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We propose a system for wireless power transfer to a rotating object using solenoid coils based on parity-time symmetry (PTS). Solenoid coils are ideal for wireless power transfer in confined spaces (e.g., they can be attached to the mechanical joints of robotic arms). Under PTS, the theorical transmission power and efficiency remain constant even when the magnetic coupling coefficient (km) changes. However, to preserve PTS, km values must be above the critical magnetic coupling coefficient (kmc) value. We conducted simulations and experiments to analyze the relationship between the rotation angle and km. Based on the results, we identified a coil arrangement for which km does not fall below kmc at any rotation angle. We maintained a transmission power of 20 W and a transmission efficiency of 80% during fast rotation with an angular velocity of 2.6 rad/s using a pair of small solenoid coils arranged with a gap of 33 mm between them. [ABSTRACT FROM AUTHOR]

This work addresses the tailoring spectral response of grating-assisted co-directional couplers (GADCs) in the context of wavelength filtering for fiber-to-the-home (FTTH) applications. Design methods for spectral response engineering by means of coupling profile apodization-type weighting techniques and also more advanced rational transfer functions fitting a predefined spectral window template are presented. Modeling results based on coupled mode theory are then applied for the design and experimental fabrication of InGaAsP/InP GADCs targeting 1.3+/1.3− µm diplexer application in FTTH access networks. The experimental results are found to be in good agreement with the modeling predictions. The design tools presented are quite general and can be easily adapted to other technology platforms, such as silicon photonics for the use of GADCs as add-drop wavelength division multiplexers. The field of parity–time symmetry is another avenue where these types of gain–loss-assisted GADCs as active components are of interest for switching applications, and the design methods presented here may find utility. [ABSTRACT FROM AUTHOR]

Parity‐time symmetry has great potential for mode selection in multimode resonators. However, in a PT‐symmetry system with saturable absorption mechanisms, the random background noise can initiate single‐mode oscillation at any of the maxima within the gain spectrum, that is, potential PT frequencies. Such randomness impedes the acquisition of high‐quality signals at desired frequencies. Here, this work proposes a method to obtain deterministic PT‐symmetry single‐mode oscillation in a filterless multimode resonator through one‐shot injection. With this technique, this work changes the system's gain spectrum and enhances the gain discrepancy. Utilizing the frequency domain saturable absorption of the resonator, oscillation at desired mode can maintain its frequency after the withdrawal of the injection signal. To validate the concept, this work establishes a polarization‐division multiplexed dual‐loop optoelectronic oscillator (OEO) with a 1‐km long cavity operated under PT‐symmetry conditions. By one‐shot injecting the PT‐OEO, this work effectively eliminates the randomness arising from the relatively flat gain spectrum, facilitating oscillation at any desired potential PT frequencies from 1.8 to 9 GHz without requiring elaborate frequency tuning structures. Moreover, the one‐shot injection technique produces ultra‐low phase noise performance, achieving a remarkable −158.6 dBc Hz−1@10 kHz. This performance level stands in close comparison with the best phase noise values recorded for OEOs. [ABSTRACT FROM AUTHOR]

The intrinsic non‐Hermiticity of photonic devices with tunable optical gain and loss makes them excellent platforms to explore and implement applications based on parity‐time symmetry, and a notable example is mode management in micro‐cavity lasers. Thus far, parity‐time‐symmetric lasers are fabricated via conventional top‐down etching processes, which are known to cause cavity sidewall roughness that is potentially detrimental to laser performance. Bottom‐up fabrication of parity‐time‐symmetric lasers, however, has seen limited success due to strict requirements on the uniformity of cavity morphology. Here, parity‐time‐symmetric lasing is demonstrated in coupled InP micro‐ring cavities grown directly by selective area epitaxy. With a facet engineering technique, ring laser cavities with a highly deterministic morphology are realized, enabling parity‐time‐symmetric laser designs. Furthermore, benefiting from the versatility and controllability of this bottom‐up process, lasing mode selectivity can be enhanced through coupling gap tuning and cavity shape engineering, leading to single‐mode lasing with a peak side mode suppression ratio exceeding 17 dB and a threefold single‐mode brightness enhancement compared to a single, uncoupled laser cavity. This work unlocks a lasing mode management strategy that is previously unavailable to bottom‐up laser cavities, which is a major step toward the realization of on‐chip, low‐loss, and single‐mode micro‐cavity lasers. [ABSTRACT FROM AUTHOR]

