Exceptional Point

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Che Ting Chan - One of the best experts on this subject based on the ideXlab platform.

  • Exceptional Point based plasmonic metasurfaces for vortex beam generation
    Optics Express, 2020
    Co-Authors: Ho Ming Dick Leung, Wensheng Gao, Ranran Zhang, Qiuling Zhao, Xia Wang, Che Ting Chan, Wing Yim Tam
    Abstract:

    An Exceptional Point occurring in a tailor-made lossy optical system has been recently found to alter optical properties in counter-intuitive ways. In the context of tunable plasmonic devices, Exceptional Points can be useful as a driving mechanism to enhance tunability. Here, we experimentally demonstrate how a plasmonic Exceptional Point can be incorporated in metasurface Q-plates to have the generated vortex beam tuned through a change of structural parameter. We have observed an orbital rotation in the far-field by 45 degrees in crossing the Exceptional Point. We expect a new generation of tunable plasmonic devices in polarization control, beam structuring and holograms, which can take advantage of the huge sensitivity from Exceptional Points.

  • dynamically encircling an Exceptional Point in anti parity time symmetric systems asymmetric mode switching for symmetry broken modes
    Light-Science & Applications, 2019
    Co-Authors: Xulin Zhang, Tianshu Jiang, Che Ting Chan
    Abstract:

    Dynamically encircling an Exceptional Point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting Point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities. By steering microwaves in an anti-parity-time symmetric system, Chinese scientists have explored the topological physics and their wave-manipulation applications in optics and photonics. Recent developments in non-Hermitian systems, i.e., open systems that can exchange energy with surroundings, have given rise to new optical devices such as isolators, sensors, and absorbers. Such systems exhibit the so-called Exceptional Points, where two or more resonances have equal frequencies and dissipations. By sending microwaves along a waveguide with specially designed boundaries, which is equivalent to looping the waveguide resonance around an Exceptional Point in a parameter space, Xu-Lin Zhang from Jilin University and Che Ting Chan from the Hong Kong University of Science and Technology have demonstrated a new method for manipulating electromagnetic waves in waveguides. Their work could pave the way for on-chip optical devices with new functionalities.

  • distinct outcomes by dynamically encircling an Exceptional Point along homotopic loops
    Physical Review A, 2019
    Co-Authors: Xulin Zhang, Che Ting Chan, Junfeng Song, Hongbo Sun
    Abstract:

    We study a two-state non-Hermitian waveguide system that carries an Exceptional Point (EP). It is commonly believed that dynamically encircling an EP exhibits a chiral behavior when the starting Point of the loop lies in the branch cut with eigenmodes being symmetric and antisymmetric modes. We show here that such statement is conditional; i.e., the dynamics can in fact be nonchiral for specially designed loops with the starting Point in the branch cut. In particular, we find that for two homotopic loops (i.e., loops that can be transformed continuously from one to another without crossing any EP), the outcomes can be completely different even if the two loops share the same starting state, enclose the same EP, and encircle the EP in the same direction. Our findings greatly enrich the understanding of the physics in dynamical processes of EP encircling in non-Hermitian systems.

  • arbitrary order Exceptional Point induced by photonic spin orbit interaction in coupled resonators
    arXiv: Optics, 2018
    Co-Authors: Shubo Wang, Bo Hou, Yuntian Chen, Zhaoqing Zhang, Che Ting Chan
    Abstract:

    Many novel properties of non-Hermitian systems are found at or near the Exceptional Points-branch Points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order Exceptional Points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order Exceptional Point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the Exceptional Point, which is protected by the transverse spin-momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the Exceptional Points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the Exceptional Point is also numerically and analytically demonstrated.

