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A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and reflection are obtained even in cases where classical effective medium theory breaks down. Magnetoelectric coupling accounts for symmetry breaking in reflection and transmission when a non-symmetric structure is illuminated from two opposite sides.

Random lasers are a special class of laser in which light is confined through multiple scattering and interference process in a disordered medium, without a traditional optical cavity. They have been widely studied to investigate fundamental phenomena such as Anderson localization, and for applications such as speckle-free imaging, benefitting from multiple lasing modes. However, achieving controlled localized multi-mode random lasing at long wavelengths, such as in the terahertz (THz) frequency regime, remains a challenge. Here, we study devices consisting of randomly-distributed pillars fabricated from a quantum cascade gain medium, and show that such structures can achieve transversemagnetic polarized (TM) multi-mode random lasing, with strongly localized modes at THz frequencies. The weak short-range order induced by the pillar distribution is sufficient to ensure high quality-factor modes that have a large overlap with the active material. Furthermore, the emission spectrum can be easily tuned by tailoring the scatterer size and filling fraction. These “designer” random lasers, realized using standard photolithography 2 techniques, provide a promising platform for investigating disordered photonics with predesigned randomness in the THz frequency range, and may have potential applications such as speckle-free imaging.

Valley polarized topological states of light allow for robust waveguiding which has been demonstrated for transverse-electric modes in THz and near-infrared parts of the spectrum. As the topological protection relies on guiding the light via a highly structured surface, direct imaging of the photonic modes at sub-unit cell resolution is of high interest but challenging in particular for transverse-magnetic modes. Here, we report mapping the transverse-magnetic modes in a valley photonic crystal waveguide using scattering-type scanning near-field optical microscopy at the optical telecom C-band wavelength. The waveguide based on a triangular air-hole motif with broken inversion symmetry is fabricated from suspended Germanium layer. We observed the launching and guiding of the transverse-magnetic edge mode along the boundary between topologically distinct domains with opposite valley Chern indices. These results are supported by theoretical simulations, and provide insight into the design and use of topological protected states for applications in densely integrated optical telecommunication devices.

Unconventional chiral particles have recently been predicted to appear in certain three-dimensional crystal structures containing three- or more-fold linear band degeneracy points (BDPs)1–4. These BDPs carry topological charges, but are distinct from the standard twofold Weyl points or fourfold Dirac points, and cannot be described in terms of an emergent relativistic field theory1. Here we report on the experimental observation of a topological threefold BDP in a three-dimensional phononic crystal. Using direct acoustic field mapping, we demonstrate the existence of the threefold BDP in the bulk band structure, as well as doubled Fermi arcs of surface states consistent with a topological charge of 2. Another novel BDP, similar to a Dirac point but carrying non-zero topological charge, is connected to the threefold BDP via the doubled Fermi arcs. The Fermi arcs form double helicoids spanning a broad frequency range (relative bandwidth >25%). We show that the non-contractibility of these arcs gives rise to the phenomenon of topologically protected negative refraction of surface states on all surfaces of the sample. Our work paves the way to using these unconventional particles for exploring new emergent physical phenomena, and may find applications in symmetry-stabilized three-dimensional zero-index metamaterials. In acoustic metamaterials, unconventional chiral quasiparticles exhibit multifold band degeneracy points, each carrying non-zero topological charges, giving rise to the topologically protected negative surface refraction.

We demonstrate that the parity-time ($\mathcal{PT}$) symmetric interfaces formed between non-Hermitian amplifying (``gainy'') and lossy topological crystals exhibit $\mathcal{PT}$ phase transitions separating phases of lossless and decaying/amplifying topological edge transport. The spectrum of these interface states exhibits exceptional points (EPs) separating (i) a $\mathcal{PT}$ symmetric real-valued regime with an evenly distributed wave function in both gainy and lossy domains and (ii) a $\mathcal{PT}$ broken complex-valued regime, in which edge states asymmetrically localize in one of the domains. Despite its complex-valued character, the edge spectrum remains gapless and connects complex-valued bulk bands through the EPs. We find that the regimes exist when the real edge spectrum is embedded into the bulk continuum without mixing, indicating that the edge states are protected against leakage into the bulk by the $\mathcal{PT}$ symmetry. Two exemplary $\mathcal{PT}$ symmetric systems, exhibiting valley and Chern topological phases, respectively, are investigated and the connection with the corresponding Hermitian systems is established. Interestingly, despite the complex bulk spectrum of the Chern insulator, the bulk-interface correspondence principle still holds, as long as the topological gap remains open. The proposed systems are experimentally feasible in photonics, which is evidenced by our rigorous full-wave simulations of $\mathcal{PT}$ symmetric silicon-based photonic graphene.

