Topological Lasers Research Articles

Topological Valley Hall Edge State Lasing

AbstractTopological lasers based on topologically protected edge states exhibit unique features and enhanced robustness of operation in comparison with conventional lasers, even in the presence of disorder, edge deformation, or local defects. Here a new class of topological lasers arising from the valley Hall edge states is proposed, which does not rely on magnetic fields. Specifically, topological lasing occurs at domain walls between two honeycomb waveguide arrays with broken spatial inversion symmetry. Two types of valley Hall edge lasing modes are found by shaping the gain landscape along the domain walls. In the presence of uniform losses and two‐photon absorption, the lasing results in the formation of stable nonlinear dissipative excitations localized on the edge of the structure, even if it has complex geometry and even if it is finite. Robustness of lasing edge states is demonstrated in both periodic and finite structures, where such states can circumvent certain corners without scattering losses or radiation into the bulk, as long as the intervalley scattering is absent. The photonic structure and mechanism proposed here for topological lasing is fundamentally different from those previously employed in topological lasers, and can be used for fabrication of practical topological lasers of various geometries.

Non-Hermitian topological end-mode lasing in polariton systems

We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to {\it enforced exceptional points} which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end-mode in a realistic model of a microcavity lattice.

Design of photonic crystal nonlinear laser power limiter based on topological edge states and optical Kerr effect.

We propose a novel topological photonic crystal nonlinear laser power limiter based on topological edge states and optical Kerr effect. In the proposed laser power limiter, a one-dimensional photonic crystal in topological edge state allows the relatively weak signal light with a certain wavelength to pass through with high transmission, but blocks most of the intense hostile or accidental laser with the same wavelength due to the change of topological edge state generated from optical Kerr effect. Taking a 1064 nm wavelength as an example, we have designed such a nonlinear laser power limiter corresponding to the wavelength. When the optical power density is low (less than 0.12 MW/cm2), the light transmission can reach 82.54%, and the transmission can be reduced to 1.04% when the optical power density is increased to 11.66 MW/cm2. Therefore, this method provides a new promising approach to realize laser protection at the desired wavelength.

Topological optics with 3D-tangle laser solitons

We analyse, theoretically and numerically, stable localized 3D- structures with radiation wavefront singularities in lasers or laser media with fast saturable absorption; radiation has a fixed polarization state. These laser solitons’ internal structure is characterized by their skeletons, which consist of vortex lines where the field vanish and radiation phase changes by 2πm with integer m – topological charge – as a result of a round-trip around the line. The vortex lines are oriented according the direction of radiation phase increase; high-order vortex lines (m>1) are unstable and split into m lines with m=1. Complexes of fundamental (without vortices when isolated) laser solitons have unclosed vortex lines. Presented are topological laser solitons with vortex lines, which are unclosed and closed, unknotted and knotted, unlinked and linked. Various types of the solitons are stable in different, but overlapping domains of the scheme parameters; a slow variation of such parameters leads to hysteretic variations of solitons’ characteristics. Such hysteresis is reversible if soliton’s topology does not change during the parameters’ variation, and irreversible in the opposite case. The increased stability of dissipative solitons and the preservation of the topological characteristics of structures under perturbations make topological laser solitons promising for information applications.

604-nm high-order vortex beams directly generated from a Pr:YLF laser with a cavity-loss-induced gain switching mechanism

In this work, we demonstrated, for the first time to the best of our knowledge, high-order vortex beams at 604 nm that were directly emitted from a Pr:YLF crystal laser. By combining a blue-diode-pumped v-type cavity for controllable Gouy phase introduction and off-axis crystal rotation for high-order HG modes generation, topological charged 604-nm vortex lasers were attained up to the third order. Furthermore, the vortex beams were found to be lasing at 604 nm that was often deemed less prone to lase compared with 607-nm in the same energy manifold. By a detailed spectroscopic study and rate equation analysis, we proposed and confirmed that the 604-nm transition of Pr:YLF crystal could be favorable in the vortex beam generation by a cavity-loss-induced gain switching process, in which the net gain at 604-nm could surpass that of 607-nm as the cavity loss was amassed beyond a threshold value.

