical field contour profile also confirmed the resonance mechanism of WGM lasing. This work can help realize single-mode WGM lasing with high quality factor and low threshold.

Enhanced nonlinear characteristics with the assistance of a [Formula: see text]-symmetric trimer system

We study the parity-time (PT) symmetry characteristics and the applications to nonlinear optics in an optical trimer system consisting of two indirectly coupled standing-mode micro-cavities and a two-level quantum emitter (QE) placed at the intersection of two cavities. We find this trimer system can exhibit analogical phenomena as those in typical [Formula: see text]-symmetric dimer systems composed of a passive cavity directly coupled to an active cavity. This system, whose [Formula: see text] symmetry is demonstrated by our analytic results, can be transformed between the [Formula: see text]-symmetric phase and the [Formula: see text]-broken phase by adjusting relevant system parameters. Then, with this system, we observe both the linear and nonlinear parts of the transmission field become remarkably enhanced and can further reach peak values around the [Formula: see text] breaking point. In addition, we show the negative correlation between the gain degree of the linear (nonlinear) transmission part and decay rate of the QE. This trimer proposal is feasible for experiments and may provide a promising platform for [Formula: see text]-symmetric optics of low-light levels. Moreover, novel phenomena arising from the QE-cavity-coupling induced nonlinearity gain could be explored to fabricate photonic devices and controllable nonlinear optical media for quantum information process and communication of photons.

Parity–time symmetric photonics

The establishment of non-Hermitian quantum mechanics (such as parity–time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to complex quantum potentials, photonics provides an ideal platform for the visualization of many conceptually striking predictions from non-Hermitian quantum theory. A rapidly developing field has emerged, namely, PT-symmetric photonics, demonstrating intriguing optical phenomena including eigenstate coalescence and spontaneous PT-symmetry breaking. The advance of quantum physics, as the feedback, provides photonics with brand-new paradigms to explore the entire complex permittivity plane for novel optical functionalities. Here, we review recent exciting breakthroughs in PT-symmetric photonics while systematically presenting their underlying principles guided by non-Hermitian symmetries. The potential device applications for optical communication and computing, biochemical sensing and healthcare are also discussed.

Hybrid Photon-Plasmon Coupling and Ultrafast Control of Nanoantennas on a Silicon Photonic Chip

Hybrid integration of nanoplasmonic devices with silicon photonic circuits holds promise for a range of applications in on-chip sensing, field-enhanced and nonlinear spectroscopy, and integrated nanophotonic switches. Here, we demonstrate a new regime of photon-plasmon coupling by combining a silicon photonic resonator with plasmonic nanoantennas. Using principles from coherent perfect absorption, we make use of standing-wave light fields to maximize the photon-plasmon interaction strength. Precise placement of the broadband antennas with respect to the narrowband photonic racetrack modes results in controlled hybridization of only a subset of these modes. By combining antennas into groups of radiating dipoles with opposite phase, far-field scattering is effectively suppressed. We achieve ultrafast tuning of photon-plasmon hybridization including reconfigurable routing of the standing-wave input between two output ports. Hybrid photonic-plasmonic resonators provide conceptually new approaches for on-chip integrated nanophotonic devices.

Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

Open, non-equilibrium systems with balanced gain and loss, known as parity-time (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT)-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetric phase is protected in the presence of a periodic disorder which leads to a positive \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetry breaking transition. We elucidate the interplay between such localization and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetry breaking phenomena in disordered \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT-symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.

Brain Organoids: Expanding Our Understanding of Human Development and Disease

Stem cell-derived brain organoids replicate important stages of the prenatal human brain development and combined with the induced pluripotent stem cell (iPSC) technology offer an unprecedented model for investigating human neurological diseases including autism and microcephaly. We describe the history and birth of organoids and their application, focusing on cerebral organoids derived from embryonic stem cells and iPSCs. We discuss new insights into organoid-based model of schizophrenia and shed light on challenges and future applications of organoid-based disease model system. This review also suggests hitherto unrevealed potential applications of organoids in combining with new technologies such as nanophotonics/optogenomics for controlling brain development and atomic force microscopy for studying mechanical forces that shape the developing brain.

