Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an appropriate gauge for the model, we clarify that the imaginary coupling components have a symmetric form in the effective Hamiltonian and hence represent non-Hermiticity. These additional factors can lift the gain- and loss-based EP degeneracies. However, they are proportional to the sum of the imaginary permittivities for involved cavity pairs. Thus, when the amplification and absorption of adjacent cavities are balanced, their contribution to the imaginary coupling is canceled, and the EP singularity can be restored. Radiation-induced imaginary couplings measure the change in net radiation loss by the interference between cavity modes. Their impact on the EP can also be counteracted by small cavity resonance detuning even in loss-biased cases. We show and analyze eligible simulation examples based on photonic crystal nanocavities, and highlight design of an ideal EP degeneracy that is protected by generalized PT symmetry and induced by radiation.
The sensitivity of perturbation sensing can be effectively enhanced with higher-order exceptional points due to the nonlinear response to frequency splitting. However, the experimental implementation is challenging since all the parameters need to be precisely prepared. The emergence of exceptional surface (ES) improves the robustness of the system to the external environment, while maintaining the same sensitivity. Here, we propose the first scalable protocol for realizing photonic high-order exceptional surface with passive resonators. By adding one or more additional passive resonators in t…
We first present a quasinormal mode (QNM) theory for coupled loss-gain resonators working near an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of the QNMs, we show how the QNMs yield a quantitatively good model to a full dipole spontaneous emission response in Maxwell's equations at various spatial positions and frequencies (linear response). We also develop a highly accurate and intuitive QNM coupled-mode theory, which can be used to rigorously model such systems using only the QNMs of the bare resonators, where the hybrid QNMs of t…
We analyze the time-domain dynamics of resonators supporting exceptional points (EPs), at which both the eigenfrequencies and the eigenmodes associated with perfect capture of an input wave coalesce. We find that a time-domain signature of the EP is an expansion of the class of waveforms which can be perfectly captured. We show that such resonators have improved performance for storage or transduction of energy. They also can be used to convert between waveforms within this class. We analytically derive these features and demonstrate them for several examples of coupled optical resonator syste…
An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here we show that such a transformation can be performed in momentum space as well, which reveals that certain gain and loss modulated systems in their parity-time (PT) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a PT transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP i…
Chiral emission can be achieved from a circularly polarized dipole emitter in a nanophotonic structure that possess special polarization properties such as a polarization singularity, namely with right or left circularly polarization (C-points). Recently, Chen et al. [Nature Physics 16, 571 (2020)] demonstrated the surprising result of chiral radiation from a linearly-polarized (LP) dipole emitter, and argued that this effect is caused by a decoupling with the underlying eigenmodes of a non-Hermitian system, working at an exceptional point (EP). Here we present a quasinormal mode (QNM) approac…
We investigate spontaneous emission from a quantum emitter located within the mode volume of a microring resonator that features chiral exceptional points. We show that this configuration offers enough degrees of freedom to exhibit a full control to either enhance or suppress the emission process. Particularly, we demonstrate that the Purcell factor can be enhanced by a factor of two beyond its value in an identical microring operating at a diabolic point. Our conclusions, which are derived using a non-Hermitian Hamiltonian formalism, are confirmed by employing full-wave simulations of realist…
The realization of higher-order exceptional points (HOEPs) can lead to orders of magnitude enhancement in light-matter interactions beyond the current fundamental limits. Unfortunately, implementing HOEPs in the existing schemes is a rather difficult task, due to the complexity and sensitivity to fabrication imperfections. Here we introduce a hierarchical approach for engineering photonic structures having HOEPs that are easier to build and more resilient to experimental uncertainties. We demonstrate our technique by an example that involves parity-time (PT) symmetric optical microring resonat…
