Parity-time Symmetric Structures Research Articles

Extraordinary optical characteristics in a one-dimensional parity-time symmetric structure of quasiperiodic two-material Octonacci optical waveguide network

We explore Exceptional Points (EPs) within a one-dimensional quasiperiodic Octonacci optical waveguide network. This network consists of segments, each composed of two-material subsegments featuring gain and loss materials, creating a parity-time-symmetric structure. We investigate the trend of EPs across generations 3 to 7 of the Octonacci sequence using the generalized eigenfunction method and transfer matrix method. Our findings reveal that as generations progress, band gaps become more pronounced, and the number of EPs significantly increases within these gaps. In particular, the third generation only supports unidirectional transparency. Bidirectional transparency appears in the fourth generation and becomes more pronounced in later generations. Coherent perfect absorption-lasing points are first seen in the seventh generation. These findings have implications for the design of all-optical devices and wideband and/or narrowband optical filters.

Exceptional refrigeration of motions beyond their mass and temperature limitations

Coaxing vibrations in the regimes of both large mass and high temperature into their motional quantum ground states is extremely challenging, because it requires an ultra-high optical power, which introduces extraneous excessive heating and intricate instabilities. Here we propose how to overcome these obstacles and cool vibrational networks by simply harnessing the power of an exceptional point (EP) induced in parity-time symmetric structures; and we reveal its exceptional cooling properties otherwise unachievable in conventional devices. In stark contrast to standard-cooling protocols, a three orders-of-magnitude amplification in net cooling rates arises from the EP-cooling mechanism, without which it vanishes. Remarkably, our EP cooling is nearly immune to both resonator mass and environmental temperature, and this overthrows the consensus that poor intrinsic factors and rugged extrinsic environment suppress cooling channels. Our study offers the possibility of isolating and engineering motional properties of large-mass and high-temperature objects for various applications in optical and acoustic sensing, gravimetry, and inertial navigation.

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.

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.

Nonlinear operation of an FP laser with PT symmetry active medium.

In this paper, an analysis of the nonlinear laser operation in an active medium made of a parity time (PT) symmetric structure placed in a Fabry-Perot (FP) resonator is demonstrated for the first time. The FP mirrors' reflection coefficients and phases, the PT symmetric structure period, primitive cell number, and the gain and loss saturation effects are taken into account in a presented theoretical model. The modified transfer matrix method is used to obtain characteristics of laser output intensity. Numerical results show that the selection of the appropriate phase of the FP resonator's mirrors makes it possible to obtain different levels of the output intensity. Moreover, for certain value of a ratio of the grating period to the operating wavelength, it is possible to obtain the bistability effect.

Parametric gap solitons in PT-symmetric optical structures

Abstract It is well known that quadratic nonlinearity and feedback through Bragg periodicity are the basis for parametric gap solitons. The major part of the relevant investigations refers to passive systems. At the same time, optical systems supplemented with active elements can demonstrate unusual properties. Asymmetry intrinsic to structures with parity-time (PT) symmetry is a bright confirmation of this statement. The interplay of nonlinearity, Bragg reflection and gain/loss profile can lead to the complicated pattern of wave interactions and novel results. In this study we address the properties of two-color solitons in complex PT symmetric periodic structures with quadratic nonlinearity. We focus on the case of single Bragg resonance. We reveal the region of parameters where stable parametric solitons may exist. We demonstrate that characteristics of forming solitons depend on the order of alteration of amplifying and absorbing layers.

Mag-Optical Modulator Based on Parity-Time Symmetric Structure

Mag-Optical Modulator Based on Parity-Time Symmetric Structure

Experimental observation of chiral inversion at exceptional points of non-Hermitian systems

Based on the quantum mechanics, the physical observables are represented by Hermitian linear operators. Derived from the conservation of energy, these Hermitian operators exhibit real eigenvalues. However, when a closed system described by an effective Hamiltonian is coupled with the surrounding environment, the dynamics of the system itself becomes non-Hermitian dynamic. In general, the eigenvalues of an open optical non-Hermitian system are complex. Parity-time symmetric structure is the system composed of complex potentials, which is neither parity symmetric nor time reversal symmetric alone but is symmetric after operations of parity inversion and time reversal have been combined. The eigenvalue of the parity-time symmetric Hamiltonian can be found to be real, despite the non-Hermitian nature of the system. One of the most attractive properties of non-Hermitian system is the exceptional point, which is degenerate at which two or more eigenvalues and eigenstates of a non-Hermitian physical system coalesce. The unique topological features of EPs, forming a self-intersecting Riemann surface, have given rise to several exotic physical properties. As a kind of phase singularity in a physical system, exceptional point of non-Hermitian system gives rise to a plethora of counterintuitive phenomenon, such as the loss-induced transmission enhancement, unidirectional reflection and asymmetric state transfer. Especially, the eigenvectors of exceptional point are self-orthogonal and an inherent chirality can be determined because of the missing dimension. Chirality lies at the heart of the most fascinating and fundamental phenomena in modern physics, and how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point is an interesting research topic. In this work, a non-Hermitian system is constructed based on the special metamaterial resonator of split-ring resonator, in which the sign of coupling coefficient can be flexibly controlled. Especially, the chiral inversion at an exceptional point of non-Hermitian system is observed experimentally. This sign of coupling coefficient controlled exceptional point not only paves a new way for studying the fundamental non-Hermitian physics in an open system, but also holds great potential in the applied photonic devices such as the efficient chiral mode converter and chiral antennas.

Model of Optical Triode Based on Pole Effect of Parity-Time Symmetric Structure

Model of Optical Triode Based on Pole Effect of Parity-Time Symmetric Structure

Azimuthal modulation of electromagnetically induced grating using structured light

We propose a theoretical scheme for creating a two-dimensional Electromagnetically Induced Grating in a three-level Lambda -type atomic system interacting with a weak probe field and two simultaneous position-dependent coupling fields—a two dimensional standing wave and an optical vortex beam. Upon derivation of the Maxwell wave equation, describing the dynamic response of the probe light in the atomic medium, we perform numerical calculations of the amplitude, phase modulations and Fraunhofer diffraction pattern of the probe field under different system parameters. We show that due to the azimuthal modulation of the Laguerre–Gaussian field, a two-dimensional asymmetric grating is observed, giving an increase of the zeroth and high orders of diffraction, thus transferring the probe energy to the high orders of direction. The asymmetry is especially seen in the case of combining a resonant probe with an off-resonant standing wave coupling and optical vortex fields. Unlike in previously reported asymmetric diffraction gratings for PT symmetric structures, the parity time symmetric structure is not necessary for the asymmetric diffraction grating presented here. The asymmetry is due to the constructive and destructive interference between the amplitude and phase modulations of the grating system, resulting in complete blocking of the diffracted photons at negative or positive angles, due to the coupling of the vortex beam. A detailed analysis of the probe field energy transfer to different orders of diffraction in the case of off-resonant standing wave coupling field proves the possibility of direct control over the performance of the grating.

Magneto-optic effect on the pole of the parity-time symmetric coupled cavities

We propose a compound structure constructed by two magnetic cavities with parity-time (PT) symmetric configuration. Through the calculations based on transfer matrix, we find that the structure system has some unique properties that the usual PT symmetric structures do not have. The four incident conditions of the structure produce two sets of transmittance spectra and four different reflectance spectra in which the unusual amplification and absorption are shown. The huge amplification and absorption can be precisely tuned through the magnetic field. Furthermore, the amplification and absorption around the pole can be reversed through the change of incidence directions. Although the analysis of the scattering matrix shows that the transmission and reflection are not nonreciprocal, the diverse modulation ways (magnetic field and incidence directions) will make the structure more useful in the design of photonic switching and optical modulator.

Parity-time symmetric gratings in 1550 nm distributed-feedback laser diodes: insight on device design rules

We build on former results from our work on parity-time symmetric gratings implemented in 1550 nm distributed-feedback laser diodes to address the design issues raised by the first trends we observed. These laser diodes are of a complex-coupled nature, with modulations of both real and imaginary parts of the effective index, with a relative phase related to the parity-time symmetry. The unidirectionality of the photonic behavior in the reflection mode is dependent on the level of extra losses incurred by the metallic grating used to implement fixed loss modulation onto a nearly uniform gain, either as a first-order or a third-order grating. The observed behavior suggests that facets play a large role in setting the desired unidirectional lasing operation points, with preferential emission on one side. We explore this issue, which is of generic interest for the coupling of parity-time symmetric structures to open space.

Phases Transitions in a Cross-Cavity Quantum Rabi Model Possessing PT Symmetric Structure

We investigated the quantum phase transitions in a cross-cavity quantum Rabi model which possesses the parity-time symmetric structure. Both the open quantum Rabi phase transition and the spontaneous parity-time symmetry breaking exist simultaneously in such system. The competition between these two phase transitions produces the plentiful phase diagram. We also propose the detection of the open cross-cavity quantum Rabi phase transition through the measurement of the parity-time symmetric or asymmetric states, which shed light on the precise detection of the few-body phase transition.