Breaking the barriers: advances in acoustic functional materials

Acoustics is a classical field of study that has witnessed tremendous developments over the past 25 years. Driven by the novel acoustic effects underpinned by phononic crystals with periodic modulation of elastic building blocks in wavelength scale and acoustic metamaterials with localized resonant units in subwavelength scale, researchers in diverse disciplines of physics, mathematics, and engineering have pushed the boundary of possibilities beyond those long held as unbreakable limits. More recently, structure designs guided by the physics of graphene and topological electronic states of matter have further broadened the whole field of acoustic metamaterials by phenomena that reproduce the quantum effects classically. Use of active energy-gain components, directed by the parity–time reversal symmetry principle, has led to some previously unexpected wave characteristics. It is the intention of this review to trace historically these exciting developments, substantiated by brief accounts of the salient milestones. The latter can include, but are not limited to, zero/negative refraction, subwavelength imaging, sound cloaking, total sound absorption, metasurface and phase engineering, Dirac physics and topology-inspired acoustic engineering, non-Hermitian parity–time synthetic active metamaterials, and one-way propagation of sound waves. These developments may underpin the next generation of acoustic materials and devices, and offer new methods for sound manipulation, leading to exciting applications in noise reduction, imaging, sensing and navigation, as well as communications.

Scattering by Finite Periodic PT-Symmetric Structures

In this work, we study the transmission properties of one-dimensional finite periodic systems with PT symmetry. A simple closed-form expression is obtained for the total transmittance from a lattice of N cells, that allows us to describe the transmission minima (maxima) when the system is in the PT-unbroken (broken) phase. Utilizing this expression, we provide the necessary conditions, independent of the number of cells, for the occurrence of a coherent perfect absorber and laser for any finite PT-symmetric periodic potential. Under these conditions, we provide a recipe for building finite periodic structures with near perfect absorption and extremely large amplification.

Topological cascade laser for frequency comb generation in PT-symmetric structures

The cascade of resonant PT-symmetric topological structures is shown to emit laser light with a frequency comb spectrum. We consider optically active topological lattices supporting edge modes at regularly spaced frequencies. When the amplified resonances in the PT-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables the engineering of the spectral features for specific applications. Topological protection makes the system very well suited for a novel generation of compact frequency comb emitters for spectroscopy, metrology, and quantum information.

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also show how this gauge field can be used to design waveguides in which sound propagates with robustness against disorder as a consequence of the change in topological polarization that occurs along a domain wall. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may potentially be exploited for the design of sound amplification by stimulated emission of radiation (SASER, the mechanical analogs of lasers).

Statistical parity-time-symmetric lasing in an optical fibre network

Parity-time (PT)-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to interesting optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realisations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robust to survive the statistical fluctuations associated with a macroscopic optical cavity. We examine the lasing dynamics in optical fibre-based coupled cavities more than a kilometre in length with balanced gain and loss. Although fluctuations can detune the cavity by more than the free spectral range, the behaviour of the lasing threshold and the laser power is that expected from a PT-stable system. Furthermore, we observe a statistical symmetry breaking upon varying the cavity loss.

Parity-time-symmetric optical systems have so far only been realized using microscopic cavities because the necessary gain-loss balance is thought to be fragile with regard to statistical fluctuations. Here, Jahromi et al.. demonstrate PT-symmetric lasing using kilometre-long fibre cavities.

Asymmetric light diffraction of an atomic grating with PT symmetry

Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.

Complex band structure of one-dimensional polariton crystal

The exceptional point (EP), at which the relevant eigenvalues and eigenstates are simultaneously identical, typically exists in non-Hermitian systems with parity-time (PT) symmetric complex potentials, and gives rise to many intriguing behaviors in various physical realms. In this work, we explore the complex band structure of one-dimensional "polariton crystals" that can be constructed in waveguide-resonator coupled systems, with PT-symmetric potential. Analysis based on the transfer matrix and the coupled mode theory shows that the complex band structure is intimately determined by the interaction between the Bragg resonance and the polariton one, the gain/loss coefficients, in addition to the coupling strength. A miniband is induced due to the interaction of these two resonances, which is a defect-like band and appears quite different for the band structure evolution. Furthermore, PT-symmetric phase transition occurs in the momentum space for certain amounts of non-Hermiticity. As the non-Hermiticity increases, the EP formed in the original polariton gap approaches another EP formed at the touch point of the folded Bragg bands (where the thresholdless transition occurs). Then they coalesce at a specific non-Hermiticity, and finally disappear. Subsequently, the transmission spectra of such polariton crystals show intriguing phenomena induced by the EPs. Our results provide a different perspective to understand PT-symmetric polariton crystals and may find applications in gain/loss induced lasing by 'polaritons'.

Nonreciprocal light propagation in coupled microcavities system beyond weak-excitation approximation

We propose a scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{P}}{\mathscr{T}}$$\end{document}PT) symmetric system (i.e., coupled active-passive cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The increased optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability, and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.