In periodic media, despite the close relationship between geometrical effects in the bulk and topological surface states, the two are typically probed separately. We show that when beams in a Weyl medium reflect off an interface with a gapped medium, the trajectory is influenced by both bulk geometrical effects and the Fermi arc surface states. The reflected beam experiences a displacement, analogous to the Goos-H\"anchen or Imbert-Fedorov shifts, that forms a half-vortex in the two-dimensional surface momentum space. The half-vortex is centered where the Fermi arc of the reflecting surface touches the Weyl cone, with the magnitude of the shift scaling as an inverse square root away from the touching-point, and diverging at the touching-point. This striking feature provides a way to use bulk transport to probe the topological characteristics of a Weyl medium., Comment: 5+8 pages, 3+4 figures

Weyl points are isolated degeneracies in reciprocal space that are monopoles of the Berry curvature. This topological charge makes them inherently robust to Hermitian perturbations of the system. However, non-Hermitian effects, usually inaccessible in condensed matter systems, are an important feature of photonics systems, and when added to an otherwise Hermitian Weyl material have been predicted to spread the Berry charge of the Weyl point out onto a ring of exceptional points, creating a Weyl exceptional ring and fundamentally altering its properties. Here, we observe the implications of the Weyl exceptional ring using real-space measurements of an evanescently-coupled bipartite optical waveguide array by probing its effects on the Fermi arc surface states, the bulk diffraction properties, and the output power ratio of the two constituent sublattices. This is the first realization of an object with topological Berry charge in a non-Hermitian system., Manuscript is 8 pages, 4 figures. Supplementary is 5 pages, 3 figures

We demonstrate intervalley Bloch oscillation (BO) and Landau-Zener tunneling (LZT) in an optically induced honeycomb lattice with a refractive-index gradient. Unlike previously observed BO in a gapped square lattice, we show nonadiabatic beam dynamics that are highly sensitive to the direction of the index gradient and the choice of the Dirac cones. In particular, a symmetry-preserving potential leads to nearly perfect LZT and coherent BO between the inequivalent valleys, whereas a symmetry-breaking potential generates asymmetric scattering, imperfect LZT, and valley-sensitive generation of vortices mediated by a pseudospin imbalance. This clearly indicates that, near the Dirac points, the transverse gradient does not always act as a simple scalar force, as commonly assumed, and the LZT probability is strongly affected by the sublattice symmetry as analyzed from an effective Landau-Zener Hamiltonian. Our results illustrate the anisotropic response of an otherwise isotropic Dirac platform to real-space potentials acting as strong driving fields, which may be useful for manipulation of pseudospin and valley degrees of freedom in graphenelike systems. MOE (Min. of Education, S’pore) Published version

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, and the nontrivial topology is a result of next-nearest couplings with non-zero staggered phases. The system exhibits a topological phase transition between trivial and spin Chern insulator phases when the sublattices are frequency detuned. Such topological phase transitions can be easily induced by thermal or electro-optic modulators, or nonlinear cross phase modulation. We use this lattice to design reconfigurable topological waveguides, with potential applications in on-chip photon routing and switching., 5+5 pages, 3+5 figures, published version

Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential equations of the problem, which often results in high-order or even exponential convergence with respect to the size of the basis set. We highlight two separate examples of that in applied electromagnetics and photonics: (i) homogenization of periodic structures, and (ii) numerical simulation of electromagnetic waves in slab geometries. Extensive numerical evidence and theoretical considerations show that Trefftz approximations can be applied much more broadly than is traditionally done: they are effective not only in physically homogeneous regions but also in complex inhomogeneous ones. Two mechanisms underlying the high accuracy of Trefftz approximations in such complex cases are pointed out. The first one is related to trigonometric interpolation and the second one -- somewhat surprisingly -- to well-posedness of random matrices., 31 pages, 11 figures

