Parity-time Research Articles

A robust parity‐time‐symmetric hybrid wireless power transfer system with extended coupling range

SummaryInductive power transmission (IPT) and capacitive power transmission (CPT) are currently the two main wireless power transfer technologies. Hybrid power transmission (HPT) systems that combine IPT and CPT can improve transmission performance and are more attractive for some charging applications such as electric bicycles (e‐bikes). However, HPT systems are more sensitive to parameter variations, and the coupling mechanism is prone to misalignment during wireless charging. Therefore, achieving stable output power and constant transfer efficiency over a wide range of coupling coefficient variations is still a major challenge for HPT systems. In this work, the parity–time (PT) symmetry theory is applied to an SS‐type HPT system, and a circuit model of the PT‐based HPT system is developed by using coupling capacitance and coupling inductance. The effect of connecting the plates to the homonymous end or heteronymous end of the coupling coils on the PT symmetry range of the HPT system is discussed. It is found that the heteronymous end connection of the coils can effectively increase the range of constant output power and stable transfer efficiency. Finally, a prototype is built to verify the feasibility and effectiveness of the proposed PT‐based HPT system. The transfer power and efficiency remain constant in the PT‐symmetric range, and the inductive and capacitive coupling coefficients are smaller compared to IPT and CPT systems with the same parameters.

Design of a high sensitivity and wide range angular rate sensor based on exceptional surface

Abstract It is found that when the parity time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point, the sensitivity can be significantly amplified at low angular rate in theory. However, in fact, the exceptional point is easily disturbed by external environmental variables, which means that it depends on harsh experimental environment and strong control ability, so it is difficult to move towards practical application. Here, we propose a new angular rate sensor structure based on exceptional surface, which have the advantages of high sensitivity and high robustness. The system consists of two fiber-optic ring resonators and two optical loop mirrors, and one of resonators contains a variable ratio coupler and a variable optical attenuator. We theoretically analyzed the system response and the effects of phase and coupling ratio on the system response, respectively. Finally, compared with conventional resonant gyro, the sensitivity of this exceptional surface angular rate sensor can be improved by about 300 times at low speed. In addition, by changing the loss coefficient in the ring resonator, it can achieve a wide range of 600 rad/s. This scheme provides a new approach for the development of ultra-high sensitivity and wide range angular rate sensors in the future.

Ultra low-power multistability in [formula omitted]-symmetric periodic structures with saturable coupling, gain and loss

The present work investigates the switching dynamics of conventional fiber Bragg gratings (FBGs) with saturable coupling and parity-time (PT)-symmetric fiber Bragg gratings (PTFBGs) with saturable coupling (SC) and saturable gain-loss (SGL) in the presence of Kerr nonlinearity (KNL) [model - I] and saturable nonlinearity (SNL) [model - II]. Both system models can generate distinct optical multistability (OM) and bistability (OB) curves, including S-shaped, ramp-like, and mixed OM curves in both unbroken and broken PT-symmetric regimes. The impact of each control parameter on controlling switching intensities, hysteresis width, and the number of stable states is thoroughly examined for both of these system models. The direction of right light incidence enables a significant reduction in the switching intensities to below 100 W/cm2, the lowest critical power ever reported in the literature of PTFBGs, thanks to the concept of both saturable coupling, gain and loss.

Observation of energy localization in nonlinear non-Hermitian systems

Energy localization in Hermitian systems has been utilized to generate ultra-sensitivity. Here, we report the interplay between non-Hermitian parity-time (PT) symmetry breaking and the mode localization transition. In our scheme, a PT-symmetric system consists of two coupled LC (inductor–capacitor) resonators: one has a linear loss and the other has a saturated gain described by a nonlinear model. The nonlinear gain is initially set to be slightly higher than the loss, and the system is operated at the exact PT-symmetric phase close to an exceptional point. The capacitance variation applied on the loss resonator, i.e., perturbation, causes PT-symmetry to break, generating complex frequencies. As a result of nonlinear gain, the resonator will grow to reach its steady state and saturate out the gain. This stable oscillation eliminates the complex frequencies, and the mode is ultimately localized at the gain side. We have observed that the voltage amplitude of the gain resonator due to the perturbation has experienced drastic changes. The amplitude ratio before and after the perturbation is sensitive to the perturbation. Our results provide an approach to study perturbation-driven localization phenomena in a PT-symmetric system and pave the way for sensors with ultrahigh sensitivity.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

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.

