There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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.

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

Three-cavity photonic molecules have been realized in several platforms, but their structures and configurations are mostly fixed with limited tunability in the coupling strengths and individual resonant frequencies. Here, we demonstrate an experimental realization of a coupled triple-cavity photonic molecule (TCPM) composed of three independently-selectable ultrahigh quality microtoroids. By precisely tuning the inter-cavity coupling strengths (via distances) and the resonant frequencies (via fine temperature control), as well as coupling the tapered optical fiber onto either the side or middle cavity, evolutions of the TCPM's supermodes are fully mapped and analyzed. Interesting phenomena, such as dark state and double anti-crossing, emerge in this TCPM system. When the quality factors of the cavities are properly chosen, transition from double electromagnetically-induced transparency to double electromagnetically-induced absorption phenomena happens. Such fully-controlled TCPM system sets a stage for future investigations of new physical effects including cavity-QED with multiple coupled cavities and topologically protected photonic states.

Realization of controllable photonic molecule based on three ultrahigh-Q microtoroid cavities

Optically nonreciprocal devices provide critical functionalities such as light isolation and circulation in integrated photonic circuits for optical communications and information processing, but have been difficult to achieve. By exploring gain-saturation nonlinearity, we demonstrate on-chip optical nonreciprocity with excellent isolation performance within telecommunication wavelengths using only one toroid microcavity. Compatible with current complementary metal-oxide-semiconductor process, our compact and simple scheme works for a very wide range of input power levels from ~10 microwatts down to ~10 nanowatts, and exhibits remarkable properties of one-way light transport with sufficiently low insertion loss. These superior features make our device become a promising critical building block indispensable for future integrated nanophotonic networks.

/pdf/on-chip-optical-nonreciprocity-using-an-active-microcavity-1rlyj31t97.pdf

On-Chip Optical Nonreciprocity Using an Active Microcavity.

http://absimage.aps.org/image/MAR17/MWS_MAR17-2016-020721.pdf

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°.

Chao Yang

Papers

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

Realization of controllable photonic molecule based on three ultrahigh-Q microtoroid cavities

On-Chip Optical Nonreciprocity Using an Active Microcavity.

Realization of controllable photonic molecule based on three ultrahigh-Q microtoroid cavities

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