Parity-time (PT) symmetry has made encouraging progress in wireless power transmission (WPT), exhibiting significant advantages in terms of system robustness and transmission efficiency. However, there are still challenges that need to be addressed, particularly when classical schemes operate at a fixed frequency in the weak coupling region, where even minor changes in coupling strength can result in excessive current surges. This paper introduced a novel PT-symmetric WPT system featuring negative resistance constructed on the receiver side. We first established a theoretical framework for the classical two-coil PT-symmetric magnetically coupled resonant WPT system and subsequently extended it to incorporate the PT-symmetric WPT system with negative resistance on the receiver. This topological coil configuration facilitated stable power delivery over a broader range, with the capability of self-tuning frequency without requiring additional frequency modulation. This adaptability enabled the system to cater to diverse scenarios and opens up a novel avenue for practical applications of PT symmetry in WPT. Finally, we designed a 10 W prototype to demonstrate the effectiveness of our topology, and the experimental results aligned with our theoretical calculations, validating the feasibility and potential of our PT-symmetric WPT system. [ABSTRACT FROM AUTHOR]

In this paper, we study Modulation Instability (MI) and its correlated gain spectrum with Parity-Time (풫풯)-symmetry. The cubic-quintic nonlinearities in the Bragg grating structure produce ultrashort pulses. The MI evaluation started with a linear stability approach, and we investigated the effects of various system functions regarding the instability gain spectra at the top and bottom sides of the Photonic BandGap (PBG), in addition to the anomalous and normal dispersion domains. The interaction of cubic and quintic (focusing and de-focusing) nonlinearity is highlighted, resulting in a new type of MI band. Due to the consequences of quintic nonlinearity, an additional MI band appears for the three dynamics associated with the gain/loss function for the edges of the bottom PBG. After enforcing the 풫풯-symmetry for the anomalous dispersion system, the dent transformed into a split under the influence of the power in the de-focusing quintic effect. Overall, MI gain and bandwidths across the entire MI gain spectrum are usually increasing. As an outcome, we are confident that these studies will aid in the generation of gap solitons in 풫풯-symmetry regimes. [ABSTRACT FROM AUTHOR]

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while 'the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system. [ABSTRACT FROM AUTHOR]

This work proposes and experimentally demonstrates a high-performance polarization space parity-time (PT) symmetric fiber ring laser to achieve a low-noise, narrow-linewidth, and highly stable single-longitudinal-mode output. The gain/loss and coupling coefficients are regulated by adjusting a polarization controller (PC) and the pumping current of an erbium-doped fiber amplifier (EDFA) within the ring cavity. The results show that the single longitudinal mode oscillation of the laser can be implemented by PT symmetry breaking. The frequency noise spectral density and the linewidth characteristics of the laser are evaluated by the short-delay self-heterodyne method. The results reveal that excellent low-frequency noise (181 Hz2/Hz at a 10 kHz offset frequency) and narrow fundamental linewidth (68 Hz) can be achieved. Additionally, the laser exhibits outstanding stability with only 0.64 pm wavelength drift over 30 min. By tuning an optical tunable filter (OTF), the wavelength tunable range of the laser can cover the entire C-band. Furthermore, the impacts of different fiber length on the frequency noise spectral density and the filter bandwidth on stability are analyzed, offering guidance for component selection in such laser systems. [ABSTRACT FROM AUTHOR]

