Enhanced sensitivity at higher-order exceptional points.

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement-specifically, a ternary, parity-time-symmetric photonic laser molecule-with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

Erratum: Enhanced sensitivity at higher-order exceptional points.

This corrects the article DOI: 10.1038/nature23280.

Optical isolation in topological-edge-state photonic arrays.

We introduce a new type of optical isolator based on breaking time reversal symmetry in dissipative finite Su-Schrieffer-Heeger (SSH) waveguide arrays that support topological edge states at one end of the structure. In the forward propagation direction, light is launched into the edge waveguide to excite the localized topological midgap state. As a result, most of the input optical power is transmitted to the output port. On the other hand, backward reflected light encounters a propagation constant mismatch in that same channel which shifts the otherwise midgap state into one of the bands and hence becomes delocalized over the whole array. We show that under these conditions, a judicious spatial distribution of the optical dissipation across the structure can produce an isolation ratio of -50 dB. The required nonreciprocal phase shift is introduced by depositing a magnetic garnet film only on the edge waveguide and, thus, the required magnetic field can be generated by an integrated micromagnet. Similar concepts can also be applied to SSH arrays made from optical resonators.

Enhancing optical isolator performance in nonreciprocal waveguide arrays.

We investigate the operation of optical isolators based on magneto-optics waveguide arrays beyond the coupled mode analysis. Semi-vectorial beam propagation simulations demonstrate that evanescent tail coupling and the effects of radiation are responsible for degrading the device's performance. Our analysis suggests that these effects can be mitigated when the array size is scaled up. In addition, we propose the use of radiation blockers in order to offset some of these effects, and we show that they provide a dramatic improvement in performance. Finally, we also study the robustness of the system with respect to fabrication tolerances using the coupled mode theory. We show that small, random variations in the system's parameters tend to average out as the number of optical guiding channels increases.

Observation of accelerating Wannier-Stark beams in optically induced photonic lattices.

We generate optical beams analogous to the Wannier-Stark states in semiconductor superlattices and observe that the two main lobes of the WS beams self-bend (accelerate) along two opposite trajectories in a uniform one-dimensional photonic lattice. Such self-accelerating features exist only in the presence of the lattice and are not observed in a homogenous medium. Under the action of nonlinearity, however, the beam structure and acceleration cannot be preserved. Our experimental observations are in qualitative agreement with theoretical predictions.

Resolving the topology of encircling multiple exceptional points.

Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling of exceptional points (EPs). To date, most work has focused on systems consisting of two modes that are tuned by two control parameters and have isolated EPs. While these systems exhibit exotic features related to EP encircling, it has been shown that richer behavior occurs in systems with more than two modes. Such systems can be tuned by more than two control parameters, and contain EPs that form a knot-like structure. Control loops that encircle this structure cause the system's eigenvalues to trace out non-commutative braids. Here we consider a hybrid scenario: a three-mode system with just two control parameters. We describe the relationship between control loops and their topology in the full and two-dimensional parameter space. We demonstrate this relationship experimentally using a three-mode mechanical system in which the control parameters are provided by optomechanical interaction with a high-finesse optical cavity.

Shockwave based nonlinear optical manipulation in densely scattering opaque suspensions.

Optical manipulation of particulate-loaded, highly scattering (opaque) suspensions is considered impossible. Here we demonstrate theoretically and experimentally optical manipulation of the local properties of such opaque suspensions. We show that the optical forces exerted by multiply-scattered light give rise to dense shock fronts of particle concentration, propagating deep inside the opaque suspensions, where the optical field is completely diffuse. We exploit these waves to demonstrate a plethora of optofluidic manipulations, ranging from optical transport and concentration of large populations of nanoparticles, to light-induced 'writing' of concentrated spots in the suspensions and light-induced phase-transition from suspension to gel in localized volumes inside the fluids.

Supersymmetric optical structures.