Experimental Demonstration of Controllable PT and Anti-PT Coupling in a Non-Hermitian Metamaterial.

Non-Hermiticity has recently emerged as a rapidly developing field due to its exotic characteristics related to open systems, where the dissipation plays a critical role. In the presence of balanced energy gain and loss with environment, the system exhibits parity-time (PT) symmetry, meanwhile as the conjugate counterpart, anti-PT symmetry can be achieved with dissipative coupling within the system. Here, we demonstrate the coherence of complex dissipative coupling can control the transition between PT and anti-PT symmetry in an electromagnetic metamaterial. Notably, the achievement of the anti-PT symmetric phase is independent of variations in dissipation. Furthermore, we observe phase transitions as the system crosses exceptional points in both anti-PT and PT symmetric metamaterial configurations, achieved by manipulating the frequency and dissipation of resonators. This work provides a promising metamaterial design for broader exploration of non-Hermitian physics and practical application with a controllable Hamiltonian.

Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing

Nonlinear optical signal processing (NOSP) has the potential to significantly improve the throughput, flexibility, and cost-efficiency of optical communication networks by exploiting the intrinsically ultrafast optical nonlinear wave mixing. It can support digital signal processing speeds of up to terabits per second, far exceeding the line rate of the electronic counterpart. In NOSP, high-intensity light fields are used to generate nonlinear optical responses, which can be used to process optical signals. Great efforts have been devoted to developing new materials and structures for NOSP. However, one of the challenges in implementing NOSP is the requirement of high-intensity light fields, which is difficult to generate and maintain. This has been a major roadblock to realize practical NOSP systems for high-speed, high-capacity optical communications. Here, we propose using a parity-time (PT) symmetric microresonator system to significantly enhance the light intensity and support high-speed operation by relieving the bandwidth-efficiency limit imposed on conventional single resonator systems. The design concept is the co-existence of a PT symmetry broken regime for a narrow-linewidth pump wave and near-exceptional point operation for broadband signal and idler waves. This enables us to achieve a new NOSP system with two orders of magnitude improvement in efficiency compared to a single resonator. With a highly nonlinear AlGaAs-on-Insulator platform, we demonstrate an NOSP at a data rate approaching 40 gigabits per second with a record low pump power of one milliwatt. These findings pave the way for the development of fully chip-scale NOSP devices with pump light sources integrated together, potentially leading to a wide range of applications in optical communication networks and classical or quantum computation. The combination of PT symmetry and NOSP may also open up opportunities for amplification, detection, and sensing, where response speed and efficiency are equally important.

Fundamental and dipole gap solitons and their dynamics in the cubic-quintic fractional nonlinear Schrödinger model with a [formula omitted]-symmetric lattice

The interplay of two linear controlled terms—fractional diffraction and parity-time (PT) symmetric lattice—gives rise to unique and interesting linear Bloch gap structures within where the nonlinear localized gap modes may exist. In this study, we explore the formation and dynamics of one-dimensional gap solitons in the cubic-quintic physical model combing the fractional diffraction and PT symmetric lattice. Two classes of gap solitons, which we name the fundamental gap solitons and dipole ones, are constructed and their stability regions within the first finite gap of the associated linear Bloch spectrum are identified by means of linear-stability analysis and direct perturbed numerical simulations. We stress that the gap solitons are always unstable under the condition of PT symmetry breaking (the imaginary part of which is above 0.5). The excitations of the stable two classes of gap solitons are also investigated by using the adiabatic variation of the system’s parameters. The results predicted here shed some light on soliton physics in physical systems with combined fractional diffraction and PT symmetric lattice and the competing nonlinearities.

Non-reciprocity in Photonic Crystal Due to Parity Time Symmetric Defect State

In this article, defect state of photonic crystal regarding parity time known as PT-symmetric is explored thoroughly. For this purpose, transfer matrix technique in setting Bloch theorem is employed to characterize the dispersion relation regarding PT-symmetric defect state. The study uncovers the northworthy wave phenomenon entitle “non-reciprocity” is exhibited. Moreover, an increasing the in-plane component of wavevector contributes two or more branches in the short wavelength boundary of the stop-band which is not observed in conventional structures. The reflectance of structure is conducted across the optical regime leads to minimum point that aligns with the wavelength of the eigen mode for wavevector value (kx = 0). These findings of research may have significant applications in various areas of photonics and optics likes filters, modern optical photonic cavity resonators and thermo-photovoltaic devices etc.