We realize an unpaired Dirac cone at the center of the Brillouin zone, using a gyromagnetic photonic crystal with broken square sublattice symmetry and broken time-reversal symmetry. The behavior of the Dirac modes can be described by a gyromagnetic effective medium model with near-zero refractive index, and Voigt parameter near unity. When two domains are subjected to opposite magnetic biases, there exist unidirectional edge states along the domain wall. This establishes a link between topological edge states and the surface waves of homogeneous magneto-optical media. MOE (Min. of Education, S’pore) Published version

We demonstrate the existence of a topologically charged contour consisting entirely of exceptional points in a non-Hermitian helical waveguide array. We observe both protected chiral edge states and the lack of conical diffraction.

We observe Bloch oscillations and Landau-Zener-tunneling at Dirac points in photonic graphene. The non-adiabatic wave dynamics depend anisotropically on the direction of an applied index gradient, resulting in imperfect Landau-Zener-tunneling and valley-dependent vortex generation.

Synthetic photonic materials created by engineering the profile of refractive index or gain/loss distribution, such as negative-index metamaterials or parity-time-symmetric structures, can exhibit electric and magnetic properties that cannot be found in natural materials, allowing for photonic devices with unprecedented functionalities. In this article, we discuss two directions along this line—non-Hermitian photonics and topological photonics—and their applications in nonreciprocal light transport when nonlinearities are introduced. Both types of synthetic structures have been demonstrated in systems involving judicious arrangement of optical elements, such as optical waveguides and resonators. They can exhibit a transition between different phases by adjusting certain parameters, such as the distribution of refractive index, loss, or gain. The unique features of such synthetic structures help realize nonreciprocal optical devices with high contrast, low operation threshold, and broad bandwidth. They provide promising opportunities to realize nonreciprocal structures for wave transport. Published version

We study the emergence and disappearance of defect states in the complex Su-Schrieffer-Heeger (cSSH) model, a non-Hermitian one-dimensional lattice model containing gain and loss on alternating sites. Previous studies of this model have focused on the existence of a non-Hermitian defect state that is localized to the interface between two cSSH domains, and is continuable to the topologically protected defect state of the Hermitian Su-Schrieffer-Heeger (SSH) model. For large gain/loss magnitudes, we find that these defect states can disappear into the continuum, or undergo pairwise spontaneous breaking of a composite sublattice/time-reversal symmetry. The symmetry-breaking transition gives rise to a pair of defect states continuable to non-topologically-protected defect states of the SSH model. We discuss the phase diagram for the defect states, and its implications for non-Hermitian defect states., Comment: 9 pages, 6 figures

A method of tuning a reconfigurable silicon photonic circuit into an arbitrary unitary operator with machine learning was proposed to bypass the traditional phase-voltage calibration process and make the prediction of applied heating voltage directly. Published version

We find that next-nearest-neighbour coupling in ring resonator lattices induces topological transitions and one-way edge modes. We design topological waveguides that are easily switchble using thermal, electro-optic, or nonlinear effects, enabling robust on-chip photon routing.

A continuous-variable quantum key distribution system based on silicon photonic chip is designed and tested. A proof-of-principle test shows the secure key-rate can reach 1.92 Mbit/s at 0 km and 37 kbit/s at 45 km distance.

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 .

Absorption of electromagnetic energy by a material is a phenomenon that underlies many applied problems, including molecular sensing, photocurrent generation and photodetection. Commonly, the incident energy is delivered to the system through a single channel, for example by a plane wave incident on one side of an absorber. However, absorption can be made much more efficient by exploiting wave interference. A coherent perfect absorber is a system in which complete absorption of electromagnetic radiation is achieved by controlling the interference of multiple incident waves. Here, we review recent advances in the design and applications of such devices. We present the theoretical principles underlying the phenomenon of coherent perfect absorption and give an overview of the photonic structures in which it can be realized, including planar and guided-mode structures, graphene-based systems, parity- and time-symmetric structures, 3D structures and quantum-mechanical systems. We then discuss possible applications of coherent perfect absorption in nanophotonics and, finally, we survey the perspectives for the future of this field.