We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically construct index potentials capable of exhibiting the same scattering and guided wave characteristics. In particular, in the Helmholtz regime, we demonstrate that one-dimensional supersymmetric pairs display identical reflectivities and transmittivities for any angle of incidence. Optical supersymmetry is then extended to two-dimensional systems where a link between specific azimuthal mode subsets is established. Finally, we explore supersymmetric photonic lattices where discreteness can be utilized to design lossless integrated mode filtering arrangements.

Spectral sensitivity near exceptional points as a resource for hardware encryption.

The spectral sensitivity near exceptional points (EPs) has been recently explored as an avenue for building sensors with enhanced sensitivity. However, to date, it is not clear whether this class of sensors does indeed outperform traditional sensors in terms of signal-to-noise ratio. In this work, we investigate the spectral sensitivity associated with EPs under a different lens and propose to utilize it as a resource for hardware security. In particular, we introduce a physically unclonable function (PUF) based on analogue electronic circuits that benefit from the drastic eigenvalues bifurcation near a divergent exceptional point to enhance the stochastic entropy caused by inherent parameter fluctuations in electronic components. This in turn results in a perfect entropy source for the generation of encryption keys encoded in analog electrical signals. This lightweight and robust analog-PUF structure may lead to a variety of unforeseen securities and anti-counterfeiting applications in radio-frequency fingerprinting and wireless communications.

Universality of light thermalization in multimoded nonlinear optical systems.

Recent experimental studies in heavily multimoded nonlinear optical systems have demonstrated that the optical power evolves towards a Rayleigh-Jeans (RJ) equilibrium state. To interpret these results, the notion of wave turbulence founded on four-wave mixing models has been invoked. Quite recently, a different paradigm for dealing with this class of problems has emerged based on thermodynamic principles. In this formalism, the RJ distribution arises solely because of ergodicity. This suggests that the RJ distribution has a more general origin than was earlier thought. Here, we verify this universality hypothesis by investigating various nonlinear light-matter coupling effects in physically accessible multimode platforms. In all cases, we find that the system evolves towards a RJ equilibrium-even when the wave-mixing paradigm completely fails. These observations, not only support a thermodynamic/probabilistic interpretation of these results, but also provide the foundations to expand this thermodynamic formalism along other major disciplines in physics.

Single-mode quasi PT-symmetric laser with high power emission.

Large-area lasers are practical for generating high output powers. However, this often comes at the expense of lower beam quality due to the introduction of higher-order modes. Here, we experimentally demonstrate a new type of electrically pumped, large-area edge-emitting lasers that exhibit a high power emission (∼0.4 W) and a high-quality beam (M2∼1.25). These favorable operational characteristics are enabled by establishing a quasi PT-symmetry between the second-order mode of a large area two-mode laser cavity and that of a single-mode auxiliary partner cavity, i.e., by implementing a partial isospectrality between the two coupled cavities. This in turn enlarges the effective volume of the higher-order modes. As a result, a selective pump applied via current injection into the main laser cavity can provide a stronger modal gain to the fundamental mode, and thus lead to lasing in the single mode regime after filtering out higher order transverse modes. The reported experimental results confirm this intuitive picture and are in good agreement with both theoretical and numerical analysis. Above all, the employed material platform and fabrication process are compatible with the industrial standards of semiconductor lasers. This work provides the first clear demonstration, beyond previous proof-of-concept studies, of the utility of PT-symmetry in building laser geometries with enhanced performance and, at the same time, useful output power levels and emission characteristics.

Tracking exceptional points above the lasing threshold.

Recent studies on exceptional points (EPs) in non-Hermitian optical systems have revealed unique traits, including unidirectional invisibility, chiral mode switching and laser self-termination. In systems featuring gain/loss components, EPs are commonly accessed below the lasing threshold, i.e., in the linear regime. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning impedes the formation of EPs, here we demonstrate that such detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the EP. Furthermore, we find that the pump imbalance at lasing EPs varies with the total pump power, enabling their continuous tracking. This work uncovers the unstable nature of EPs above laser threshold in coupled semiconductor lasers, offering promising opportunities for the realization of self-pulsing nanolaser devices and frequency combs.