Exceptional points are investigated in two different one-dimensional photonic crystals. Both periodic structures are parity-time-symmetric (PT) and have a three-layer unit-cell containing gain and loss medium in which a dielectric film is sandwiched between them. However, the unit-cell of one structure is not parity-time-symmetric solely, and the system has low symmetry. The introduction of a graphene layer leads to the appearance of new exceptional points, which their properties are strongly dependent on the chemical potential of graphene. Coherent perfect absorbing lasing (CPAL) points, their spectra, and Goos-Hänchen (GH) shifts are considered with the gain–loss factor and also with the chemical potential of graphene. In the low symmetry structure, to obtain maximum values of spectra, the small gain–loss factor is needed. Results of GH calculations show that both structures depict GH shifts at two different angles with small shift values. By increasing the chemical potential of graphene, GH shifts get high values, where, the angle dependency of GH shifts in the symmetric structures is considerable. [ABSTRACT FROM AUTHOR]

Parity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices. [ABSTRACT FROM AUTHOR]

Summary: In recent years, the electric vehicle (EV) industry has developed rapidly, and research on wireless charging systems for the EV is very meaningful. This paper proposes a magnetic coupling resonant ultra‐high voltage EV wireless charging system based on parity‐time symmetry to meet the need of high transmission efficiency and high transmission power for the EV wireless charging system. Through the application of magnetic coupling resonance and parity‐time symmetry, the charging system can maintain constant transmission efficiency within a larger spatial range, which greatly reduces the high‐precision requirements for coil alignment. Through the proposed intelligent coil alignment system, the alignment degree of the power transmission coil, user experience, and energy transmission efficiency can be improved further, promoting the intelligence of the charging system. At the same time, an ultra‐high voltage booster module is added to the primary side of the system to provide high‐power input for the EV charging system. Simulation analysis and experiments verify the rationality and practicability of the charging system. Finally, the practical significance of the proposed system applied to power grid inspection work is discussed. [ABSTRACT FROM AUTHOR]

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF. [ABSTRACT FROM AUTHOR]

Non‐Hermitian Hamiltonians may still possess real eigenvalues in case of the existence of parity‐time (PT) symmetry. Exceptional points (EPs) occur at the phase transition from real to complex eigenvalues due to PT‐symmetry breaking in the parameter space. Magnonic devices use magnons to carry, transport, and process information, which have the advantages of low energy dissipation, wave‐based computing, and nonlinear data processing. The combination of PT‐symmetry and magnonics may lead to novel physics as well as unprecedented functional device applications. Recently, the research of PT‐symmetry in magnetism has developed rapidly. In this review, the theoretical predictions as well as experimental findings of PT‐symmetry in magnetism are summarized. First, a brief introduction to PT symmetry, EPs, and anti‐PT symmetry is presented. Second, the theoretical and experimental progress of magnonic PT symmetry are summarized. Third, the theoretical predictions of higher‐order EPs and anti‐PT symmetry in magnonic systems are given. Finally, the study concludes by discussing the future challenges and research prospects in magnonic PT‐symmetry, and proposals for experimental observations of magnonic higher‐order EPs and anti‐PT symmetry are suggested. [ABSTRACT FROM AUTHOR]

Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.

Abstract Non‐Hermitian Hamiltonians may still possess real eigenvalues in case of the existence of parity‐time (PT) symmetry. Exceptional points (EPs) occur at the phase transition from real to complex eigenvalues due to PT‐symmetry breaking in the parameter space. Magnonic devices use magnons to carry, transport, and process information, which have the advantages of low energy dissipation, wave‐based computing, and nonlinear data processing. The combination of PT‐symmetry and magnonics may lead to novel physics as well as unprecedented functional device applications. Recently, the research of PT‐symmetry in magnetism has developed rapidly. In this review, the theoretical predictions as well as experimental findings of PT‐symmetry in magnetism are summarized. First, a brief introduction to PT symmetry, EPs, and anti‐PT symmetry is presented. Second, the theoretical and experimental progress of magnonic PT symmetry are summarized. Third, the theoretical predictions of higher‐order EPs and anti‐PT symmetry in magnonic systems are given. Finally, the study concludes by discussing the future challenges and research prospects in magnonic PT‐symmetry, and proposals for experimental observations of magnonic higher‐order EPs and anti‐PT symmetry are suggested.