Lasing with Topological Weyl Semimetal

Lasing behavior of optically active planar topological Weyl semimetal (TWS) is investigated in view of the Kerr and Faraday rotations. Robust topological character of TWS is revealed by the presence of Weyl nodes and relevant surface conductivities. We focus our attention on the surfaces where no Fermi arcs are formed, and thus Maxwell equations contain topological terms. We explicitly demonstrate that two distinct lasing modes arise because of the presence of effective refractive indices which lead to the birefringence phenomena. Transfer matrix is constructed in such a way that reflection and transmission amplitudes involve 2 × 2 matrix-valued components describing the bimodal character of the TWS laser. We provide associated parameters of the topological laser system yielding the optimal impacts. We reveal that gain values corresponding to the lasing threshold display a quantized behavior, which occurs due to topological character of the system. Our proposal is supported by the corresponding graphical demonstrations. Our observations and predictions suggest a concrete way of forming TWS laser and coherent perfect absorber; and are awaited to be confirmed by an experimental realization based on our computations.

Electrically pumped topological laser with valley edge modes.

Quantum cascade lasers are compact, electrically pumped light sources in the technologically important mid-infrared and terahertz region of the electromagnetic spectrum1,2. Recently, the concept of topology3 has been expanded from condensed matter physics into photonics4, giving rise to a new type of lasing5-8 using topologically protected photonic modes that can efficiently bypass corners and defects4. Previous demonstrations of topological lasers have required an external laser source for optical pumping and have operated in the conventional optical frequency regime5-8. Here we demonstrate an electrically pumped terahertz quantum cascade laser based on topologically protected valley edge states9-11. Unlike topological lasers that rely on large-scale features to impart topological protection, our compact design makes use of the valley degree of freedom in photonic crystals10,11, analogous to two-dimensional gapped valleytronic materials12. Lasing with regularly spaced emission peaks occurs in a sharp-cornered triangular cavity, even if perturbations are introduced into the underlying structure, owing to the existence of topologically protected valley edge states that circulate around the cavity without experiencing localization. We probe the properties of the topological lasing modes by adding different outcouplers to the topological cavity. The laser based on valley edge states may open routes to the practical use of topological protection in electrically driven laser sources.

Inherent strain homogenization for fast residual deformation simulation of thin-walled lattice support structures built by laser powder bed fusion additive manufacturing

Numerical simulation of residual deformation in metallic components with dense lattice support structures by the laser powder bed fusion (L-PBF) additive manufacturing process has been a significant challenge due to the very high computational expense in performing both finite element meshing and analysis. In this work, the modified inherent strain method is extended to enable efficient residual deformation simulation of l-PBF components with lattice support structures. The asymptotic homogenization method is employed to obtain the equivalent mechanical properties including the anisotropic elastic modulus and inherent strains given the topological configuration and laser scanning strategy of the thin-walled lattice support structures. A key finding is that the in-plane homogenized inherent strain values decrease with increasing volume density, which can be attributed to the directional dependence of inherent strains for the AM-processed material. Based on the homogenized mechanical properties and inherent strains, the thin-walled lattice support structures can be considered to be an effective solid continuum so that the simulation can be accelerated significantly to obtain residual deformation. Good accuracy of the homogenized mechanical property and inherent strains is validated by comparing the simulated residual deformation with experimental deformation measurement of several lattice structured beams of different volume densities. Efficiency of the proposed method is also demonstrated through numerical examples to have 80 % reduction in number of elements and nearly 10x speedup in computing time. In addition, the scalability of the proposed method is also verified through application to a complex L-PBF component fabricated with thin-walled support structures.