In the nonlinear optics regime, photonic devices that have topologically nontrivial photonic bandstructures are predicted to support a novel class of "topological solitons", which inherit exotic features of linear topological edge states such as unidirectional edge propagation. We present a detailed theoretical study of the conditions under which topological solitons can arise, and how they can be used to implement nonlinear optical isolators. Such isolators can achieve large isolation ratios, while being robust to lattice defects. Our results are based on theoretical analysis backed by numerical simulations of coupled-waveguide lattice and ring resonator lattice structures.

Computer simulation of electromagnetic fields in devices with slab geometries is a notoriously difficult problem, which becomes more challenging when there is no simple periodicity along the in-plane direction (e.g., random slab lasers). We present a method, called “FLAME-FFT”, to efficiently solve the scattering problem for slabs containing identical but non-periodically-placed scattering elements. It is based on precomputing solutions for periodic local lattices, and using Trefftz approximations to convert the solutions into stencil coefficients. Radiation boundary conditions at the upper and lower layers are implemented with Fast Fourier Transforms.

The development of nanoplasmonic devices, such as plasmonic circuits and metamaterial superlenses in the visible to ultraviolet frequency range, is hampered by the lack of low-loss plasmonic media. Recently, strong plasmonic response was reported in a certain class of topological insulators. Here, we present a first-principles density functional theory analysis of the dielectric functions of topologically insulating quaternary (Bi,Sb)2(Te,Se)3 trichalcogenide compounds. Bulk plasmonic properties, dominated by interband transitions, are observed from 2 to 3 eV and extend to higher frequencies. Moreover, trichalcogenide compounds are better plasmonic media than gold and silver at blue and UV wavelengths. By analyzing thin slabs, we also show that these materials exhibit topologically protected surface states, which are capable of supporting propagating plasmon polariton modes over an extremely broad spectral range, from the visible to the mid-infrared and beyond, owing to a combination of inter- and intra-surface band transitions. MOE (Min. of Education, S’pore) Published version

We study non-Hermitian photonic lattices that exhibit competition between conservative and non-Hermitian (gain/loss) couplings. A bipartite sublattice symmetry enforces the existence of non-Hermitian flat bands, which are typically embedded in an auxiliary dispersive band and give rise to non-diffracting "compact localized states". Band crossings take the form of non-Hermitian degeneracies known as exceptional points. Excitations of the lattice can produce either diffracting or amplifying behaviors. If the non-Hermitian coupling is fine-tuned to generate an effective $\pi$ flux, the lattice spectrum becomes completely flat, a non-Hermitian analogue of Aharonov-Bohm caging in which the magnetic field is replaced by balanced gain and loss. When the effective flux is zero, the non-Hermitian band crossing points give rise to asymmetric diffraction and anomalous linear amplification., Comment: Revised manuscript. 8 pages, 5 figures

We show for the first time that, contrary to common expectations, transition to superconductivity affects plasmonic behaviour of niobium at optical frequencies. This result is unexpected as photon energy is orders of magnitude higher than the binding energy of the Cooper pairs, the superconducting charge carriers.

It is shown that the concept of topological phase transitions can be used to design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger (SSH) model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio., 11 pages, 7 figures

Multimode terahertz (THz) laser emission around 3.2 THz in one-dimensional (1-D) disordered systems with 20% disorder. Simulation and experimental work provide evidence for spatial localization of light of defect modes within the bandgap frequency window.

We propose a practical design to implement of a topological insulator laser. Due to the topological protection, the topological laser maintains a high slope efficiency and single mode lasing even in the presence of defects and disorder.

