On June 29th, Prof. Jian Wang and Prof. Lin Chen from Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Prof.Andrea Alù from the City University of New York, Prof. Cheng-Wei Qiu from the Department of Electrical and Computer Engineering, National University of Singapore published a new review article in Nature Nanotechnology. The paper is entitled Exceptional points and non-Hermitian photonics at the nanoscale.
Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl-exceptional-rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic applications.
Recent advances in non-Hermitian physics have been opening numerous opportunities for a wide range of basic research and engineering applications. In a Hermitian system the total energy is conserved, and the associated Hamiltonian has a real eigen-energy spectrum, corresponding to the intuitive requirement that energy is a real-valued quantity. In non-Hermitian systems, on the contrary, energy is exchanged with the environment, and the corresponding Hamiltonian generally features a complex spectrum. Remarkably, non-Hermitian systems that obey parity-time (PT) symmetry, i.e., that remain identical upon a sequential application of a spatial parity operation (inversion) and a time-reversal operation, can still support a real eigen-spectrum, despite being open systems. At the same time, the spectrum of a PT-symmetric Hamiltonian is not necessarily real, and as a non-Hermiticity parameter is varied, it can spontaneously become complex, switching from a symmetric to a broken phase4. The transition between the symmetric and the broken phase arises at a so-called exceptional point (EP), which features a unique degeneracy of the eigenspectrum and associated eigenstates, associated with a wide range of unusual phenomena. At the EP, the eigenspace of the system has lower dimensions than the system itself. This is different than more common spectral degeneracies, such as diabolic points (DPs) of a Hermitian system, for which only the eigenvalues are degenerate but the eigenstates are not. While these concepts have been originally introduced in the context of quantum mechanics and of Hamiltonians, the Schrodinger equation and the Helmholtz equation follow similar second-order partial differential forms, hence optical platforms have been extensively explored to realize PT-symmetric systems and explore EP physics. For instance, the peculiar optical transparency emerging at a spontaneous symmetry breaking transition and the eigenstates at PT-symmetric and PT-broken points were observed by implementing a complex index distribution in coupled optical waveguides (Fig. 1a).
In this review, we discuss the latest discoveries in the context of EPs in various nanoscale platforms, and the burgeoning applications in nanophotonics. In the first section, we review the latest theoretical progress related to EPs, including EPs in novel nanophotonic systems, higher-order EPs, and bulk Fermi arcs. In the second section, we review the latest advances in EP sensing, and how noise may affect the overall sensitivity, followed by some discussion on attempts to address these issues (Fig. 1b). The third section focuses on the latest progress on asymmetric transmission based on EP encircling in terms of high transmission efficiency, compact size, multiple modes, and their applications in mode-locked lasers (Fig. 1c). In the fourth section, we review recent advances on non-reciprocal wave propagation based on the combination of non-linearity and Eps in novel nanophotonic systems, and the latest progress on how non-linearity may enable intriguing optical phenomena in non-Hermitian systems (Fig. 1d). In the last section, we review the implementation of Eps in topological photonics (Fig. 1e), and summarize the opportunities, challenges and outlook of EPs for nanophotonic applications. We note that several review papers have been published a few years ago on this topic – yet they have not covered the latest progress related to EPs and EP-associated emerging technologies.
Fig. 1. Exceptional points (EPs) and their applications. a, PT-symmetry in coupled optical systems. b, Sensors operated near EPs.
c, Asymmetric transmission by encircling EPs. d, EPs and optical nonlinearities. e, EPs in topological photonics.
A wide range of optical platforms, from coupled cavities/waveguides and photonic crystals to metasurfaces, are available to enable and realize non-Hermitian photonic phenomena. The unique features of EPs associated with the degeneracies of the eigenvalue spectrum and self-intersecting Riemann surfaces, as well as PT-symmetry in non-Hermitian systems, open a wide range of applications in nanophotonics, including EP sensors, asymmetric transmission, non-reciprocal wave propagation, and topological photonics. In these scenarios, PT-symmetry and EPs are accessible with flexible control over the coupling and loss-gain distributions. Intriguing optical phenomena, associated with the above applications, are enabled by taking advantage of the strong and anomalous energy spectrum near EPs.
