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

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.

Controlling and reversing the effects of loss are major challenges in optical systems. For lasers, losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. In this work, we show how to turn losses into gain by steering the parameters of a system to the vicinity of an exceptional point (EP), which occurs when the eigenvalues and the corresponding eigenstates of a system coalesce. In our system of coupled microresonators, EPs are manifested as the loss-induced suppression and revival of lasing. Below a critical value, adding loss annihilates an existing Raman laser. Beyond this critical threshold, lasing recovers despite the increasing loss, in stark contrast to what would be expected from conventional laser theory. Our results exemplify the counterintuitive features of EPs and present an innovative method for reversing the effect of loss.

http://science.sciencemag.org/content/sci/346/6207/328.full.pdf

Loss-induced suppression and revival of lasing.

When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called exceptional point occurs, which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such non-Hermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.

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Reversing the pump dependence of a laser at an exceptional point

High-power broad-area diode lasers are the most efficient light sources, with 90-μm stripe GaAs-based 940-980 nm single emitters delivering > 10 W optical output at a power conversion efficiency ηE(10 W) > 65%. A review of efforts to increase ηE is presented here and we show that for well-optimized structures, the residual losses are dominated by the p -side waveguide and nonideal internal quantum efficiency ηi . The challenge in measuring efficiency to sufficient precision is also discussed. We show that ηE can most directly be improved using low heat sink temperature THS with ηE(10 W) reaching > 70% at THS = -50 °C. In contrast, increases in ηE at THS = 25 °C require improvements in both material quality and design, with growth studies targeting increased ηi and reduced threshold current and design studies seeking to mitigate the impact of the p-side waveguide. “Extreme, double asymmetric” (EDAS) designs are shown to substantially reduce p-side losses, at the penalty of increased threshold current. The benefit of EDAS designs is shown here using diode lasers with 30-μm stripes, (in development as high beam quality sources for material processing). Efficiency increases of ~ 10% relative to conventional designs are demonstrated at high powers.

Efficient High-Power Laser Diodes

We show theoretically, that the detuning between the resonance frequencies of differently pumped DFB sections gives rise to two different pulsation mechanisms, 1) dispersive self Q-switching of a single-mode and 2) beating oscillations between two modes of nearly equal threshold gain. Our analysis is based on the dynamic coupled wave equations accomplished with carrier rate equations. We demonstrate the existence of certain isolated values of the detuning between both sections, at which two longitudinal eigenmodes become degenerate. In the degeneration point, the longitudinal excess factor of spontaneous emission has a singularity and the system of eigenmodes becomes incomplete. We derive reduced equations governing the dynamics in the vicinity of degeneration points. For an example device, the numerical integration of these equations clearly demonstrates the two different self pulsations with repetition rates of more than 100 GHz.

Mechanisms of fast self pulsations in two-section DFB lasers

High-power quantum well lasers with high brightness in the spectral range between 650 nm and 1080 nm will be presented. Improved layer structures with a narrow vertical far-field divergence down to angles of 15deg (full-width at half-maximum) were developed. For these layer structures, optimized tapered lasers were processed to achieve laterally a nearly diffraction-limited beam quality with beam propagation factors smaller than 2. Depending on the emission wavelength, the tapered devices reach an output power up to 12 W and a brightness of 1 GWmiddotcm-2middotsr-1.

High-Brightness Quantum Well Tapered Lasers

An effective index model for vertical-cavity surface-emitting lasers (VCSELs) is reexamined. In a systematic manner, the basic equations are derived. Instead of effective indices of plane reference waveguides, effective frequencies of plane reference resonators appear. Calculations of the threshold gain and lasing wavelength of a long-wavelength VCSEL show the usefulness of the method and clarify the waveguiding mechanisms in VCSELs, Both dispersion and waveguiding influence the lasing wavelength remarkably.

The effective frequency method in the analysis of vertical-cavity surface-emitting lasers

We compare the results of different optical vertical-cavity surface-emitting laser models on the position-dependent effects of thin oxide apertures Both scalar and vectorial models as well as hybrid models are considered Physical quantities that are compared are resonance wavelength, threshold material gain, and modal stability For large device diameters and low-order modes, the agreement between the different models is quite good Larger differences occur when considering smaller devices and higher order modes It is also observed that the spread in the resonance wavelengths is smaller than that for the threshold material gain

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H. Wenzel

Papers

Efficient High-Power Laser Diodes

Mechanisms of fast self pulsations in two-section DFB lasers

High-Brightness Quantum Well Tapered Lasers

The effective frequency method in the analysis of vertical-cavity surface-emitting lasers

Comparison of optical VCSEL models on the simulation of oxide-confined devices