Recently discovered valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional gapped valleytronic materials such as bilayer graphene or MoS2. Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states at the internal domain wall between two VPCs with spectrally overlapping bandgap zones and opposite half-integer valley-Chern indices. We experimentally demonstrate the robustness of the kink states in VPCs that support degenerate transverse-electric-like (TE) and transverse-magnetic-like (TM) topological phases, thus enabling polarization multiplexing in a single topological waveguide. The propagation direction of the kink states is locked to the valleys of the reverse Brave lattice and, therefore, cannot be reversed in the absence of inter-valley scattering. At the intersection between the internal domain wall and the external edge separating the VPCs from free space, the kink states are shown to exhibit >97% out-coupling efficiency into directional free-space beams. This constitutes the first experimental demonstration of meron-like valley-projected topological phases with half-integer valley-Chern indices., 19 pages, 4 figures

We demonstrate two-qubits controlled unitary quantum gates in a single silicon photonic chip. It can greatly reduce the size and complexity of the functional quantum circuits without decomposition it into plenty of elementary logic gates.

We numerically study amorphous analogues of a two-dimensional photonic Chern insulator. The amorphous lattices consist of gyromagnetic rods that break time-reversal symmetry, with the lattice sites generated by a close-packing algorithm. The level of short-range order is adjustable, and there is no long-range order. The topologically nontrivial gaps of the photonic Chern insulator are found to persist into the amorphous regime, so long as there is sufficient short-range order. Strongly nonreciprocal robust transmission occurs via edge states, which are shown to propagate ballistically despite the absence of long-range order, and to be exponentially localized along the lattice edge. Interestingly, there is an enhancement of nonreciprocal transmission even at very low levels of short-range order, where there are no discernable spectral gaps., Comment: 6 pages, 4 figures

We uncover two anomalous features in the nonlocal transport behavior of two-dimensional metallic materials with spin-orbit coupling. Firstly, the nonlocal resistance can have negative values and oscillate with distance, even in the absence of a magnetic field. Secondly, the oscillations of the nonlocal resistance under an applied in-plane magnetic field (Hanle effect) can be asymmetric under field reversal. Both features are produced by direct magnetoelectric coupling, which is possible in materials with broken inversion symmetry but was not included in previous spin diffusion theories of nonlocal transport. These effects can be used to identify the relative contributions of different spin-charge conversion mechanisms. They should be observable in adatom-functionalized graphene, and may provide the reason for discrepancies in recent nonlocal transport experiments on graphene., Comment: 5 pages, 3 figures, and Supplementary Materials, to appear in Phys. Rev. Lett

We investigate the effects of non-Hermiticity on topological pumping, and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear. We show that this can be understood in terms of the effects of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally, in a non-Hermitian microwave network containing variable gain amplifiers., 7 pages, 7 figures. The first author did the experiment, and the second author did the theoretical study

An AlN photonic chip for quantum wavelength convention and modulation is designed and fabricated. The waveguide has low loss down to 1.2 dB/cm. Fast switching using Pockels effect and second harmonic generation is achieved.

An integrated photonic chip for continuous-variable quantum key distribution is designed and fabricated. The modulation speed reaches 0.4 GHz. High extinction ratio up to 40 dBm for polarization multiplexing components is achieved.

We present the experimental observation of type-II optical Weyl points and corresponding Fermi arcs in a three-dimensional photonic structure. We employ a system composed of an array of staggered helical waveguides fabricated using the direct laser writing technique. Weyl points are established by observing conical diffraction and Fermi arcs are demonstrated by showing surface confinement (and deconfinement) at wavelengths above (below) the Weyl point.

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble., Comment: Various typos were corrected. Minor inconsistencies throughout the manuscript were fixed. In Section II B. Additional description regarding choice of Trefftz cell, was added. In Section III A. Detailed description about units (used in our calculation) was added

We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs., 7 pages, 2 figures

A 2D quantum walk on an integrated quantum photonic circuit is demonstrated by using a multilayer low-loss Si 3 N 4 waveguide lattice, which has promising applications in quantum computing and quantum communication, etc.

We present, in theory and experiments, the first Topological Insulator Lasers: lasers where the cavity acts as a “superconductor for light”, maintaining slope high efficiency even in the presence of defects and disorder.