Although there is an ongoing vibrant discussions on whether EP sensors can be actually beneficial in the presence of noise, experimental efforts have demonstrated exceptional sensitivities166, and in this review we have discussed noise limitations to reciprocal and linear systems. Non-reciprocal and non-linear devices may overcome such limits, even without the need for signal amplification88. Meanwhile, the output metrics are not necessarily the frequency splitting for EP sensors, particularly when quantitative detection is not required. In such cases, the transmission intensity or loss rate of a monochromatic wave is adequate to serve as the sensor readout, eliminating the need for complex circuitry or spectrum analyzers. The nonlinear variation of the output intensity away from the EP can also be beneficial to enhance the dynamic range compared to a conventional sensor. In addition, experiments have demonstrated that, when deviating from the EP, the decay rate of light traveling in a diffraction grating would abruptly change from linear to exponential167. Such a conspicuous change would be a clear demonstration of the onset of perturbations in environmental parameters.
On-chip mode conversion/multiplexing and lasing can largely benefit from EP encircling but still suffer from limitations. Firstly, although the transmission efficiency in one direction has been boosted to near-unity with Hamiltonian hopping and fast encirclement of EPs along the Hamiltonian boundaries99,100, the transmission efficiency in the opposite direction is close to zero since the current EP-encircling strategies rely on purely loss systems. The final solution to the transmission efficiency for double directions may rely on involving gain materials in EP encircling, though this poses further challenges to device fabrication. Secondly, the current scheme largely enables the asymmetrical conversion of a pair of fundamental modes, which restricts the multiplexing capacity. Further promising steps towards increasing the multiplexing capacity can be taken by exploring novel optical structures with EP encircling to enable asymmetrical conversion for complex field modes, such as multiple modes, high-order modes, polarization states, and orbital angular momentum. A substantial step has been taken to enable asymmetrical polarization-locked conversion by L-shaped silicon waveguides that support two orthogonal polarization modes168. Thirdly, an EP-encircling laser provides an appealing approach to the implementation of mode-locked lasing, suggesting promising application prospects in on-chip light source108. The current EP-encircling lasing mode has been limited to locking low-order modes with double coupled waveguides. This technology can benefit from multiple waveguide arrays supporting single-optical-mode output, which is expected to significantly increase the lasing power169. Besides, the aforementioned strategies of asymmetrical conversion for complex field modes can be further introduced to enrich the functionalities of EP-encircling laser.
Non-Hermitian systems with nonlinearities have been implemented in on-chip waveguide systems, taking advantage of the strong nonlinearity accumulated over long distances. Recently, high-Q resonances supported by photonic crystal slabs have attracted much attention in optics and photonics for their strong mode localization and field amplitude, which is beneficial for enhanced nonlinear effects. With the increasing radiation loss induced by geometric asymmetry, these resonances become non-Hermitian with exotic band structures, such as EPs170, Fermi arcs31,33, and exceptional rings142. The combination of non-Hermitian optics and nonlinear effects in planar structures may pave the way to deepen the understanding of the fundamental concepts of chirality, non-reciprocity, and topological optics, to be applied for sensing application and asymmetric transmission, and even to facilitate the studies on nanoscale optical communications. In addition, many interesting theoretical models and phenomena such as saturable-gain-induced asymmetric transmission, optical isolation, and lossless non-Hermitian system are expected to be achieved in nanoscale optics.
Undoubtedly, understanding and exploiting non-Hermiticity associated with EPs in linear and nonlinear topological photonics can offer numerous research opportunities, both for fundamental research and future applications. One of the most important topics is to establish a universal theoretical framework that spans non-Hermiticity, topology, nonlinearity, and even other advanced concepts like low symmetries in photonics. This would be useful to qualitatively and even quantitatively describe their mutual interplay, thereby precisely and flexibly regulating and utilizing a variety of convoluted interactions with different mechanisms. As a promising step in this direction, topological lasers in nonlinear, non-Hermitian and topological lattice systems have been studied based on quench dynamics starting from one site171. Another topic of interest is to extensively explore novel mechanisms behind the synergy between non-Hermiticity associated with EPs and various other concepts and symmetries148,155,162,165. This will benefit not only the developments of photonic concepts for non-Hermitian systems supporting EPs, but also the establishment of photonic applications possessing topological robustness, exceptional sensitivity, flexible reconfigurability, dynamic tunability, and remote controllability.
This work has been supported by the National Natural Science Foundation of China (grant numbers 11674118 and 12074137), the State Key Laboratory of Artificial Microstructure and Mesoscopic Physics (Peking University), the State Key Laboratory of Advanced Technology for Materials Synthesis and Processing (Wuhan University of Technology), the Air Force Office of Scientific Research MURI programme and the Simons Foundation.
Paper Link: https://www.nature.com/articles/s41565-023-01408-0