Chiral exceptional points (CEPs) have been shown to emerge in traveling wave resonators via asymmetric back scattering from two or more nano-scatterers. Here, we provide a new perspective on the formation of CEPs based on the coupled oscillator model. Our approach provides an intuitive understanding for the modal coalescence that signals the emergence of CEPs, and emphasizes the role played by dissipation throughout this process. In doing so, our model also unveils an otherwise unexplored connection between CEPs and other types of exceptional points associated with parity-time symmetric photon…
Chiral exceptional bound states in the continuum: a higher-order singularity for on-chip control of quantum emission
School of Integrated Circuits, Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳）集成芯片学院）；Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University（东南大学物理学院量子材料与器件教育部重点实验室）；Institute for Quantum Science and Technology, National University of Defense Technology（国防科技大学量子科学与技术研究院）
Optical microresonators are of paramount importance in photonic circuits requiring fine spectral filtering or resonant light recirculation. Key performance metrics improve with increasing resonance quality factor (Q) across all applications. The performance of silicon photonic circuits is often hampered by the low-quality factor of planar silicon microresonators, typically of Q~10^4-10^5. On the other hand, bulk whispering gallery mode resonators provide a wide range of materials with intriguing optical properties and exceptionally high resonant quality factors Q>10^7. However, the efficient c…
Chiral-Mode Control around a Hermitian Diabolic Point in Discrete Non-Hermitian Coupled Resonators
Institute of Science Tokyo（东京科学大学）；NTT Basic Research Laboratories, NTT Inc（日本电报电话公司基础研究中心）；Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）；School of Engineering and Technology, Central Michigan University（中央密歇根大学工程与技术学院）；NTT Nanophotonics Center, NTT Inc（日本电报电话公司纳米光子学中心）
We propose to use exceptional points (EPs) to construct diffraction-free beam propagation and localized power oscillation in lattices. Specifically, here we propose two systems to utilize EPs for diffraction-free beam propagation, one in synthetic gauge lattices and the other one, in unidirectionally coupled resonators where each resonator individually is capable of creating orbital angular momentum beams (OAM). In the second system, we introduce the concept of robust and tunable OAM beam propagation in discrete lattices. We show that one can create robust OAM beams in an arbitrary number of s…
Exceptional points (EPs) -- spectral singularities of non-Hermitian linear systems -- have recently attracted great interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent studies revealed issues with EP sensors in noisy environments. Here we propose a single-mode Kerr-nonlinear resonator for exceptional sensing in noisy environments. Based on the resonator's dynamic hysteresis, we define a signal that displays a square-root singularity akin to an EP. In contrast to EP sensors, our sensor has a signal-to-noise ratio that incr…
Exceptional points (EPs), singularities of non-Hermitian physics where complex spectral resonances degenerate, are one of the most exotic features of nonequilibrium open systems with unique properties. For instance, the emission rate of quantum emitters placed near resonators with EPs is enhanced (compared to the free-space emission rate) by a factor that scales quadratically with the resonance quality factor. Here, we verify the theory of spontaneous emission at EPs by measuring photoluminescence from photonic-crystal slabs that are embedded with a high-quantum-yield active material. While ou…
We propose two non-Hermitian arrays consisting of $N=2l+1$ waveguides and exhibiting parity-time ($\mathcal{PT}$) or anti-$\mathcal{PT}$ symmetry for investigating light transfer dynamics based on $N$th-order exceptional points (EPs). The $\mathcal{PT}$-symmetric array supports two $N$th-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. Light transfer dynamics in this array exhibits radically different behaviors, i.e. a unidirectional oscillation behavior in the unbroken phase, an edge-towards localization behavior in the broken phase, and a …
Anisotropic mirrors are used to form a laser resonator exhibiting non-Hermitian, parity-time (PT) symmetric, polarization states. The relative angle of the two mirrors principal axes is used to control the degree of non-hermiticity. A sharp symmetry-breaking transition is observed at a specific angle, called the exceptional point, where the two states coalesce into a single polarization state and the interference pattern produced by counter-propagating (CP) waves vanishes. At a smaller angle, in the unbroken PT symmetry regime, the polarization state experiencing higher losses is suppressed. I…