Symmetric sonic crystals: From asymmetric echoes to supersonic speeds

Parity-time symmetric structures based on balanced distributions of gain and loss have attracted significant attention in acoustic metamaterial research since they allow one to sculpture the flow of sound waves in complete new ways. We compute complex Bloch waves in fluidic non-Hermitian sonic crystals and demonstrate how band coalescence can lead to exceptionally large group velocities permitting supersonic wave propagation in symmetric slabs. Further, by controlling the degree of non-hermiticity in such systems, we found that asymmetrically reflected pulses can be readily amplitude-tuned, which might find potential use in echocardiography, sonar and echo suppressors.

Tunable elastic parity-time symmetric structure based on the shunted piezoelectric materials

We theoretically and numerically report on the tunable elastic Parity-Time (PT) symmetric structure based on shunted piezoelectric units. We show that the elastic loss and gain can be archived in piezoelectric materials when they are shunted by external circuits containing positive and negative resistances. We present and discuss, as an example, the strongly dependent relationship between the exceptional points of a three-layered system and the impedance of their external shunted circuit. The achieved results evidence that the PT symmetric structures based on this proposed concept can actively be tuned without any change of their geometric configurations.

Shadow-free multimers as extreme-performance meta-atoms

We generalize the concept of parity-time symmetric structures with the goal to create meta-atoms exhibiting extraordinary abilities to overcome the presumed limitations in the scattering of overall lossless particles, such as non-zero forward scattering and the equality of scattering and extinction powers for all lossless particles. Although the forward scattering amplitude and the extinction cross section of our proposed meta-atoms vanish, they scatter incident energy into other directions, with controllable directionality. These meta-atoms possess extreme electromagnetic properties not achievable for passive scatterers. As an example, we study meta-atoms consisting of two or three small dipole scatters. We consider possible microwave realizations in the form of short dipole antennas loaded by lumped elements. The proposed meta-atom empowers extraordinary response of a shadow-free scatterer and theoretically enables most unusual material properties when used as a building block of an artificial medium.

磁光效应下PT对称结构独特的非互易传输模式

磁光效应下PT对称结构独特的非互易传输模式

Optical Parity-Time Symmetric Structure with Vee- and Lambda-Configuration Atomic Vapors

In optical parity-time symmetry, the electric permittivity of an electromagnetic structure should have a real part, which is an even function of spatial coordinates, and an imaginary part, which is an odd function of coordinates. Since a Vee- and a Lambda-configuration three-level atomic vapor can be driven by both control and probe beams, and can exhibit both frequency-sensitive and field-controlling optical responses, the dielectric “constants” of these two atomic vapors can be tuned by manipulating the applied external control fields. The requirement for realizing optical parity-time symmetry can be fulfilled in quantum-coherent multilevel atomic vapors. A design based on Vee- and Lambda-configuration three-level atomic vapors for achieving optical parity-time symmetric interface is suggested in this paper. Under certain parameter conditions, an optical parity-time symmetric interface can possibly be fabricated in the present scenario of quantum-coherent multilevel atomic vapors.

Modal Gain Analysis of Parity-Time-Symmetric Distributed Feedback Lasers

Parity-time (PT) symmetry has been demonstrated in the frame of classic optics and its applications in laser science have resulted in interesting mode selection mechanisms. PT symmetry breaking gratings (also called unidirectional Bragg gratings) have strong reflection when light is injected from one end, but they are transparent when injected from the other end. Such gratings are obtained through periodic modulations of both real and imaginary part of refractive index with a fixed phase relation. In this paper, we investigate distributed feedback (DFB) laser structures based on PT symmetric diffractive gratings. Our modal gain analysis shows that the PT DFB laser structure exhibits much stronger modal discrimination than the one using conventional diffractive gratings, so it will provide better single-mode operation performance. In addition, we analyze the influence of uncertain facet reflectivities on these DFB structures. We show that PT symmetric DFB structures are more stable against the perturbation of facet reflections.

Reciprocal and unidirectional scattering of parity-time symmetric structures

Parity-time symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in -symmetric system is closely related to the type of symmetry, that is, the axial (reflection) symmetry leads to reciprocal reflection (transmission). The results are further elucidated by studying the scattering of rhombic ring form coupled resonators with enclosed synthetic magnetic flux. The nonreciprocal phase shift induced by the magnetic flux and gain/loss break the parity and time-reversal symmetry but keep the parity-time symmetry. The reciprocal reflection (transmission) and unidirectional transmission (reflection) are found in the axial (reflection) -symmetric ring centre. The explorations of symmetry and asymmetry from symmetry may shed light on novel one-way optical devices and application of -symmetric metamaterials.