  • hybrid Exceptional Point and its dynamical encircling in a two state system
    Physical Review A, 2018
    Co-Authors: Xulin Zhang, Che Ting Chan
    Abstract:

    Exceptional Points are degeneracies in non-Hermitian systems. A two-state system with parity-time (PT) symmetry usually has only one Exceptional Point beyond which the eigenmodes are PT-symmetry broken. The so-called symmetry recovery, i.e., eigenmodes become PT-symmetric again, typically occurs in multi-state systems. Here we show that a two-state ferromagnetic waveguide system can have an Exceptional Point and a subsequent symmetry recovery due to the presence of accidental degeneracy Points when the system is lossless. By introducing a parameter space where both Exceptional Points reside, we designed a system in which the trajectory in the parameter space can be controlled in situ using an adiabatically tunable external field, allowing us to explore the topological and chiral character of the system by encircling zero, one or two Exceptional Points. We performed microwave experiments to demonstrate the presence of the Exceptional Point, symmetry recovery, and the effects arising from their dynamical encircling.

Xulin Zhang - One of the best experts on this subject based on the ideXlab platform.

  • dynamically encircling an Exceptional Point in anti parity time symmetric systems asymmetric mode switching for symmetry broken modes
    Light-Science & Applications, 2019
    Co-Authors: Xulin Zhang, Tianshu Jiang, Che Ting Chan
    Abstract:

    Dynamically encircling an Exceptional Point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting Point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities. By steering microwaves in an anti-parity-time symmetric system, Chinese scientists have explored the topological physics and their wave-manipulation applications in optics and photonics. Recent developments in non-Hermitian systems, i.e., open systems that can exchange energy with surroundings, have given rise to new optical devices such as isolators, sensors, and absorbers. Such systems exhibit the so-called Exceptional Points, where two or more resonances have equal frequencies and dissipations. By sending microwaves along a waveguide with specially designed boundaries, which is equivalent to looping the waveguide resonance around an Exceptional Point in a parameter space, Xu-Lin Zhang from Jilin University and Che Ting Chan from the Hong Kong University of Science and Technology have demonstrated a new method for manipulating electromagnetic waves in waveguides. Their work could pave the way for on-chip optical devices with new functionalities.

  • distinct outcomes by dynamically encircling an Exceptional Point along homotopic loops
    Physical Review A, 2019
    Co-Authors: Xulin Zhang, Che Ting Chan, Junfeng Song, Hongbo Sun
    Abstract:

    We study a two-state non-Hermitian waveguide system that carries an Exceptional Point (EP). It is commonly believed that dynamically encircling an EP exhibits a chiral behavior when the starting Point of the loop lies in the branch cut with eigenmodes being symmetric and antisymmetric modes. We show here that such statement is conditional; i.e., the dynamics can in fact be nonchiral for specially designed loops with the starting Point in the branch cut. In particular, we find that for two homotopic loops (i.e., loops that can be transformed continuously from one to another without crossing any EP), the outcomes can be completely different even if the two loops share the same starting state, enclose the same EP, and encircle the EP in the same direction. Our findings greatly enrich the understanding of the physics in dynamical processes of EP encircling in non-Hermitian systems.

  • hybrid Exceptional Point and its dynamical encircling in a two state system
    Physical Review A, 2018
    Co-Authors: Xulin Zhang, Che Ting Chan
    Abstract:

    Exceptional Points are degeneracies in non-Hermitian systems. A two-state system with parity-time (PT) symmetry usually has only one Exceptional Point beyond which the eigenmodes are PT-symmetry broken. The so-called symmetry recovery, i.e., eigenmodes become PT-symmetric again, typically occurs in multi-state systems. Here we show that a two-state ferromagnetic waveguide system can have an Exceptional Point and a subsequent symmetry recovery due to the presence of accidental degeneracy Points when the system is lossless. By introducing a parameter space where both Exceptional Points reside, we designed a system in which the trajectory in the parameter space can be controlled in situ using an adiabatically tunable external field, allowing us to explore the topological and chiral character of the system by encircling zero, one or two Exceptional Points. We performed microwave experiments to demonstrate the presence of the Exceptional Point, symmetry recovery, and the effects arising from their dynamical encircling.

