Mercedeh Khajavikhan

Thresholdless nanoscale coaxial lasers

The effects of cavity quantum electrodynamics (QED), caused by the interaction of matter and the electromagnetic field in subwavelength resonant structures, have been the subject of intense research in recent years. The generation of coherent radiation by subwavelength resonant structures has attracted considerable interest, not only as a means of exploring the QED effects that emerge at small volume, but also for its potential in applications ranging from on-chip optical communication to ultrahigh-resolution and high-throughput imaging, sensing and spectroscopy. One such strand of research is aimed at developing the ‘ultimate’ nanolaser: a scalable, low-threshold, efficient source of radiation that operates at room temperature and occupies a small volume on a chip. Different resonators have been proposed for the realization of such a nanolaser—microdisk and photonic bandgap resonators, and, more recently, metallic, metallo-dielectric and plasmonic resonators. But progress towards realizing the ultimate nanolaser has been hindered by the lack of a systematic approach to scaling down the size of the laser cavity without significantly increasing the threshold power required for lasing. Here we describe a family of coaxial nanostructured cavities that potentially solve the resonator scalability challenge by means of their geometry and metal composition. Using these coaxial nanocavities, we demonstrate the smallest room-temperature, continuous-wave telecommunications-frequency laser to date. In addition, by further modifying the design of these coaxial nanocavities, we achieve thresholdless lasing with a broadband gain medium. In addition to enabling laser applications, these nanoscale resonators should provide a powerful platform for the development of other QED devices and metamaterials in which atom–field interactions generate new functionalities.

Parity-time–symmetric microring lasers

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. The interplay between gain and loss can provide a route to control laser emission. Compensating optical loss for laser gain Optical loss is thought to be detrimental to the operation of a laser, typically resulting in poor beam quality, multimode emission, and low efficiencies. Now results that take their cue from theoretical ideas of parity-time symmetry and implement them into the design of coupled laser components show that loss and gain can actually work together. Feng et al. and Hodaei et al. designed laser systems based on microring cavities to carefully control the amount of loss and gain within each component. The interplay between the loss and gain resulted in enhanced and cleaner emission from their lasers. Science, this issue p. 972, p. 975

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.

Electrically pumped sub-wavelength metallo-dielectric pedestal pillar lasers

Electrically driven subwavelength scale metallo-dielectric pedestal pillar lasers are designed and experimentally demonstrated. The metallo-dielectric cavity significantly enhances the quality factor (Q > 1500) of the wavelength and subwavelength scale lasers and the pedestal structure significantly reduces the threshold gain (< 400 cm(-1)) which can potentially enable laser operation at room temperature. We observed continuous wave lasing in 750 nm gain core radius laser at temperatures between 77 K and 140 K with a threshold current of 50 μA (at 77 K). We also observed lasing from a 355 nm gain core radius laser at temperatures between 77 K and 100 K.