Active topological photonics

Abstract Topological photonics emerged as a novel route to engineer the flow of light. Topologically protected photonic edge modes, which are supported at the perimeters of topologically nontrivial insulating bulk structures, are of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there has been a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolutionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of remarkable realizations are topological lasers with unidirectional light output under time-reversal symmetry breaking and topologically protected polariton and micro/nanocavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non-Hermitian and parity-time symmetric quantum physics and are, in general, difficult to access using fermionic condensed matter systems. Here, we review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are determined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent research on topological photonic systems in which gain and loss, themselves, essentially influence topological properties of the bulk systems. We believe that active topological photonics provides powerful means to advance micro/nanophotonics systems for diverse applications and topological physics, itself, as well.

Several New Semiconductor Lasers and Status, Challenges and Insights of Related Industries

As the basis of the whole laser industry, the semiconductor laser industry is not only large-scaled but also has strong radiation and driving capacities. The semiconductor lasers are widely used in industrial, military, and living consumption fields such as optical communication, optical information processing, novel manufacturing, laser display, and biological and medical sensing. To adapt to the gradually expanding application range and satisfy the new requirements of different application scenarios, various new mechanisms, concepts, and structures have been introduced into the semiconductor laser industry through interdisciplinary penetration, greatly optimizing the wavelength coverage, beam quality, device volume, power consumption, modulation speed, and output power of the semiconductor lasers. This paper introduces several rapidly developed new semiconductor lasers by comparing their physical connotation, structural design, and preparation methods. Considering the current development status of related industries in China, we suggest that the development of the semiconductor laser industry should be closely combined with industrial application. The performance of the semiconductor lasers should be optimized in a closed-loop manner relying on the market capacity and the strong systematic development ability in China to promote the key technologies. New principles, structures, and processes should be continually introduced into this industry through interdisciplinary integration. Meanwhile, using the policy-oriented advantages in China, we suggest to increase investment in vertical external cavity surface emitting lasers, micro-nano lasers, and topological insulator lasers and conduct mass production and controllable production, thus to seize the leading position in international competition in the related fields.

Tutorial: Computing Topological Invariants in 2D Photonic Crystals

AbstractThe field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple methods for diagnosing the topology of optical systems remain elusive for an important part of the community. Herein, a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals is provided. The fundamental properties of wave propagation in lattices with a space‐dependent periodic electric permittivity is first described. Next, an introduction to topological invariants is provided, proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, the tutorial is complemented with a few practical examples of photonic crystal systems showing different topological properties, such as photonic valley‐Chern insulators, photonic crystals presenting an “obstructed atomic limit”, photonic systems supporting fragile topology, and finally photonic Chern insulators, where the magnetic permeability is also periodically modulated.

A high-performance topological bulk laser based on band-inversion-induced reflection.

Topological insulators are materials that behave as insulators in the bulk and as conductors at the edge or surface due to the particular configuration of their bulk band dispersion. However, up to date possible practical applications of this band topology on materials' bulk properties have remained abstract. Here, we propose and experimentally demonstrate a topological bulk laser. We pattern semiconductor nanodisk arrays to form a photonic crystal cavity showing topological band inversion between its interior and cladding area. In-plane light waves are reflected at topological edges forming an effective cavity feedback for lasing. This band-inversion-induced reflection mechanism induces single-mode lasing with directional vertical emission. Our topological bulk laser works at room temperature and reaches the practical requirements in terms of cavity size, threshold, linewidth, side-mode suppression ratio and directionality for most practical applications according to Institute of Electrical and Electronics Engineers and other industry standards. We believe this bulk topological effect will have applications in near-field spectroscopy, solid-state lighting, free-space optical sensing and communication.

Theory of chiral edge state lasing in a two-dimensional topological system

We theoretically study topological laser operation in a bosonic Harper-Hofstadter model featuring a saturable optical gain. Crucial consequences of the chirality of the lasing edge modes are highlighted, such as a sharp dependence of the lasing threshold on the geometrical shape of the amplifying region and the possibility of ultraslow relaxation times and of convectively unstable regimes. The different unstable regimes are characterized in terms of spatio-temporal structures sustained by noise and a strong amplification of a propagating probe beam is anticipated to occur in between the convective and the absolute (lasing) thresholds. The robustness of topological laser operation against static disorder is assessed.