Sculpturing of photonic crystals by ion beam lithography: towards complete photonic bandgap at visible wavelengths.

Three dimensional (3D) ion beam lithography (IBL) is used to directly pattern 3D photonic crystal (PhC) structures in crystalline titania. The process is maskless and direct write. The slanted pore 3D structures with pore diameters of 100 nm having aspect ratio of 8 were formed. It is shown that chemical enhancement of titania removal up to 5.2 times is possible in XeF2 gas for the closest nozzle-to-sample distance; the enhancement was ∼ 1.5 times for the actual 3D patterning due to a sample tilt. Tolerances of structural parameters and optimization of IBL processing required for the fabrication of PhCs with full photonic bandgap in visible spectral range in rutile are outlined. Application potential of 3D-IBL is discussed.

Optical control of thermocapillary effects in complex nanofluids.

We study the strong coupling of light and nanoparticle suspensions and their surface tension effect in capillaries. We show experimentally and theoretically that increasing the intensity of a narrow laser beam passing through a capillary far away from the surface results in a significant decrease in the fluid level. The underlying mechanism relies on light-induced redistribution of nanoparticles in the bulk and the surface of the fluid, facilitating continuous optical control over the surface position. The experiments manifest optical control from afar over properties of fluid surfaces.

Crossing exceptional points without phase transition.

We show that the theoretical framework linking exceptional points (EPs) to phase transitions in parity-time (PT) symmetric Hamiltonians is incomplete. Particularly, we demonstrate that the application of the squaring operator to a Jx PT lattice dramatically alter the topology of its Riemann surface, eventually resulting in a system that can cross an EP without undergoing a symmetry breaking. We elucidate on these rather surprising results by invoking the notion of phase diagrams in higher dimensional parameter space. Within this perspective, the canonical PT symmetry breaking paradigm arises only along certainprojections of the Riemann surface in the parameter space.

Supersymmetric laser arrays.

Scaling up the radiance of coupled laser arrays has been a long-standing challenge in photonics. In this study, we demonstrate that notions from supersymmetry-a theoretical framework developed in high-energy physics-can be strategically used in optics to address this problem. In this regard, a supersymmetric laser array is realized that is capable of emitting exclusively in its fundamental transverse mode in a stable manner. Our results not only pave the way toward devising new schemes for scaling up radiance in integrated lasers, but also, on a more fundamental level, could shed light on the intriguing synergy between non-Hermiticity and supersymmetry.

Symmetry in optics and photonics: a group theory approach.

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.

Winding around non-Hermitian singularities.

Non-Hermitian singularities are ubiquitous in non-conservative open systems. Owing to their peculiar topology, they can remotely induce observable effects when encircled by closed trajectories in the parameter space. To date, a general formalism for describing this process beyond simple cases is still lacking. Here we develop a general approach for treating this problem by utilizing the power of permutation operators and representation theory. This in turn allows us to reveal a surprising result that has so far escaped attention: loops that enclose the same singularities in the parameter space starting from the same point and traveling in the same direction, do not necessarily share the same end outcome. Interestingly, we find that this equivalence can be formally established only by invoking the topological notion of homotopy. Our findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics.

Topological hybrid silicon microlasers.

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications. Here, we bridge this gap and present an experimental investigation of an active topological photonic system, demonstrating a topological hybrid silicon microlaser array respecting the charge-conjugation symmetry. The created new symmetry features favour the lasing of a protected zero mode, where robust single-mode laser action in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid implemented on a silicon-on-insulator substrate, and is thereby readily suitable for integrated silicon photonics with applications in optical communication and computing.

Power circulation via negative energy-flux wormholes in optical nanowaveguides.

We show that energy circulation within a pulse is possible when it propagates in a high-contrast dielectric nanowire. This process is accomplished through electromagnetic "wormhole" regions, in which the Poynting vector associated with the guided mode is negative with respect to the direction of propagation. For demonstration purposes this mechanism is elucidated in AlGaAs and silicon nanowaveguides. The effect of dispersion on the power circulation is also considered.