Topological insulator laser: Experiments

Topological protection for lasers Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science, this issue p. eaar4003, p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. INTRODUCTION Physical systems that exhibit topological invariants are naturally endowed with robustness against perturbations, as was recently demonstrated in many settings in condensed matter, photonics, cold atoms, acoustics, and more. The most prominent manifestations of topological systems are topological insulators, which exhibit scatter-free edge-state transport, immune to perturbations and disorder. Recent years have witnessed intense efforts toward exploiting these physical phenomena in the optical domain, with new ideas ranging from topology-driven unidirectional devices to topological protection of path entanglement. But perhaps more technologically relevant than all topological photonic settings studied thus far is, as proposed by the accompanying theoretical paper by Harari et al., an all-dielectric magnet-free topological insulator laser, with desirable properties stemming from the topological transport of light in the laser cavity. RATIONALE We demonstrate nonmagnetic topological insulator lasers. The topological properties of the laser system give rise to single-mode lasing, robustness against fabrication defects, and notably higher slope efficiencies compared to those of the topologically trivial counterparts. We further exploit the properties of the active topological platform by assembling topological insulator lasers from S-chiral microresonators that enforce predetermined unidirectional lasing even in the absence of magnetic fields. RESULTS Our topological insulator laser system is an aperiodic array of 10 unit cell–by–10 unit cell coupled ring resonators on an InGaAsP quantum wells platform. The active lattice uses the topological architecture suggested in the accompanying theoretical paper. This two-dimensional setting is composed of a square lattice of ring resonators coupled to each other by means of link rings. The intermediary links are judiciously spatially shifted to introduce a set of hopping phases, establishing a synthetic magnetic field and two topological band gaps. The gain in this laser system is provided by optical pumping. To promote lasing of the topologically protected edge modes, we pump the outer perimeter of the array while leaving the interior lossy. We find that this topological insulator laser operates in single mode even considerably above threshold, whereas the corresponding topologically trivial realizations lase in multiple modes. Moreover, the topological laser displays a slope efficiency that is considerably higher than that in the corresponding trivial realizations. We further demonstrate the topological features of this laser by observing that in the topological array, all sites emit coherently at the same wavelength, whereas in the trivial array, lasing occurs in localized regions, each at a different frequency. Also, by pumping only part of the topological array, we demonstrate that the topological edge mode always travels along the perimeter and emits light through the output coupler. By contrast, when we pump the trivial array far from the output coupler, no light is extracted from the coupler because the lasing occurs at stationary modes. We also observe that, even in the presence of defects, the topological protection always leads to more efficient lasing compared to that of the trivial counterpart. Finally, to show the potential of this active system, we assemble a topological system based on S-chiral resonators, which can provide new avenues to control the topological features. CONCLUSION We have experimentally demonstrated an all-dielectric topological insulator laser and found that the topological features enhance the lasing performance of a two-dimensional array of microresonators, making them lase in unison in an extended topologically protected scatter-free edge mode. The observed single longitudinal-mode operation leads to a considerably higher slope efficiency as compared to that of a corresponding topologically trivial system. Our results pave the way toward a new class of active topological photonic devices, such as laser arrays, that can operate in a coherent fashion with high efficiencies. Topological insulator laser. (A) Top-view image of the lasing pattern (topological edge mode) in a 10 unit cell–by–10 unit cell array of topologically coupled resonators and the output ports. (B) Output intensity versus pump intensity for a topological insulator laser and its trivial counterpart. The enhancement of the slope efficiency is about threefold. Comparing the power emitted in the single mode of the topological array to that of the highest power mode in the trivial array, the topological outperforms the trivial by more than a factor of 10