  • hybrid Exceptional Point and its dynamical encircling in a two state system
    Physical Review A, 2018
    Co-Authors: Xulin Zhang, Che Ting Chan
    Abstract:

    Hybrid Exceptional Points (HEPs) are non-Hermitian degeneracies that exhibit different dispersion relations (e.g., linear or square-root) along different directions in the parameter space. Here, we show that a two-state system consisting of coupled ferromagnetic waveguides applied with a bias magnetic field can support the presence of a HEP. A configuration is designed to dynamically encircle the HEP, showing a nonchiral behavior due to the unique topological structure of energy surfaces around the HEP. This is in contrast to the chiral dynamics found when an Exceptional Point is encircled dynamically. We performed numerical simulations and microwave experiments to demonstrate the topological transition enabled by the HEP in the proposed system.

  • dynamically encircling an Exceptional Point in anti pt symmetric systems asymmetric mode switching for symmetry broken states
    arXiv: Optics, 2018
    Co-Authors: Xulin Zhang, Hongbo Sun, Tianshu Jiang, Che Ting Chan
    Abstract:

    Dynamically encircling an Exceptional Point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is reversed. Here we show that the dynamical encircling of an EP in anti-PT-symmetric systems can also result in chiral dynamics if the starting/end Point lies in the PT-broken phase, in contrast to PT-symmetric systems where chiral dynamics emerges if the starting/end Point lies in the PT-unbroken phase. For many applications, such as signal processing using waveguides, the asymmetric mode switching of symmetry-broken modes in anti-PT-symmetric systems is more useful since each eigenmode is localized in one waveguide only. We develop an analytic theory for anti-PT-symmetric chiral dynamics and perform experiments using three waveguides to demonstrate the asymmetric mode switching. The new wave-manipulation phenomena observable in anti-PT-symmetric systems may pave the way towards designing on-chip optical systems with novel functionalities.

Liang Feng - One of the best experts on this subject based on the ideXlab platform.

  • Exceptional Point engineered glass slide for microscopic thermal mapping
    Nature communications, 2018
    Co-Authors: Han Zhao, Zhaowei Chen, Ruogang Zhao, Liang Feng
    Abstract:

    Thermal sensing with fine spatial resolution is important to the study of many scientific areas. While modern microscopy systems allow optical detection at high spatial resolution, their intrinsic functions are mainly focused on imaging but limited in detecting other physical parameters, for example, mapping thermal variations. Here, with a coating of an optical Exceptional Point structure, we demonstrate a low-cost but efficient multifunctional microscope slide, supporting real-time monitoring and mapping of temperature distribution and heat transport in addition to conventional microscopic imaging. The square-root dependency associated with an Exceptional Point leads to enhanced thermal sensitivity for precise temperature measurement. With a microscale resolution, real-time thermal mapping is conducted, showing dynamic temperature variation in a spatially defined area. Our strategy of integrating low-cost and efficient optical sensing technologies on a conventional glass slide enables simultaneous detection of multiple environmental parameters, producing improved experimental control at the microscale in various scientific disciplines.

  • Exceptional Point engineered glass slide for microscopic thermography
    Conference on Lasers and Electro-Optics, 2018
    Co-Authors: Han Zhao, Zhaowei Chen, Ruogang Zhao, Liang Feng
    Abstract:

    We demonstrate a thermosensitive glass slide with enhanced sensitivity by exploiting an optical Exceptional Point. The non-Hermitian Exceptional Point of the glass slide creates novel functionality for highly-sensitive thermal mapping compatible with conventional microscope systems.

  • unidirectional lasing in semiconductor microring lasers at an Exceptional Point invited
    Photonics Research, 2017
    Co-Authors: Stefano Longhi, Liang Feng
    Abstract:

    Recent experiments demonstrated that chiral symmetry breaking at an Exceptional Point (EP) is a viable route to achieve unidirectional laser emission in microring lasers. By a detailed semiconductor laser rate equation model, we show here that unidirectional laser emission at an EP is a robust regime. Slight deviations from the EP condition can break preferential unidirectional lasing near threshold via a Hopf instability. However, above a “second” laser threshold, unidirectional emission is restored.