Classes of non-parity-time-symmetric optical potentials with exceptional-point-free phase transitions

Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schrödinger equation with a complex potential. In this Letter, new classes of non-parity-time (PT)-symmetric complex potentials featuring conjugate-pair eigenvalue symmetry are constructed by operator symmetry methods. Due to this eigenvalue symmetry, it is shown that the spectrum of these complex potentials is often all-real. Under parameter tuning in these potentials, a phase transition can also occur, where pairs of complex eigenvalues appear in the spectrum. A distinctive feature of the phase transition here is that the complex eigenvalues may bifurcate out from an interior continuous eigenvalue inside the continuous spectrum; hence, a phase transition takes place without going through an exceptional point. In one spatial dimension, this class of non-PT-symmetric complex potentials is of the form V(x)=h^'(x)-h²(x), where h(x) is an arbitrary PT-symmetric complex function. These potentials in two spatial dimensions are also derived. Diffraction patterns in these complex potentials are further examined, and unidirectional propagation behaviors are demonstrated.

Pump induced lasing suppression in Yb:Er-doped microlasers

A pump source is one of the essential prerequisites in order to achieve lasing in a system, and, in most cases, a stronger pump leads to higher laser power at the output. However, this behavior may be suppressed if two pump beams are used. In this work, we show that lasing around the 1600 nm band can be suppressed completely if two pumps, at wavelengths of 980 nm and 1550 nm, are applied simultaneously to an Yb:Er-doped microlaser, whereas it can be revived by switching one of them off. This phenomenon can be explained by assuming that the presence of one pump (980 nm) changes the role of the other pump (1550 nm); more specifically, the 1550 nm pump starts to consume the population inversion instead of increasing it when the 980 nm pump power exceeds a certain value. As a result, the two pump fields lead to a closed-loop transition within the gain medium (i.e., the erbium ions). This study unveils an interplay similar to coherence effects between different pump pathways, thereby providing a reference for designing the laser pump, and may have applications in lasing control.

Single whispering-gallery mode lasing in polymer bottle microresonators via spatial pump engineering

Single-mode lasing in whispering-gallery mode (WGM) microresonators is challenging to achieve. In bottle microresonators, the highly non-degenerated WGMs are spatially well-separated along the long-axis direction and provide mode-selection capability. In this work, by engineering the pump intensity to modify the spatial gain profiles of bottle microresonators, we demonstrate a simple and general approach to realizing single-mode WGM lasing in polymer bottle microresonators. The pump intensity is engineered into an interference distribution on the bottle microresonator surface. By tuning the spacing between axial positions of the interference pump patterns, the mode intensity profiles of single-bottle WGMs can be spatially overlapped with the interference stripes, intrinsically enabling single-mode lasing and selection. Attractive advantages of the system, including high side-mode suppression factors >20 dB, large spectral tunability >8 nm, low-lasing threshold and reversible control, are presented. Our demonstrated approach may have a variety of promising applications, ranging from tunable single-mode lasing and sensing to nonlinear optics.

Microscopic description of irreversibility in quantum Lorentz gas by complex spectral analysis of the Liouvillian outside the Hilbert space

Irreversible process of a weakly coupled one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouvillian. Without any phenomenological operations, such as a coarse-graining of space-time or a truncation of the higher order correlation, we obtained irreversible processes on a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free-length. The list of development of the complex spectral analysis of the Hamiltonian (instead of the Liouvillian) in quantum optical systems and in quantum nano-devices is also presented.

Tailoring Eigenmodes at Spectral Singularities in Graphene-based PT Systems

The spectral singularity existing in PT-synthetic plasmonic system has been widely investigated. Only lasing-mode can be excited resulting from the passive characteristic of metallic materials. Here, we investigated the spectral singularity in the hybrid structure composed of the photoexcited graphene and one-dimensional PT-diffractive grating. In this system, both lasing- and absorption-modes can be excited with the surface conductivity of photoexcited graphene being loss and gain, respectively. Remarkably, the spectral singularity will disappear with the optically pumped graphene to be lossless. In particular, we find that spectral singularities can exhibit symmetry-modes, when the loss and gain of the grating is unbalanced. Meanwhile, by tuning the loss (gain) of graphene and non-PT diffraction grating, lasing- and absorption-modes can also be excited. We hope that tunable optical modes at spectral singularities can have some applications in designing novel surface-enhanced spectroscopies and plasmon lasers.