Topological insulator laser: Theory

Topological protection for lasers Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science, this issue p. eaar4003, p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. INTRODUCTION Topological insulators emerged in condensed matter physics and constitute a new phase of matter, with insulating bulk and robust edge conductance that is immune to imperfections and disorder. To date, topological protection is known to be a ubiquitous phenomenon, occurring in many physical settings, ranging from photonics and cold atoms to acoustic, mechanical, and elastic systems. So far, however, most of these studies were carried out in entirely passive, linear, and conservative settings. RATIONALE We propose topological insulator lasers: lasers whose lasing mode exhibits topologically protected transport without magnetic fields. Extending topological physics to lasers is far from natural. In fact, lasers are built on foundations that are seemingly inconsistent with the essence of topological insulators: They require gain (and thus are non-Hermitian), they are nonlinear entities because the gain must be saturable, and they are open systems because they emit light. These properties, common to all lasers, cast major doubts on the possibility of harnessing topological features to make a topological insulator laser. Despite this common mindset, we show that the use of topological properties leads to highly efficient lasers, robust to defects and disorder, with single-mode lasing even at conditions high above the laser threshold. RESULTS We demonstrate that topological insulator lasers are theoretically possible and experimentally feasible. We consider two configurations involving planar arrays of coupled active resonators. The first is based on the Haldane model, archetypical for topological systems. The second model, geared toward experiment, constitutes an aperiodic array architecture creating an artificial magnetic field. We show that by introducing saturable gain and loss, it is possible to make these systems lase in a topological edge state. In this way, the lasing mode exhibits topologically protected transport; the light propagates unidirectionally along the edges of the cavity, immune to scattering and disorder, unaffected by the shape of the edges. Moreover, we show that the underlying topological properties not only make the system robust to fabrication and operational disorder and defects, they also lead to a highly efficient single-mode lasing that remains single-mode even at gain values high above the laser threshold. The figure describes the geometry and features of a topological insulator laser based on the Haldane model while adding saturable gain, loss, and an output port. The cavity is a planar honeycomb lattice of coupled microring resonators, pumped at the perimeter with a lossy interior. We show that under these conditions, lasing occurs at the topological edge mode, which has unidirectional flux and is extended around the perimeter with almost-uniform intensity. The topological cavities exhibit higher efficiency than the trivial cavity, even under strong disorder. For the topological laser with a small gap, the topological protection holds as long as the disorder level is smaller than the gap size. DISCUSSION The concept of the topological insulator laser alters current understanding of the interplay between disorder and lasing, and opens exciting possibilities at the interface of topological physics and laser science, such as topologically protected transport in systems with gain. We show here that the laser system based on the archetypal Haldane model exhibits topologically protected transport, with features similar to those of its passive counterpart. This behavior means that this system is likely to have topological invariants, despite the nonhermiticity. Technologically, the topological insulator laser offers an avenue to make many semiconductor lasers operate as one single-mode high-power laser. The topological insulator laser constructed from an aperiodic array of resonators was realized experimentally in an all-dielectric platform, as described in the accompanying experimental paper by Bandres et al. Topological insulator laser based on the Haldane model and its efficiency. (A) Planar honeycomb lattice of coupled microring resonators pumped at the perimeter. The topological lasing mode has unidirectional flux with almost-uniform intensity, which builds up as the mode circulates and drops when passing the output coupler. (B) Slope efficiency (in arbitrary units) versus disorder strength for three cases differing only in the Haldane phase (of the next-to-nearest neighbor coupling): a topological laser with the maximum gap (blue; Haldane phase of π/2), one with a small topological gap (red; Haldane phase of π/8), and a topologically trivial laser with no gap (black; Haldane phase of 0). Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. These attributes make topological insulator systems ideal candidates for enabling applications in quantum computation and spintronics. We propose a concept that exploits topological effects in a unique way: the topological insulator laser. These are lasers whose lasing mode exhibits topologically protected transport without magnetic fields. The underlying topological properties lead to a highly efficient laser, robust to defects and disorder, with single-mode lasing even at very high gain values. The topological insulator laser alters current understanding of the interplay between disorder and lasing, and at the same time opens exciting possibilities in topological physics, such as topologically protected transport in systems with gain. On the technological side, the topological insulator laser provides a route to arrays of semiconductor lasers that operate as one single-mode high-power laser coupled efficiently into an output port.

Etch-free low loss silicon waveguides using hydrogen silsesquioxane oxidation masks

An etch-free fabrication technique for creating low loss silicon waveguides in the silicon-on-insulator material system is proposed and demonstrated. The approach consists of local oxidation of a silicon-on-insulator chip covered with a e-beam patterned hydrogen silsesquioxane mask. A single oxidation step converts hydrogen silsesquioxane to a glass-like compound and simultaneously defines the waveguides, bypassing the need for any wet or dry etching steps. The spectral response of ring resonators fabricated using this technique was used to characterize the waveguide losses. Intrinsic Q-factors as high as 1.57 × 10(6), corresponding to a waveguide loss of 0.35 dB/cm, were measured.

Compact chip-scale filter based on curved waveguide Bragg gratings

We propose a method for miniaturization of filters based on curved waveguide Bragg gratings, so that long structures can be packed into a small area on a chip. This eliminates the stitching errors introduced in the fabrication process, which compromise the performance of long Bragg gratings. Our approach relies on cascading curved waveguide Bragg gratings with the same radius of curvature. An analytical model for the analysis of these devices was developed, and a filter based on this model was designed and fabricated in a silicon on insulator platform. The filter had a total length of 920μm, occupied an area of 190μm×114μm, and exhibited a stop band of 1.7nm at 1.55μm and an extinction ratio larger than 23dB.

Nonlinear reversal of thePT-symmetric phase transition in a system of coupled semiconductor microring resonators

A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase transition point. The conclusions of our analysis are in agreement with experimental data.

Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion

We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate-irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.