Lower urinary tract dysfunction (LUTD) has a great effect on patients' daily life and mental health. Currently, the most mature invasive treatment is sacral neuromodulation (SNM) that needs to be implanted into buttocks and work for 1–2 years. However, most existing SNM stimulators use disposable batteries with a limited lifespan. And existing stimulators are rigid and lack biomechanical compatibility. To address the above problems, wireless power transferring (WPT) is proposed for SNM based on parity–time (PT) symmetry principle to meet buttocks application requirements, where has thick fat and skin tissue. The receiver coil in the SNM stimulator is designed to be as small and flexible as possible to fit implantation. PT technology allows for efficient and stable wireless power transmission without being significantly affected by the misalignment and bending caused by body movement and can penetrate 15 mm fat–skin tissue and achieve 78% transmission efficiency. Furthermore, the flexible wireless sacral nerve stimulator is developed, and the effectiveness of the system is verified. The system could potentially reduce patient discomfort because the implanted device is flexible and can output a stable voltage stimulation signal. [ABSTRACT FROM AUTHOR]

By studying the eigenvalues and eigenvectors of a non-Markovian anti parity-time (APT) symmetric system, we investigate the possibility of exceptional points (EPs) that may arise within it. Our work is motivated by a recently studied APT-symmetric experimental configuration consisting of a pair of time-delay coupled semiconductor lasers (SCLs). In such a system, a single time-delay represents the memory. The time-delayed coupling makes the system's effective Hamiltonian infinite-dimensional and leads to novel features in the corresponding eigenvalues and eigenvectors. In particular, we demonstrate analytically and numerically that unlike a typical PT-symmetric dimer with zero time-delay, which has one second-order EP, our time-delayed system has parameter regimes that give rise to either one, two, or zero second-order EPs and one third-order EP, and one can select these regimes though a judicious choice of the time-delay and coupling. [ABSTRACT FROM AUTHOR]

This research introduces a novel methodology of harnessing liquids to facilitate the realization of parity-time (PT)-symmetric optical waveguides on highly integrated microscale platforms. Additionally, we propose a realistic and detailed fabrication process flow, demonstrating the practical feasibility of fabricating our optofluidic system, thereby bridging the gap between theoretical design and actual implementation. Extensive research has been conducted over the past two decades on PT-symmetric systems across various fields, given their potential to foster a new generation of compact, power-efficient sensors and signal processors with enhanced performance. Passive PT-symmetry in optics can be achieved by evanescently coupling two optical waveguides and incorporating an optically lossy material into one of the waveguides. The essential coupling distance between two optical waveguides in air is usually less than 500 nm for near-infrared wavelengths and under 100 nm for ultraviolet wavelengths. This necessitates the construction of the coupling region via expensive and time-consuming electron beam lithography, posing a significant manufacturing challenge for the mass production of PT-symmetric optical systems. We propose a solution to this fabrication challenge by introducing liquids capable of dynamic flow between optical waveguides. This technique allows the attainment of evanescent wave coupling with coupling gap dimensions compatible with standard photolithography processes. Consequently, this paves the way for the cost-effective, rapid and large-scale production of PT-symmetric optofluidic systems, applicable across a wide range of fields.

Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau–Zener transition in atomic, molecular, and optical physics, the band structure of condensed matter physics and the dispersion relation of relativistic quantum physics. We revisit this fundamental phenomenon in the simple example of a spinless relativistic quantum particle traveling in (1+1)-dimensional space-time and establish its relation to a spin-1/2 system evolving under a PT -symmetric Hamiltonian. This relation allows us to simulate 1-dimensional eigenvalue problems with a single qubit. Generalizing this relation to the eigenenergy problem of a bulk system with N spatial dimensions reveals that its eigenvalue problem can be mapped onto the time evolution of the edge state with (N − 1) spatial dimensions governed by a non-Hermitian Hamiltonian. In other words, the bulk eigenenergy state is encoded in the edge state as a hologram, which can be decoded by the propagation of the edge state in the temporal dimension. We argue that the evolution will be PT -symmetric as long as the bulk system admits parity symmetry. Our work finds the application of PT -symmetric and non-Hermitian physics in quantum simulation and provides insights into the fundamental symmetries. [ABSTRACT FROM AUTHOR]

We propose and experimentally investigate a symmetric parity-time (PT) coupled optoelectronic oscillator (COEO) based on a polarization-dependent spatial structure. In such a COEO system, the gain/loss and coupling coefficients of two orthogonal polarization optical waves can be controlled by adjusting the polarization controller (PC) and the bias voltage of a Mach-Zehnder modulator (MZM). The single-mode selection of a microwave signal can be implemented by the PT symmetry breaking of a special mode. The performance of the proposed COEO is experimentally examined, and a 10.0 GHz microwave signal with a phase noise of −109.1 dBc/Hz @ 10 kHz and a side mode suppression ratio of 51.4 dB is generated. Moreover, an optical frequency comb with a comb tooth spacing of 10.0 GHz and a bandwidth of 100 GHz within a 10 dB amplitude variation can be simultaneously generated. [ABSTRACT FROM AUTHOR]

A stable and tunable parity-time (PT) symmetric single-longitudinal-mode fiber laser using a nonreciprocal Sagnac loop is proposed, which is experimentally and numerically demonstrated. The nonreciprocal Sagnac loop only including a 3-dB optical coupler (OC) and a polarization controller (PC) is incorporated into a fiber ring cavity, in which the nonreciprocal light transmission between frequency-degenerate clockwise (CW) and counterclockwise (CCW) resonator modes is induced to suppress multiple-longitudinal-mode oscillation of the laser. The two light paths along the CW and CCW directions in the Sagnac loop are respectively defined as the gain and loss loops of the PT-symmetric laser, due to a controllable birefringence induced by the PC. By controlling the polarization states of the two light waves, the PT symmetry is broken when the gain coefficient is larger than the coupling coefficient, single-mode lasing is thus achieved. Experimental results show that the optical signal to noise ratio (OSNR) of the single-mode lasing at 1550 nm is 43.0 dB, proving the great superiority of PT symmetry for lasing mode selection. By tuning an optical tunable band-pass filter incorporated into the fiber cavity, the wavelength of single-mode lasing varies from 1530 to 1560 nm, and their 3-dB Lorentzian linewidth varies within a range from 529 to 687 Hz. During a 30-min observation period, the variations of wavelength drift and OSNR of the single-mode lasing are less than 6 pm and 2.42 dB, respectively. The advantages of the proposed scheme are obvious, which include simple structure, low cost, simple operation, and good stability.

Topological edge states arise in non-Hermitian parity-time (⁠|$\mathcal {PT}$|⁠)-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken |$\mathcal {PT}$| symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in |$\mathcal {PT}$| -symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the |$\mathcal {PT}$| -symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in |$\mathcal {PT}$| -symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in |$\mathcal {PT}$| -symmetric non-Hermitian systems in general. [ABSTRACT FROM AUTHOR]

Whispering gallery mode (WGM) microcavities have attracted wide attention due to their small mode volume, ultra-high Q value, and low threshold. However, in rotationally symmetric WGM microcavities, multiple longitudinal mode laser radiation can be generated, and the directionality of the radiation is poor, which limits its practical applications. Finding effective methods to achieve single-mode radiation of WGM lasers is a key issue for microcavity lasers to move toward practical applications. This review focuses on several methods of single-mode modulation of WGM lasing in recent years, including reducing cavity size, adding mode selection structure, based on the vernier effect, parity-time symmetry breaking, deformed microcavity, etc. This review aims to provide a reference for researchers in related fields and deepen their understanding of the physical mechanism of single-mode modulation of WGM lasing. [ABSTRACT FROM AUTHOR]