Cooperative Raman Spectroscopy for Real-Time In Vivo Nano-Biosensing

In the last few decades, the development of miniature biological sensors that can detect and measure different phenomena at the nanoscale has led to transformative disease diagnosis and treatment techniques. Among others, biofunctional Raman nanoparticles have been utilized in vitro and in vivo for multiplexed diagnosis and detection of different biological agents. However, existing solutions require the use of bulky lasers to excite the nanoparticles and similarly bulky and expensive spectrometers to measure the scattered Raman signals, which limit the practicality and applications of this nano-biosensing technique. In addition, due to the high path loss of the intra-body environment, the received signals are usually very weak, which hampers the accuracy of the measurements. In this paper, the concept of cooperative Raman spectrum reconstruction for real-time in vivo nano-biosensing is presented for the first time. The fundamental idea is to replace the single excitation and measurement points (i.e., the laser and the spectrometer, respectively) by a network of interconnected nano-devices that can simultaneously excite and measure nano-biosensing particles. More specifically, in the proposed system, a large number of nanosensors jointly and distributively collect the Raman response of nano-biofunctional nanoparticles (NBPs) travelling through the blood vessels. This paper presents a detailed description of the sensing system and, more importantly, proves its feasibility, by utilizing the accurate models of optical signal propagation in intra-body environment and low-complexity estimation algorithms. The numerical results show that with a certain density of NBPs, the reconstructed Raman spectrum can be recovered and utilized to accurately extract the targeting intra-body information.

Robustness and mode selectivity in parity-time (PT) symmetric lasers

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.

Wave propagation through disordered media without backscattering and intensity variations

A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multi-path interference. Here we show that these intensity variations can be entirely suppressed by adding disorder-specific gain and loss components to the medium. The resulting constant-intensity waves in such non-Hermitian scattering landscapes are free of any backscattering and feature perfect transmission through the disorder. An experimental demonstration of these unique wave states is envisioned based on spatially modulated pump beams that can flexibly control the gain and loss components in an active medium.

Experimental Realization of Floquet PT-Symmetric Systems

We provide an experimental framework where periodically driven PT-symmetric systems can be investigated. The setup, consisting of two ultra high frequency oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT-symmetric broken domains bounded by exceptional point degeneracies. These domains are analyzed and understood using an equivalent Floquet frequency lattice with local PT symmetry. Management of these PT-phase transition domains is achieved through the amplitude and frequency of the drive.

Controllable oscillatory lateral coupling in a waveguide-microdisk-resonator system

We report a theoretical and experimental study of coupling between a whispering-gallery-mode (WGM) microdisk resonator and a fiber taper which exchange energies at two distinct regions. We observe an oscillatory behavior in the coupling strength as a function of the distance between the two coupling regions when a fiber taper is moved laterally above the resonator at fixed vertical distance. This oscillation is clearly seen in the linewidth of the resonance as well as in the on-resonance transmission. A theoretical model considering for two-point coupling successfully explains the experimental observations as being a result of the interference between the light fields coupled into and out of the resonator at two distinct regions and the light transmitted through the waveguide. Critical coupling in two-region coupling is a collective result of the coupling at two different coupling regions, and does not require critical coupling at both or at any one of the two coupling regions. This relaxes the conditions for achieving critical coupling in waveguide-resonator systems. The discovery of this previously unnoticed oscillatory behavior in two-region coupling between a WGM resonator and a waveguide will benefit both fundamental studies and practical applications based on WGM resonators.

Universal Critical Behaviours in Non-Hermitian Phase Transitions

Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 - 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 - 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.

Control of exceptional points in photonic crystal slabs

Various ways of controlling the extent of the ring of exceptional points in photonic crystal slabs are investigated. The extent of the ring in photonic crystal slabs is found to vary with the thickness of the slab. This enables recovery of Dirac cones in open, non-Hermitian systems, such as a photonic crystal slab. In this case, all three bands exhibit a bound state in the continuum in close proximity of the Γ point. These results may lead to new designs of small photonic-crystal-based lasers exhibiting high-quality factors.

𝒫𝒯 symmetric phase transition and photonic transmission in an optical trimer system

Parity-time (𝒫𝒯) symmetric structures have exhibited potential applications in developing various robust quantum devices. In an optical trimer with balanced loss and gain, we analytically study the 𝒫𝒯 symmetric phase transition by investigating the spontaneous symmetric breaking. We also illustrate the asymmetric photonic transmission behaviors in both of the 𝒫𝒯 symmetric and 𝒫𝒯 symmetry broken phases. We find (i) the non-periodical dynamics of photonic transmission in the 𝒫𝒯 symmetry broken phase instead of 𝒫𝒯 symmetric phase can be regarded as a signature of phase transition; and (ii) it shows asymmetric photonic transmission behavior in both of the phases but comes from different underlying physical mechanisms. The obtained results may be useful to implement the photonic devices based on coupled-cavity system.

Detecting topological exceptional points in a parity-time symmetric system with cold atoms

We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to sweep the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the atomic interferometry. Since the proposed operations and detection are experimentally feasible, our scheme may pave a promising way to explore the novel properties of non-Hermitian systems.

Dual-color single-mode lasing in axially coupled organic nanowire resonators

Miniaturized lasers with multicolor output and high spectral purity are of crucial importance for yielding more compact and more versatile photonic devices. However, multicolor lasers usually operate in multimode, which largely restricts their practical applications due to the lack of an effective mode selection mechanism that is simultaneously applicable to multiple wavebands. We propose a mutual mode selection strategy to realize dual-color single-mode lasing in axially coupled cavities constructed from two distinct organic self-assembled single-crystal nanowires. The unique mode selection mechanism in the heterogeneously coupled nanowires was elucidated experimentally and theoretically. With each individual nanowire functioning as both the laser source and the mode filter for the other nanowire, dual-color single-mode lasing was successfully achieved in the axially coupled heterogeneous nanowire resonators. Furthermore, the heterogeneously coupled resonators provided multiple nanoscale output ports for delivering coherent signals with different colors, which could greatly contribute to increasing the integration level of functional photonic devices. These results advance the fundamental understanding of the lasing modulation in coupled cavity systems and offer a promising route to building multifunctional nanoscale lasers for high-level practical photonic integrations.

Coherent-trapped helical mode in parity-time symmetric metamaterials

Coaxial optical subwavelength elements support helical modes Lm with different topological indexes m. Here we propose to couple the two bright L_±1 modes with the dark one L₀ via a parity-time (PT) symmetric perturbation. We show that the cascading coupled configuration is similar to a three-level atomic system, and supports a special hybridized mode Lc via a classic analog of coherent-population-trapping effect. Resonant frequency of Lc is independent of the PT-symmetric perturbation. Populations in L_±1 can be manipulated by tuning the PT-symmetric perturbation, and no population is trapped in L₀. Since the L_±1 modes are associated with optical waves of opposite circular polarizations, the polarization of transmitted wave is independent of the polarization of incidence but solely determined by the PT-symmetric perturbation. Such an effect can be utilized to manipulate the polarization state of light. Numerical simulation in a well-designed coaxial metamaterial verifies our analysis.

High-order exceptional points in optomechanics

We study mechanical cooling in systems of coupled passive (lossy) and active (with gain) optical resonators. We find that for a driving laser which is red-detuned with respect to the cavity frequency, the supermode structure of the system is radically changed, featuring the emergence of genuine high-order exceptional points. This in turn leads to giant enhancement of both the mechanical damping and the spring stiffness, facilitating low-power mechanical cooling in the vicinity of gain-loss balance. This opens up new avenues of steering micromechanical devices with exceptional points beyond the lowest-order two.

General theory of spontaneous emission near exceptional points

We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes.

An integrated parity-time symmetric wavelength-tunable single-mode microring laser

Mode control in a laser cavity is critical for a stable single-mode operation of a ring laser. In this study we propose and experimentally demonstrate an electrically pumped parity-time (PT)-symmetric microring laser with precise mode control, to achieve wavelength-tunable single-mode lasing with an improved mode suppression ratio. The proposed PT-symmetric laser is implemented based on a photonic integrated circuit consisting of two mutually coupled active microring resonators. By incorporating multiple semiconductor optical amplifiers in the microring resonators, the PT-symmetry condition can be achieved by a precise manipulation of the interplay between the gain and loss in the two microring resonators, and the incorporation of phase modulators in the microring resonators enables continuous wavelength tuning. Single-mode lasing at 1,554.148 nm with a sidemode suppression ratio exceeding 36 dB is demonstrated and the lasing wavelength is continuously tunable from 1,553.800 to 1,554.020 nm.

PT-Symmetric Scattering in Flow Duct Acoustics

We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amounts of mean-flow-induced effective gain and loss, displays all the features of a parity-time (PT) symmetric system. Using a scattering matrix formalism, we observe, experimentally, the properties which reflect the PT symmetry of the scattering acoustical system: the existence of spontaneous symmetry breaking with symmetry-broken pairs of scattering eigenstates showing amplification and reduction, and the existence of points with unidirectional invisibility.

Topologically protected bound states in photonic parity-time-symmetric crystals

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.