Floquet topological insulator laser

We introduce a class of topological lasers based on the photonic Floquet topological insulator concept. The proposed system is realized as a truncated array of lasing helical waveguides, where the pseudomagnetic field arises due to twisting of the waveguides along the propagation direction that breaks the time-reversal symmetry and opens up a topological gap. When sufficient gain is provided in the edge channels of the array, the system lases into topological edge states. Topological lasing is stable only in certain intervals of the Bloch momenta that ensure a dynamic, but stable balance between the linear amplification and nonlinear absorption leading to the formation of breathing edge states. We also illustrate topological robustness of the edge currents by simulating lattice defects and triangular arrangements of the waveguides.

Symmetry and Topology in Non-Hermitian Physics

We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, point-like and line-like vacant regions. On the basis of these concepts and K-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons.

Topological magnon amplification

Topology is quickly becoming a cornerstone in our understanding of electronic systems. Like their electronic counterparts, bosonic systems can exhibit a topological band structure, but in real materials it is difficult to ascertain their topological nature, as their ground state is a simple condensate or the vacuum, and one has to rely instead on excited states, for example a characteristic thermal Hall response. Here we propose driving a topological magnon insulator with an electromagnetic field and show that this causes edge mode instabilities and a large non-equilibrium steady-state magnon edge current. Building on this, we discuss several experimental signatures that unambiguously establish the presence of topological magnon edge modes. Furthermore, our amplification mechanism can be employed to power a topological travelling-wave magnon amplifier and topological magnon laser, with applications in magnon spintronics. This work thus represents a step toward functional topological magnetic materials.

Phase-dependent topological interface state and spatial adiabatic passage in a generalized Su-Schrieffer-Heeger model

We extend the Su-Schrieffer-Heeger model to include both an additional real intercell coupling and a complex intracell coupling whose phase can be interpreted as the Peierls phase associated with a synthetic gauge field. Using different Peierls phases, we can realize a heterostructure supporting a topologically protected interface state, depending on the existence of one trivial and two nontrivial phases of distinct winding numbers. The spatial adiabatic passage of this localized state from the inner interface to either open boundary can be attained simply by modulating the corresponding Peierls phase, while its decay or growth rate is controlled by the on-site parity-time symmetric loss and gain terms. Our results provide a scheme to achieve dynamical control of topologically protected states while being of potential interest to topological lasers with an adjustable spatial profile.

Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional points, the boundary modes, and the band topology. Our findings serve as guiding principles for the design of applications, for example, in photonic lattices. For instance, periodic Dirac systems with non-Hermitian mass terms can be used as topological lasers. Periodic Dirac systems with non-Hermitian anti-commuting terms, on the other hand, exhibit exceptional points at the surface, whose non-trivial topology could be utilized for optical devices.

Lasing at K Points of a Honeycomb Plasmonic Lattice.

We study lasing at the high-symmetry points of the Brillouin zone in a honeycomb plasmonic lattice. We use symmetry arguments to define singlet and doublet modes at the K points of the reciprocal space. We experimentally demonstrate lasing at the K points that is based on plasmonic lattice modes and two-dimensional feedback. By comparing polarization properties to T-matrix simulations, we identify the lasing mode as one of the singlets with an energy minimum at the K point enabling feedback. Our results offer prospects for studies of topological lasing in radiatively coupled systems.

Realization of a three-dimensional photonic topological insulator.

Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic crystals, which have a photonic bandgap thatforbids light propagation in all directions1-3. Recently, inspired by the discoveries of topological insulators4,5, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators6-8, with promising applications in topological lasers9,10 and robust optical delay lines11. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a 'weak' topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries.