In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

The ability to control the modes oscillating within a laser resonator is of fundamental importance. In general, the presence of competing modes can be detrimental to beam quality and spectral purity, thus leading to spatial as well as temporal fluctuations in the emitted radiation. We show that by harnessing notions from parity-time (PT) symmetry, stable single–longitudinal mode operation can be readily achieved in a system of coupled microring lasers. The selective breaking of PT symmetry can be used to systematically enhance the maximum attainable output power in the desired mode. This versatile concept is inherently self-adapting and facilitates mode selectivity over a broad bandwidth without the need for other additional intricate components. Our experimental findings provide the possibility to develop synthetic optical devices and structures with enhanced functionality.

http://science.sciencemag.org/content/sci/346/6212/975.full.pdf

Parity-time–symmetric microring lasers

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Edge States and Topological Invariants of Non-Hermitian Systems.

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

Exploiting the interplay between gain, loss and the coupling strength between different optical components creates a variety of new opportunities in photonics to generate, control and transmit light. Inspired by the discovery of real eigenfrequencies for non-Hermitian Hamiltonians obeying parity–time (PT) symmetry, many counterintuitive aspects are being explored, particularly close to the associated degeneracies also known as ‘exceptional points’. This Review explains the underlying physical principles and discusses the progress in the experimental investigation of PT-symmetric photonic systems. We highlight the role of PT symmetry and non-Hermitian dynamics for synthesizing and controlling the flow of light in optical structures and provide a roadmap for future studies and potential applications. This Review discusses recent developments in the area of non-Hermitian physics, and more specifically the special case of non-Hermitian optical systems with parity–time symmetry.

Parity-time symmetry and exceptional points in photonics.

On-chip parity–time-symmetric optics is experimentally demonstrated at a wavelength of 1,550 nm in two directly coupled, high-Q silica microtoroid resonators with balanced effective gain and loss. Switchable optical isolation with a nonreciprocal isolation ratio between −8 dB and +8 dB is also shown. The findings will be useful for potential applications in optical isolators, on-chip light control and optical communications. Compound-photonic structures with gain and loss1 provide a powerful platform for testing various theoretical proposals on non-Hermitian parity–time-symmetric quantum mechanics2,3,4,5 and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Such structures can be designed as optical analogues of complex parity–time-symmetric potentials with real spectra. However, the beam dynamics can exhibit unique features distinct from conservative systems due to non-trivial wave interference and phase-transition effects. Here, we experimentally realize parity–time-symmetric optics on a chip at the 1,550 nm wavelength in two directly coupled high-Q silica-microtoroid resonators with balanced effective gain and loss. With this composite system, we further implement switchable optical isolation with a non-reciprocal isolation ratio from −8 dB to +8 dB, by breaking time-reversal symmetry with gain-saturated nonlinearity in a large parameter-tunable space. Of importance, our scheme opens a door towards synthesizing novel microscale photonic structures for potential applications in optical isolators, on-chip light control and optical communications.

Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators

We experimentally demonstrate an all-optical analog to electromagnetically induced transparency (EIT) on chip using coupled high-Q silica microtoroid cavities with Q-factors above 106. The transmission spectrum of the all-optical analog to EIT is precisely controlled by tuning the distance between the two microtoroids, as well as the detunings of the resonance frequencies of the two cavities.

Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroid cavities

We experimentally demonstrate the electromagnetically induced transparency (EIT)-like effect using a double-wheel microcavity coupled with a silica microtoroid cavity. To match the resonant modes of the two microcavities, we shift the resonant wavelength of the double-wheel microcavity by 1.5 nm via the optical gradient force. The EIT-like transmission spectrum is precisely controlled by changing the distance and the frequency detuning between the two coupled microcavities.

Optomechanically tuned electromagnetically induced transparency-like effect in coupled optical microcavities

We experimentally demonstrate high optical quality factor silica microdisk resonators on a silicon chip with large wedge angles by reactive ion etching. For 2-μm-thick microresonators, we have achieved wedge angles of 59°, 63°, 70°, and 79° with optical quality factors of 2.4×107, 8.1×106, 5.9×106, and 7.4×106, respectively, from ∼80  μm-diameter microresonators in the 1550 nm wavelength band. Also, for 1-μm-thick microresonators, we have obtained an optical quality factor of 7.3×106 with a wedge angle of 74°.

High-Q silica microdisk optical resonators with large wedge angles on a silicon chip

Top-illuminated PIN photodetectors (PDs) are widely utilized in telecommunication systems, and more efforts have been focused on optimizing the optical responsibility and bandwidth for high-speed and capacity applications. In this work, we develop an integrated top-illuminated InP/InGaAs PIN PD with a back reflector by using a microtransfer printing (µ-TP) process. An improved µ-TP process, where the tether of silicon nitride instead of photoresist, is selected to support an underetched III-V device on an InP substrate before transfer. According to theoretical simulations and experimental measurements, the seamless integration of the PD with a back reflector through µ-TP process makes full use of the 2nd or even multiple reflecting light in the absorption layer to optimize the maximum responsibility. The integrated device with a 5 µm square p-mesa possesses a high optical responsibility of 0.78 A/W and 3 dB bandwidth of 54 GHz using a 500 nm i-InGaAs absorption layer. The present approach for top-illuminated PIN PDs demonstrates an advanced route in which a thin intrinsic layer is available for application in high-performance systems.

Guanyu Li

Papers

Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators

Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroid cavities

Optomechanically tuned electromagnetically induced transparency-like effect in coupled optical microcavities

High-Q silica microdisk optical resonators with large wedge angles on a silicon chip

Responsibility optimization of a high-speed InP/InGaAs photodetector with a back reflector structure.