Parity-time Symmetric Systems Research Articles

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.

Independent control of circularly polarized light with exceptional topological phase coding metasurfaces

Exceptional points, as degenerate points of non-Hermitian parity-time symmetric systems, have many unique physical properties. Due to its flexible control of electromagnetic waves, a metasurface is frequently used in the field of nanophotonics. In this work, we developed a parity-time symmetric metasurface and implemented the 2π topological phase surrounding an exceptional point. Compared with Pancharatnam-Berry phase, the topological phase around an exceptional point can achieve independent regulation of several circular polarization beams. We combined the Pancharatnam-Berry phase with the exceptional topological phase and proposed a composite coding metasurface to achieve reflection decoupling of different circular polarizations. This work provides a design idea for polarimetric coding metasurfaces in the future.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.

Switchable and tunable orthogonal single-polarization dual wavelength SLM fiber laser based on parity-time symmetric system and PM-FBG

A dual-wavelength narrow linewidth orthogonal single polarization fiber laser based on a parity-time (PT) symmetric system is proposed and demonstrated, which achieves the function of tunable and switchable wavelength, and single longitudinal mode (SLM) operation. The PT symmetric system composes of a single physical loop, which includes two polarization controllers (PCs) and a polarization beam splitter (PBS). By modulating PCs to match gain, loss and coupling coefficient, the switchable wavelength and stable SLM laser output have been achieved. Through stretching the polarization maintaining fiber Bragg grating (PM-FBG), the wavelength adjustment range from 1549 nm to 1551 nm is obtained. In the process of tuning, the full width at half maxima (FWHM) linewidths and polarization states at each wavelength have been measured and keep basically stable. The measured FWHM linewidths are less than 13.66 kHz and 11.89 kHz. Further, the stable orthogonal single polarization state has been realized. The degree of polarization (DOP) at each wavelength exceeds 97% and basically remains unchanged during 20 min.

Role of losses and coupling in bright-dark metasurfaces mimicking non-Hermitian parity-time symmetric systems

All real systems are essentially non-conservative in nature, which is non-Hermitian in the fundamental premises of the quantum realm. Such open systems obeying parity-time (PT) symmetry can offer intriguing physics, which has sparked much attention in recent years. The thoughtful interplay of loss and gain in PT-symmetric systems can tune the eigenstates from real to complex space passing through a singular point known as an exceptional point (EP) with concurrently coalescing the discrete eigenstates. In this regard, artificially engineered near-field coupled metasurfaces provide a remarkable podium to introduce as well as control loss and coupling strength simultaneously, manifesting a practical channel to attain EP. Motivated by this notion, we have theoretically explored near-field coupled dark-bright-mode assisted terahertz metasurfaces imitating a typical non-Hermitian PT-symmetric system. Structurally, such metasurfaces are realized by utilizing a pair of orthogonally twisted near-field coupled split-ring resonators (bright-dark-resonators). We have meticulously examined such a system with two distinctive approaches, i.e., the loss parameter and inter-resonator coupling strength. Eventually, our exploration demonstrates that judicious modulation of the loss parameter can invoke an undemanding route to approach the other wisely elusive exceptional point. We believe that this comprehensive study of non-Hermitian quantum systems in a photonic context can lead to the development of accurate and precise ultra-sensitive sensors besides other futuristic photonic devices.

Requisites on material viscoelasticity for exceptional points in passive dynamical systems

Recent progress in non-Hermitian physics and the notion of exceptional point (EP) degeneracies in elastodynamics have led to the development of novel metamaterials for the control of elastic wave propagation, hypersensitive sensors, and actuators. The emergence of EPs in a parity-time symmetric system relies on judiciously engineered balanced gain and loss mechanisms. Creating gain requires complex circuits and amplification mechanisms, making engineering applications challenging. Here, we report strategies to achieve EPs in passive non-Hermitian elastodynamic systems with differential loss derived from viscoelastic materials. We compare different viscoelastic material models and show that the EP emerges only when the frequency-dependent loss-tangent of the viscoelastic material remains nearly constant in the frequency range of operation. This type of loss tangent occurs in materials that undergo stress-relaxation over a broad spectrum of relaxation times, for example, materials that follow the Kelvin–Voigt fractional derivative (KVFD) model. Using dynamic mechanical analysis, we show that a few common viscoelastic elastomers, such as polydimethylsiloxane and polyurethane rubber, follow the KVFD behavior such that the loss tangent becomes almost constant after a particular frequency. The material models we present and the demonstration of the potential of a widely available material system in creating EPs pave the way for developing non-Hermitian metamaterials with hypersensitivity to perturbations or enhanced emissivity.

Ultra-Narrow Bandwidth Microwave Photonic Filter Implemented by Single Longitudinal Mode Parity Time Symmetry Brillouin Fiber Laser.

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.

Generation of an ultrashort pulse train through ultrafast parity-time symmetry switching.