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

Parity–time (PT) symmetry challenges the long-held theoretical basis that only Hermitian operators correspond to observable phenomena in quantum mechanics. Non-Hermitian Hamiltonians satisfying PT symmetry also have a real-valued energy spectrum. In the field of inductor–capacitor (LC) passive wireless sensors, PT symmetry is mainly used for improving performance in terms of multi-parameter sensing, ultrahigh sensitivity, and longer interrogation distance. For example, the proposal of both higher-order PT symmetry and divergent exceptional points can utilize a more drastic bifurcation process around exceptional points (EPs) to accomplish a significantly higher sensitivity and spectral resolution. However, there are still many controversies regarding the inevitable noise and actual precision of the EP sensors. In this review, we systematically present the research status of PT-symmetric LC sensors in three working areas: exact phase, exceptional point, and broken phase, demonstrating the advantages of non-Hermitian sensing concerning classical LC sensing principles. [ABSTRACT FROM AUTHOR]

This work proposes and experimentally demonstrates a high-performance polarization space parity-time (PT) symmetric fiber ring laser to achieve a low-noise, narrow-linewidth, and highly stable single-longitudinal-mode output. The gain/loss and coupling coefficients are regulated by adjusting a polarization controller (PC) and the pumping current of an erbium-doped fiber amplifier (EDFA) within the ring cavity. The results show that the single longitudinal mode oscillation of the laser can be implemented by PT symmetry breaking. The frequency noise spectral density and the linewidth characteristics of the laser are evaluated by the short-delay self-heterodyne method. The results reveal that excellent low-frequency noise (181 Hz2/Hz at a 10 kHz offset frequency) and narrow fundamental linewidth (68 Hz) can be achieved. Additionally, the laser exhibits outstanding stability with only 0.64 pm wavelength drift over 30 min. By tuning an optical tunable filter (OTF), the wavelength tunable range of the laser can cover the entire C-band. Furthermore, the impacts of different fiber length on the frequency noise spectral density and the filter bandwidth on stability are analyzed, offering guidance for component selection in such laser systems.

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.

Parity-time (PT) symmetry has garnered significant attention in the field of photonics owing to its remarkable properties. High-performance lasers, which require simultaneous gain and loss, serve as an ideal platform for harnessing the exceptional properties of PT symmetry. In this study, we present and experimentally verify a polarimetric PT-symmetry fiber laser that uses a polarization-maintaining fiber Bragg grating (PM-FBG). This design allows for tunable, switchable dual-wavelength operation with narrow linewidth and orthogonal single-polarization characteristics. By converting two equal-length yet distinct polarization states into two spatial subspaces sharing a common wavelength space, we can achieve PT symmetry. Regulating the polarization controllers (PCs) enables interconversion between PT-symmetry phases. During the PT-symmetric phase (or PT exact phase), a dual-wavelength laser is realized with wavelength fluctuations below 0.098 nm and power fluctuations below 2.175 dB. At this stage, light propagates through both ordinary and extraordinary wavelength-spaces. During the PT-broken phase, one waveguide has a net gain and the other incurs a net loss, leading to a single longitudinal mode (SLM) laser output. The wavelength and power fluctuations of left-wavelength λ1 and right-wavelength λ2 remain below 0.002 nm and 0.770 dB over a 20-minute period, during single-wavelength operation. By adjusting the axial strain on the PM-FBG, the laser output can be tuned within the wavelength range of 1549.754 nm to 1551.690 nm, while maintaining a linewidth variation of less than 0.130 kHz. As the wavelength is adjusted, the azimuth sum of λ1 and λ2 consistently remains close to 90 degrees, accompanied by degrees of polarizations exceeding 99%.