  • Exceptional Point engineered glass slide for microscopic thermal mapping
    arXiv: Optics, 2017
    Co-Authors: Han Zhao, Zhaowei Chen, Ruogang Zhao, Liang Feng
    Abstract:

    Thermal sensing with fine spatial resolution is important to the study of many scientific areas. While modern microscopy systems allow easy optical detection at high spatial resolution, their intrinsic functions are mainly focused on imaging but limited in detecting other physical parameters, for example, mapping thermal variations. Here, with a coating of an optical Exceptional Point structure on a conventional glass slide, we demonstrate a novel low-cost and efficient multifunctional microscope slide, supporting real-time monitoring and mapping of temperature distribution and heat transport in addition to conventional microscopic imaging. The square-root dependency associated with an Exceptional Point leads to enhanced thermal sensitivity that is critical for the precise measurement of the temperature. With a microscale resolution, real-time thermal mapping is conducted, showing dynamic temperature variation in a spatially-defined area. Our strategy of integrating low-cost and efficient optical sensing technologies on a conventional glass slide is expected to enable simultaneous detection of multiple environmental parameters, thereby leading to new opportunities for improved experimental control in many scientific research disciplines.

  • demonstration of a large scale optical Exceptional Point structure
    Optics Express, 2014
    Co-Authors: Liang Feng, Xuefeng Zhu, Sui Yang, Hanyu Zhu, Peng Zhang, Xiaobo Yin, Yuan Wang, Xiang Zhang
    Abstract:

    We report a large-size (4-inch) optical Exceptional Point structure at visible frequencies by designing a multilayer structure of absorbing and non-absorbing dielectrics. The optical Exceptional Point was implemented as indicated by the realized unidirectional reflectionless light transport at a wafer scale. The associated abrupt phase transition is theoretically and experimentally confirmed when crossing over the Exceptional Point in wavelengths. The large scale demonstration of phase transition around Exceptional Points will open new possibilities in important applications in free space optical devices.

Filippo Capolino - One of the best experts on this subject based on the ideXlab platform.

  • enhanced sensitivity of degenerate system made of two unstable resonators coupled by gyrator operating at an Exceptional Point
    arXiv: Applied Physics, 2021
    Co-Authors: Kasra Rouhi, Alireza Nikzamir, Alexander Figotin, Filippo Capolino
    Abstract:

    We demonstrate that a circuit comprising two unstable LC resonators coupled via a gyrator supports an Exceptional Point of degeneracy (EPD) with purely real eigenfrequency. Each of the two resonators includes either a capacitor or an inductor with a negative value, showing purely imaginary resonance frequency when not coupled to the other via the gyrator. With external perturbation imposed on the system, we show analytically that the resonance frequency response of the circuit follows the square-root dependence on perturbation, leading to possible sensor applications. Furthermore, the effect of small losses in the resonators is investigated, and we show that losses lead to instability. In addition, the EPD occurrence and sensitivity are demonstrated by showing that the relevant Puiseux fractional power series expansion describes the eigenfrequency bifurcation near the EPD. The EPD has the great potential to enhance the sensitivity of a sensing system by orders of magnitude. Making use of the EPD in the gyrator-based circuit, our results pave the way to realize a new generation of high-sensitive sensors to measure small physical or chemical perturbations.

  • high power backward wave oscillator using folded waveguide with distributed power extraction operating at an Exceptional Point
    IEEE Transactions on Electron Devices, 2021
    Co-Authors: Tarek Mealy, Ahmed F Abdelshafy, Filippo Capolino
    Abstract:

    The concept of Exceptional Point of degeneracy (EPD) is used to conceive an Exceptional synchronization regime that is able to enhance the level of output power and power conversion efficiency for backward-wave oscillators (BWOs) operating at millimeter-wave and terahertz frequencies. Standard BWOs operating at such high frequency ranges typically generate output power not exceeding tens of watts with very poor power conversion efficiency in the order of 1%. The novel concept of Exceptional synchronization for the BWO based on a folded waveguide is implemented by engineering distributed gain and power extraction along the slow-wave waveguide. The distributed power extraction along the folded waveguide is useful to satisfy the necessary conditions to have an EPD at the synchronization Point. Particle-in-cell (PIC) simulation results show that BWO operating at an EPD regime is capable of generating output power exceeding 3 kW with conversion efficiency of exceeding 20% at frequency of 88.5 GHz.