We propose a scheme for the direct generation of an ultrashort pulse train as well as the further compression of pulsed lasers based on the nonlinearity inherent to parity-time (PT) symmetric optical systems. Implementation of optical parametric amplification in a directional coupler of χ(2) waveguides enables ultrafast gain switching through pump-controlled breaking of PT symmetry. We theoretically demonstrate that pumping such a PT symmetric optical system with a periodically amplitude-modulated laser enables periodic gain switching, which can directly convert a continuous-wave signal laser into a train of ultrashort pulses. We further demonstrate that by engineering the PT symmetry threshold, an apodized gain switching that enables the production of ultrashort pulses without side lobes. This work suggests a new approach for exploring the non-linearity inherent to various PT symmetric optical structures to extend optical manipulation capabilities.

Polar magneto-optic Kerr and Faraday effects in finite periodic PT -symmetric systems

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $\theta^{R}_1$, is always equal to the $\theta^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $\theta^{R^{r/l}}_2$ are related to the $\theta^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR.

Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points.

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

Parity-time symmetry breaking optical nanocircuit.

Gain and loss balanced parity-time (PT) inversion symmetry has been achieved across multiple platforms including acoustics, electronics, and photonics. Tunable subwavelength asymmetric transmission based on PT symmetry breaking has attracted great interest. However, due to the diffraction limit, the geometric size of an optical PT symmetric system is much larger than the resonant wavelength, which limits the device miniaturization. Here, we theoretically studied a subwavelength optical PT symmetry breaking nanocircuit based on the similarity between a plasmonic system and an RLC circuit. Firstly, the asymmetric coupling of an input signal is observed by varying the coupling strength and gain-loss ratio between the nanocircuits. Furthermore, a subwavelength modulator is proposed by modulating the gain of the amplified nanocircuit. Notably, the modulation effect near the exceptional point is remarkable. Finally, we introduce a four-level atomic model modified by the Pauli exclusion principle to simulate the nonlinear dynamics of a PT symmetry broken laser. The asymmetric emission of a coherent laser is realized by full-wave simulation with a contrast of about 50. This subwavelength optical nanocircuit with broken PT symmetry is of great significance for realizing directional guided light, modulator and asymmetric-emission laser at subwavelength scales.

Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect (PSHE) in antisymmetric parity-time (APT) metamaterials with incidence of Gaussian beams is proposed here. We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials. Furthermore, detailed discussions are provided on the APT scattering matrix, eigenstate ratio, and response near exceptional points in the case of loss or gain. In contrast to the unidirectional non-reflection in parity-time (PT) symmetric systems, the transverse shift that arises from both sides of the APT structure is consistent. By effectively adjusting the parameters of APT materials, we achieve giant displacements of the transverse shift. Finally, we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials. By increasing the number of layers, Bragg oscillations can be generated, leading to an increase in resonant peaks in transverse shift. This study presents a new approach to achieving giant transverse shifts in the APT structure. This lays a theoretical foundation for the fabrication of related nano-optical devices.

Designing Optimal Linear Detectors: A Bottom-Up Approach

This paper develops a systematic approach to realizing linear detectors with an optimized sensitivity, allowing for the detection of extremely weak signals. First, general constraints are derived on a specific class of input-output transfer functions of a linear detector. Then a physical realization of transfer functions in that class is found using the quantum network synthesis technique, which allows for the inference of the physical setup directly from the input-output transfer function. By exploring a minimal realization which has the minimum number of internal modes, it is shown that the optimal such detectors are internal squeezing schemes. Then, investigating nonminimal realizations, which is motivated by parity-time symmetric systems, a quantum nondemolition measurement is systematically recovered.

Coherent Perfect Absorption in Higher Order Systems

We investigate the phenomenon of coherent perfect absorption in a high-order system with three passive resonators coupled to a super-surface to form this three-state coherent perfect absorber. The effective parity time (PT) symmetry in the passive system has received much attention, and in this open three-state PT symmetric system, the incident wave is used as the effective gain instead of balancing the material gain and loss. We analyze the variation of coherent perfect absorption of this system with the coupling coefficient of the system by simulation.

Dual-loop parity-time symmetric system with a rational loop length ratio.

By exploring the relationship between the gain/loss and the coupling coefficient, parity-time (PT) symmetry has been well explored in the photonics and optoelectronics fields to achieve unique functions, such as sidemode suppression, non-reciprocal light propagation, and unidirectional invisibility. In general, a PT-symmetric system has an architecture with two identical coupled resonators or loops. In this Letter, we explore the possibility of implementing a PT-symmetric system having an architecture with one resonator having a loop length that is a rational number of times the length of the other resonator, to increase the sidemode suppression ratio. A theoretical analysis is performed, which is validated by a proof-of-concept experiment in which a fiber ring laser having two loops with a length ratio being a rational number of 200/3, supporting single-longitudinal-mode lasing at 1555.88 nm, is demonstrated. Thanks to the non-identical loop lengths, the sidemode suppression ratio is increased, which is 53.2 dB in the experiment.

Nonreciprocal transmission of electromagnetic waves with nonlinear active plasmonic metasurfaces

Nonreciprocity is important for optical information processing, full-duplex communications, and protection of sensitive laser equipment from unwanted reflections. However, it is very challenging to obtain strong nonreciprocal response in optical frequencies, especially when nanoscale configurations are considered. In this work, we solve this problem by demonstrating a compact bifacial plasmonic metasurface that acts as an ultrathin nonreciprocal transmission filter at near-infrared frequencies. The proposed nanostructure is simple to be practically implemented, since it is composed of two silver nanostripes with different dimensions placed on both sides of an ultrathin active dielectric spacing layer. The introduced gain leads to an exceptional point formation in the linear operation regime, where unidirectional perfect transmission due to loss compensation is achieved from the presented non-Hermitian parity-time symmetric nanoscale system. The demonstrated plasmonic metasurface breaks the Lorentz reciprocity law at the nanoscale when its nonlinear response is considered, mainly due to its spatially asymmetric geometry combined with enhanced nonlinearity. Strong and broadband nonreciprocity with unity transmission contrast from opposite directions is realized under relatively low-input laser intensity values. Furthermore, asymmetric nonlinear third-harmonic generation with a pronounced contrast is also illustrated by the same nonreciprocal metasurface design. The findings of this work can lead to the realization of various self-induced nonreciprocal nanophotonic configurations, such as integrated ultrafast switches, ultrathin protective coatings, and asymmetric directional imaging devices.

Generation of second-order sideband and slow-fast light effects in a PT-symmetric optomechanical system

We theoretically study the second-order sideband generation and slow-fast light effects in a parity-time (PT) symmetric optomechanical system, which consists of an active cavity and a passive cavity containing optical parametric amplifier (OPA). Compared to the double-passive nonlinear system, we find that the second-order sideband efficiency can be significantly enhanced by the tunneling strength in the PT-symmetric system with OPA. The flexible manipulation of the second-order generation also can be realized by modulating OPA gain and phase. Moreover, the fast and slow light effects in the optomechanical system are discussed. When the tunneling strength J=3κ1, the time of the second-order sideband group delay can be effectively prolonged in a PT-symmetric cavity in the presence of OPA. The results may have some guidance for the enhancement of second-order sideband efficiency, which has potential applications in optical communication and storage.

Enhancement of the conversion efficiency of optical spin-orbit interactions in PT symmetric systems.

The optical spin-orbit interaction (SOI) caused by momentum-dependent Pancharatnam-Berry phase (PB) provides new opportunities in the development of spin-optical devices, but the relatively low conversion efficiency limits its application. Here, through rigorous full-wave analyses on it in a parity-time (PT) symmetric system with thickness less than a wavelength, we find that the conversion efficiency of the SOI can be enhanced in both transmission and reflection in a wide range of incidence angles. When the parameters of the PT symmetric system meet the requirement of coherent perfect absorbers-laser mode, the effective anisotropy between the TM and TE components (e.g., a difference of their Fresnel coefficients) within the beam will be amplified dramatically, which results in significantly enhanced conversion efficiency of SOIs (up to 106). These findings offer an effective way to modulate the SOIs with an ultra-thin PT symmetric system, and may exhibit applications in spin-orbit optical devices.

PT symmetric single-mode line-defect photonic crystal lasers with asymmetric loss design.

The exploration of parity-time (PT) symmetry in micro-/nano-cavity lasers has recently gained immense research interest. The PT symmetric phase transition to single-mode lasing has been achieved by arranging the spatial distribution of optical gain and loss in single or coupled cavity systems. In terms of photonic crystal (PhC) lasers, a non-uniform pumping scheme is usually employed to enter the PT symmetry-breaking phase in a longitudinal PT symmetric system. Instead, we use a uniform pumping scheme to enable the PT symmetric transition to the desired single lasing mode in line-defect PhC cavities based on a simple design with asymmetric optical loss. The flexible control of gain-loss contrast is realized by removing a few rows of air holes in PhCs. We obtain single-mode lasing with a side mode suppression ratio (SMSR) of around 30 dB without affecting the threshold pump power and linewidth. The output power of the desired mode is six times higher than that in multimode lasing. This simple approach enables single-mode PhC lasers without sacrificing the output power, threshold pump power, and linewidth of a multimode cavity design.

Comprehensive study of singular points in a PT-symmetric Thue-Morse multilayer

Parity-time symmetric optical systems have a non-Hermitian Hamiltonian with a purely real spectrum. These systems have been extensively explored owing to their ability to generate exotic photon transport phenomena. In this work, we report the spectral singularity of the one-dimensional aperiodic odd-generation Thue-Morse photonic lattice with parity time symmetry. We showed that this multilayer in addition to obvious unidirectional and bidirectional transparencies, displays interesting and singular properties including absorption, lasing and coherent perfect absorption-lasing singularities. Based on the transfer matrix and scattering matrix (S matrix) methods, the behavior of these singular points and reflectionless and invisibility properties of the structure is analyzed with respect to the thickness of the passive film sandwiched between active layers due to phase shift changes, frequency and incident angle of light. The available values of the structural parameters are investigated to obtain extraordinary transmission and reflection phenomena. These optical systems may possess the potential in the design of novel lasing and coherent perfect absorption optical devices with adjustable applications.