We consider -symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain–loss coefficient, these systems are protected from spontaneous -symmetry breaking. If the nonhermitian part of the array matrix has cross-compensating structure, the total power in such a system remains bounded—or even constant—at all times. We identify two-, three-, and four-waveguide arrays with cross-compensatory nonlinear gain and loss that constitute completely integrable Hamiltonian systems. [ABSTRACT FROM AUTHOR]

Under vanishing and non-vanishing boundary conditions, we consider general soliton solutions of a fully PT-symmetric multidimensional non-local nolinear Schrödinger equation with time reversal. Concrete expressions could be written as N × N Gram-type determinants by employing Hirota's bilinearity and the KP hierarchy reduction, for positive integer N. Furthermore, the typical dynamics and behaviours of high-order soliton solutions are illustrated graphically. [ABSTRACT FROM AUTHOR]

Optical parity-time ( $\mathcal{PT}$ ) symmetry has triggered a plethora of theoretical and experimental studies, and as a result non-Hermitian photonics is one of the frontiers of optics today. From unidirectional invisibility and coherent perfect absorbers to wireless power transfer and ultrasensitive sensors, non-hermiticity led to numerous important applications that rely on gain-loss synthetic structures. In particular, one such structure is that of complex photonic lattices that may exhibit exceptional points (EPs) around which the corresponding sensitivity is increased by orders of magnitude. Here, we investigate a new multiparametric family of non-Hermitian lattices that respects $\mathcal{PT}$ -symmetry, and examine their spectral sensitivity in terms of pseudospectra, as well, the angular excitation of the underlying EPs.

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

The first good prediction of the multipole soliton solution for the non-integrable equation, i.e., the saturable nonlinear Schrödinger equation under the PT-symmetric potential, is achieved using the physical information neural network. In addition, we construct multipole (tripole to sextupole) soliton families in saturable nonlinear media with fractional diffraction under the PT-symmetric potential, and quadrupole, pentapole and sextupole solitons can coexist for the same parameters. The existence of multipole solitons is modulated by the modulation intensity of the PT-symmetric potential and Lévy index altogether, while the stable domain of multipole solitons is modulated by both the power and Lévy index together. With the increase in the modulation intensity of the PT-symmetric potential and Lévy index, the existence domain of multipole solitons gradually enlarges. When the soliton power is conserved, with the add of the Lévy index, the peak amplitudes at the outermost part of the profiles of real and imaginary parts for the multipole soliton increase, while the peak amplitudes at other positions decrease, and yet the soliton width increases. In addition, the strong saturable nonlinearity not only reduces the stability of tripole solitons but also inhibits the instability of quadrupole and pentapole solitons. However, the saturable nonlinear intensity exists a threshold for the stability modulation of sextupole solitons, beyond which the stability of sextupole solitons is no longer modulated by the saturable nonlinearity. [ABSTRACT FROM AUTHOR]

The proof-of-concept of the exploitation of Coherent Perfect Absorption (CPA) in electrically-injected distributed-feedback laser sources is reported. Capitalizing on the essence of CPA as "light extinction by light", an integrated laser-modulator scheme emerges. The key ingredient compared to conventional single-frequency laser diodes is a careful periodic in-phase modulation of both real and imaginary parts of the complex grating index profile that enables both single-frequency operation and 40 dB line purity at the Bragg frequency. It is shown that this combination is most apt for the operation of CPA as a modulation mechanism that respects the laser spectral purity. The specific proof-of-concept is based on an ultra-short external cavity formed by a metallic micro-mirror, whose role is to generate the second beam of more conventional CPA interferometric approaches. The implemented complex-coupled grating is compatible with existing industrial technologies and promising for real-life laser source applications. Furthermore, the concept can be directly transferred to other material platforms and other wavelengths ranging from terahertz to ultraviolet., (© 2024 The Author(s). Small published by Wiley‐VCH GmbH.)

Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition to the well-established methods for characterizing time-invariants in non-Hermitian systems.

Manipulating single emitter radiation is essential for quantum information science. Significant progress has been made in enhancing the radiation efficiency and directivity by coupling quantum emitters with microcavities and plasmonic antennas. However, there has been a great challenge to generate complex radiation patterns such as vortex beam from a single emitter. Here, we report a chiral plasmonic nanocavity, which provides a strong local chiral vacuum field at an exceptional point. We show that a single linear dipole emitter embedded in the nanocavity will radiate to vortex beam via anomalous spontaneous emission with a Purcell enhancement factor up to ∼1000. Our scheme provides a new field manipulation method for chiral quantum optics and vortex lasers at the nanoscale.