  • high power x band relativistic backward wave oscillator with Exceptional synchronous regime operating at an Exceptional Point
    Physical review applied, 2021
    Co-Authors: Tarek Mealy, Ahmed F Abdelshafy, Filippo Capolino
    Abstract:

    An Exceptional Point of degeneracy (EPD) is induced in a system made of a linear electron beam interacting with an electromagnetic (EM) guided mode in a vacuum tube made of a corrugated circular metallic waveguide with distributed output ports. This scheme enables an Exceptional synchronous regime in backward-wave oscillators (BWOs) where the electron beam provides distributed gain to the EM mode with distributed power extraction. Particle-in-cell (PIC) simulation results demonstrate that the proposed EPD BWO has a starting-oscillation current that scales quadratically with BWO length to a nonvanishing value, which does not occur in standard BWOs and demonstrates the occurrence of the EPD and hence the Exceptional synchronism operational regime. The degeneracy of two interactive hot modes is also verified by observing the coalescence of their complex-valued wave numbers at the EPD frequency. Observations on the kinetic energy distribution of the electrons along the BWO demonstrate that the proposed EPD-BWO regime is capable of achieving higher power conversion efficiency at higher levels of power generation due to its ability to maintain the synchronism for longer BWO lengths compared to the standard BWO regime of operation.

  • high power backward wave oscillator using folded waveguide with distributed power extraction operating at an Exceptional Point
    arXiv: Applied Physics, 2021
    Co-Authors: Tarek Mealy, Ahmed F Abdelshafy, Filippo Capolino
    Abstract:

    The concept of Exceptional Point of degeneracy (EPD) is used to conceive a degenerate synchronization regime that is able to enhance the level of output power and power conversion efficiency for backward wave oscillators (BWOs) operating at millimeter-wave and Terahertz frequencies. Standard BWOs operating at such high frequency ranges typically generate output power not exceeding tens of watts with very poor power conversion efficiency in the order of 1%. The novel concept of degenerate synchronization for the BWO based on a folded waveguide is implemented by engineering distributed gain and power extraction along the slow-wave waveguide. The distributed power extraction along the folded waveguide is useful to satisfy the necessary conditions to have an EPD at the synchronization Point. Particle-in-cell (PIC) simulation results shows that BWO operating at an EPD regime is capable of generating output power exceeding 3 kwatts with conversion efficiency of exceeding 20% at frequency of 88.5 GHz.

  • backward wave oscillator with distributed power extraction operating at an Exceptional Point of degeneracy
    International Vacuum Electronics Conference, 2020
    Co-Authors: Tarek Mealy, Ahmed F Abdelshafy, Filippo Capolino
    Abstract:

    We propose a new and efficient degenerate synchronous regime for backward wave oscillators (BWO) based on an Exceptional Point of degeneracy (EPD) in the RF-electron beam interactive system. Compared to conventional BWOs, we introduce distributed power extraction all the way along the BWO structure. The EPD is obtained in the interactive RF-beam system by the simultaneous presence of distributed gain (due to the electron beam) and power extraction. Current PIC simulation results show that at a guiding magnetic field of 2.6 T, electron beam of 600 kV and 1740 A, an output power of 0.5 GW is extracted with power conversion efficiency of 47% and oscillation frequency of 9.7 GHz. This paper shows the feasibility of this new concept, and performance could be further improved.

Franziska Schäfer - One of the best experts on this subject based on the ideXlab platform.

  • scattering experiments with microwave billiards at an Exceptional Point under broken time reversal invariance
    Physical Review E, 2014
    Co-Authors: S. Bittner, H. L. Harney, A Richter, B Dietz, M Miskioglu, Franziska Schäfer
    Abstract:

    Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called Exceptional Point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the Point of transition between both regions. There a spontaneous breaking of PT occurs.

  • Scattering experiments with microwave billiards at an Exceptional Point under broken time-reversal invariance
    Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2014
    Co-Authors: S. Bittner, H. L. Harney, M. Miski-oglu, Barbara Dietz, A Richter, Franziska Schäfer
    Abstract:

    Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called Exceptional Point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the Point of transition between both regions. There a spontaneous breaking of PT occurs.