In-plane elastic waves in piezoelectric metamaterials with Parity–Time symmetry

The propagation of in-plane waves in piezoelectric metamaterial involves the coupling of longitudinal (i.e. quasi–pressure), transverse (i.e. quasi–shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in–plane wave shows new characteristics. The exceptional point caused by non–Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity–Time symmetry appears and brings in pairs of exceptional points to achieve a complete transmission with a unidirectional zero reflection.

Advances in Semiconductor Lasers Based on Parity-Time Symmetry.

Semiconductor lasers, characterized by their high efficiency, small size, low weight, rich wavelength options, and direct electrical drive, have found widespread application in many fields, including military defense, medical aesthetics, industrial processing, and aerospace. The mode characteristics of lasers directly affect their output performance, including output power, beam quality, and spectral linewidth. Therefore, semiconductor lasers with high output power and beam quality are at the forefront of international research in semiconductor laser science. The novel parity-time (PT) symmetry mode-control method provides the ability to selectively modulate longitudinal modes to improve the spectral characteristics of lasers. Recently, it has gathered much attention for transverse modulation, enabling the output of fundamental transverse modes and improving the beam quality of lasers. This study begins with the basic principles of PT symmetry and provides a detailed introduction to the technical solutions and recent developments in single-mode semiconductor lasers based on PT symmetry. We categorize the different modulation methods, analyze their structures, and highlight their performance characteristics. Finally, this paper summarizes the research progress in PT-symmetric lasers and provides prospects for future development.

Entanglement dynamics of two non-Hermitian qubits

The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.

Parity-time imbalance induced by balanced gain and loss medium in non-Hermitian photonic crystals

Photonic crystals, including gain and loss materials, show numerous intriguing features than the ordinary photonic crystals. In this work, using the full wave simulation, we numerically investigate the photonic crystals with gain and loss which are satisfying the parity-time (PT) symmetry condition to reveal the effect of PT symmetry on the optical properties of photonic crystals, including the exceptional point, distribution of electromagnetic fields and edge states. This work reveals a novel mechanism of coexistence and competition between topological states and non-Hermiticity in all-dielectric photonic crystals and provides an innovative understanding of non-Hermiticity in topological photonic systems.

Tunable narrow linewidth fiber laser based on parity-time symmetric double rings and variable optical attenuator

A tunable narrow linewidth fiber ring laser based on parity-time (PT) symmetric double rings and variable optical attenuator (VOA) is demonstrated. The laser is composed of a fiber loop mirror (FLM), which creates two coupled rings: the reflective ring and the transmissive ring. The loss of the transmissive ring can be controlled by tuning the VOA, which balances with the gain of the reflective ring. When the PT symmetry is broken, a single-longitudinal-mode (SLM) laser is realized. The laser can be tuned by an optical tunable filter (OTF), and the tuning range is 38 nm, spanning from 1525 nm to 1563 nm. In the whole tuning process, the linewidth of the laser is at the sub-kHz level, and the optical signal to noise ratios (OSNR) is over 53 dB. The fluctuation of wavelength and power are less than 0.02 nm and 0.52 dB in an hour, respectively.

Half quantized Hall effect

Here we report a half-quantized Hall effect in a metal or semimetal. The Hall conductance is half quantized and the longitudinal conductance is nonzero. Consequently, the Hall resistivity is not quantized. The half quantization occurs when the parity symmetry or time reversal symmetry emerges near the Fermi surface or Fermi level while the symmetry is broken in the whole system. A recent experiment reports the observation of the half-quantized Hall conductance in a magnetically-doped topological insulator. We discover that a single gapless Dirac cone exists in the band structure and has half-quantized conductance when the Fermi level intercepts the gapless surface states in which the parity symmetry is invariant. As there are no localized chiral edge states in the gapless and metallic system, we find that the chiral edge current is carried by the gapless surface states. The current density peaks at the edge and decays in a power law rather than the exponential decay as in the conventional quantum anomalous Hall effect. The half quantized Hall conductance is a signature of parity anomaly in a single gapless Dirac cone on a lattice. We term the nontrivial quantum phase as “parity anomalous semimetal”. The work opens the door to exploring novel topological states of matter with fractional topological invariants.

Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations

The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrödinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up.

Parity time symmetry all-optical microwave oscillator using a polarization dependent Sagnac loop

An all-optical microwave oscillator based on parity-time symmetry was proposed and experimentally demonstrated. It mainly consists of a big feedback loop, an active small loop and a polarization-dependent Sagnac loop. The microwave seed signal originates from the beating between the continuous wave and the Stokes wave. The function of microwave envelope detection and feedback modulation are implemented through cross gain modulation of two semiconductor optical amplifiers. By employing the parity time symmetry loops and the Vernier effect, the single mode selectivity capability of the oscillator has been enhanced, and a single mode microwave signal with high quality can be generated. In the experiment, a highly quality microwave signal with a frequency of 10.71 GHz was generated. The single side band phase noise can reach −94.1 dBc/Hz@10 kHz and the side mode suppression ratio of the generated microwave signal reaches 41 dB. Compared to the previously reported all-photonic microwave oscillator, the single side band phase noise is improved by 7 dB at a frequency offset of 10 kHz, and by 20 dB at a frequency offset of 100 Hz. The results indicate that our proposed scheme significantly improves the quality of the generated microwave signals.

Giant and tunable photonic spin Hall effect in a parity-time symmetric structure with a Dirac semimetal material

The optical parity-time (PT) symmetry structure can yield unique properties, including periodicity, discreteness, nonlinearity, and so on. However, the component materials in these PT symmetry structures have been primarily restricted by their lack of tunability. Here, by utilizing the external stimulus-dependent optical properties of the Dirac semimetal, we report the theoretical prediction of the large and controllable photonic spin Hall effect in the PT symmetry structure with the slab of the Dirac semimetal. We provide evidence that the PT symmetry structure with the Dirac semimetal exhibits a large spin shift as high as the half of the waist at a certain incident angle, which is the conventionally theoretical upper limit. Due to the exceptional points, the spin shift can be enhanced effectively. Furthermore, we unravel that a small change in the Fermi energy of the Dirac semimetal on the order of 0.01 eV is able to engineer both the magnitude and sign of the spin shift. In particular, there is a transition in the spectrum of the spin shift when we vary the Fermi energy of the Dirac semimetal, where the number of the spin shift peak changes from one to two. Our results reveal the interplay between the light and the PT symmetry structure with the Dirac semimetal, which offers the possibility of developing Dirac semimetal-based spin-dependent photonic devices.

Planar Bilayer PT-Symmetric Systems and Resonance Energy Transfer

Parity-time (PT) symmetry provides an outstanding improvement of photonic devices’ performance due to the remarkable physics behind it. Resonance energy transfer (RET) as an important characteristic mediating the molecules that can be tailored in the PT-symmetric environment, too. We study how planar bilayer PT-symmetric systems affect the process of resonance energy transfer occurring in the vicinity thereof. First, we investigate the reflectance and transmittance spectra of such systems by calculating reflection and transmission coefficients as well as total radiation amplification as functions of medium parameters. We obtain that reflectance and total amplification are greatest near the exceptional points of the PT-symmetric system. Then, we perform numerical calculations of the RET rate and investigate its dependence on the complex permittivity of the PT-symmetric medium, dipole orientation, frequency of radiation and layer thickness. Optically thick PT-symmetric systems may operate at lower gain at the expense of the appearance of chaotic-like behaviors. These appear owing to the dense oscillations in the reflectance and transmittance spectra and vividly manifest themselves as stochastic-like positions of the exceptional points for PT-symmetric bilayers. The RET rate, being a result of the field interference, can be significantly amplified and suppressed near exceptional points exhibiting a Fano-like lineshape.

Nonlocal Metasurface with Chiral Exceptional Points in the Telecom-Band.

The exceptional point (EP) is the critical phase transition point in parity-time (PT) symmetry systems, offering many unique physical phenomena, such as a chiral response. Achieving chiral EP in practical applications has been challenging due to the delicate balance required between gain and loss and complicated fabrication, limiting both working band and device miniaturization. Here, we proposed a nonlocal metasurface featuring orthogonal gold nanorods, where loss modulation is achieved through rod size and lattice pitch. By tuning the coupling strength, we experimentally observed the PT symmetry phase transition and chiral EP in the telecom-band. The experimental and simulated circular conversion dichroism at EP reach 0.79 and 0.99, respectively. We also demonstrated an abrupt phase flip of a specific component near EP theoretically. This work provides a feasible scheme for exploring EP in polarized space within the telecom-band, which may find applications in polarization control, wavelength division multiplexing, ultrasensitive sensing, imaging, etc.