We investigate the scattering properties of coupled parity-time (PT) symmetric chiral nanospheres with scattering matrix formalism. The exceptional points, i.e., spectral singularities at which the eigenvalues and eigenvectors simultaneously coalesce in the parameter space, of scattering matrix can be tailored by the chirality of the nanospheres. We also calculate the scattering, absorption and extinction cross sections of the PT-symmetric chiral scatter under illumination by monochromatic left- and right-circularly polarized plane waves. We find that the scattering cross section of the nanostructures exhibits an asymmetry when the plane waves are incident from the loss and gain regions, respectively, especially in the broken phase, and the optical cross section exhibits circular dichroism, i.e., differential extinction when the PT-symmetric scatter is endowed with chirality. In particular, under illumination by linearly polarized monochromatic plane waves without intrinsic chirality, the ellipticity of scattered fields in the forward direction, denoting the chirality of light, becomes larger when the scatter is in the PT-symmetry-broken phase. Our findings demonstrate that the gain and loss can control the optical chirality and enhance the chiroptical interactions and pave the way for studying the resonant chiral light–matter interactions in non-Hermitian photonics.

We propose and experimentally investigate a symmetric parity-time (PT) coupled optoelectronic oscillator (COEO) based on a polarization-dependent spatial structure. In such a COEO system, the gain/loss and coupling coefficients of two orthogonal polarization optical waves can be controlled by adjusting the polarization controller (PC) and the bias voltage of a Mach-Zehnder modulator (MZM). The single-mode selection of a microwave signal can be implemented by the PT symmetry breaking of a special mode. The performance of the proposed COEO is experimentally examined, and a 10.0 GHz microwave signal with a phase noise of −109.1 dBc/Hz @ 10 kHz and a side mode suppression ratio of 51.4 dB is generated. Moreover, an optical frequency comb with a comb tooth spacing of 10.0 GHz and a bandwidth of 100 GHz within a 10 dB amplitude variation can be simultaneously generated.

By studying the eigenvalues and eigenvectors of a non-Markovian anti parity-time (APT) symmetric system, we investigate the possibility of exceptional points (EPs) that may arise within it. Our work is motivated by a recently studied APT-symmetric experimental configuration consisting of a pair of time-delay coupled semiconductor lasers (SCLs). In such a system, a single time-delay represents the memory. The time-delayed coupling makes the system’s effective Hamiltonian infinite-dimensional and leads to novel features in the corresponding eigenvalues and eigenvectors. In particular, we demonstrate analytically and numerically that unlike a typical PT-symmetric dimer with zero time-delay, which has one second-order EP, our time-delayed system has parameter regimes that give rise to either one, two, or zero second-order EPs and one third-order EP, and one can select these regimes though a judicious choice of the time-delay and coupling.

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT -symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT -symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green's matrix retrieval and Marchenko-type Green's matrix retrieval in PT -symmetric materials. [ABSTRACT FROM AUTHOR]

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The in‐memory processor has played an essential role in overcoming the von Neumann bottleneck, which arises from the partition of memory and a processing unit. Although photonic technologies have recently attracted attention for ultrafast and power‐efficient in‐memory computing, the realization of an all‐optical in‐memory processor remains a challenge. This difficulty originates from the contradiction between robustness and sensitivity in wave dynamics, requiring both noise‐immune memory states and modulation‐sensitive transitions between these states. Here, a building block that provides an all‐optical transition between topologically protected memory states is proposed. A nonlinear photonic molecule that satisfies parity‐time (PT) symmetry, revealing multiple oscillation quenching states with different degeneracies determined by PT‐symmetric phases is investigated. In terms of topology for dynamical systems, these quenching states support topologically protected dynamical trajectories suitable for stable memory states. An all‐optical bidirectional transition between these states, which allows incoherent memory switching is demonstrated. The result provides design criteria for all‐optical in‐memory processors with multilevel operations, enabling the classical‐wave counterpart of electronic memristors. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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