Ultrashort electron bunches are useful for applications like ultrafast imaging and coherent radiation production. Currently, however, the shortest achievable bunches, at attosecond time scales, have only been realized in the single or very few electron regime, limited by Coulomb repulsion and electron energy spread. Using ab initio simulations and theoretical analysis, we show that highly-charged bunches are achievable by subjecting relativistic (few MeV-scale) electrons to a superposition of terahertz and optical pulses. Using realistic electron bunches and laser pulse parameters which are within the reach of current compact setups, we provide two detailed examples: one with final bunches of ~1 fC contained within sub-400 as durations, and one with bunches of >25 electrons contained within 20 as durations. Our results reveal a route to achieve such extreme combinations of high charge and attosecond pulse durations with existing technology., 14 pages, 3 figures

Unpaired Dirac cones are bandstructures with two bands crossing at a single point in the Brillouin zone. It is known that photonic bandstructures can exhibit pairs of Dirac cones, similar to graphene; unpaired cones, however, have not observed in photonics, and have been observed in condensed-matter systems only among topological insulator surface states. We show that unpaired Dirac cones occur in a 2D photonic lattice that is not the surface of a 3D system. These modes have unusual properties, including conical diffraction and antilocalization immune to short-range disorder, due to the absence of "intervalley" scattering between Dirac cones.

Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called 'Weyl points,' carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the first experimental observation of Weyl points of light at optical frequencies. These are also the first observations of 'type-II' Weyl points for photons, which have strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by (1) observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and (2) observing the associated Fermi arc surface states. The realization of Weyl points at optical frequencies allow these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics.

Topologically nontrivial photonic lattices can reveal topological effects inaccessible in condensed matter systems, and have promising applications including unidirectional light propagation robust against disorder [1]. The first design scalable to optical frequencies employed the Floquet photonic topological insulator concept, in which a time periodic Floquet Hamiltonian was emulated by a helical waveguide array [2]. While unidirectional edge modes were observed, other interesting effects associated with Floquet topological phases were inaccessible due to the lack of tunable phase transitions and high bending losses in this design.

Spintronics---the all-electrical control of the electron spin for quantum or classical information storage and processing---is one of the most promising applications of the two-dimensional material graphene. Although pristine graphene has negligible spin-orbit coupling (SOC), both theory and experiment suggest that SOC in graphene can be substantially enhanced by extrinsic means, such as functionalization by adatom impurities. We present a theory of transport in graphene that accounts for the full spin-coherent dynamics of the carriers, including hitherto-neglected spin precession processes during resonant scattering with dilute impurities. We identify a novel "anisotropic spin precession scattering" process, specific to two dimensions and extrinsic SOC, which contributes to a large current-induced spin polarization in graphene. The theory also yields a comprehensive description of the spin relaxation mechanisms in impurity-decorated graphene: the Elliot-Yafet and Dyakonov-Perel relaxation rates are both present, and we find that the latter can dominate for some choices of carrier density and impurity strength. This provides theoretical foundations for designing future graphene-based integrated spintronic devices., 22 pages, 4 figures

We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet bandstructure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the bandstructure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anderson localization. Unlike previous designs, the effective gauge field strength can be controlled via lattice parameters such as the inter-helix distance, significantly reducing radiative losses and enabling applications such as switchable topological wave-guiding., Revised manuscript. 6+7 pages, 5+5 figures. To appear in Phys. Rev. Lett

International audience; We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.

We show theoretically that a photonic topological insulator can support edge solitons that are strongly self-localized and propagate unidirectionally along the lattice edge. The photonic topological insulator consists of a Floquet lattice of coupled helical waveguides, in a medium with local Kerr nonlinearity. The soliton behavior is strongly affected by the topological phase of the linear lattice. The topologically nontrivial phase gives a continuous family of solitons, while the topologically trivial phase gives an embedded soliton that occurs at a single power, and arises from a self-induced local nonlinear shift in the inter-site coupling. The solitons can be used for nonlinear switching and logical operations, functionalities that have not yet been explored in topological photonics. We demonstrate using solitons to perform selective filtering via propagation through a narrow channel, and using soliton collisions for optical switching., 6+7 pages, 4+7 figures. To appear in Phys. Rev. Lett

Multi-mode random terahertz lasing with strongly localized modes has been realized for the first time, by fabricating two dimensional randomly distributed quantum cascade pillars with a small short-range order.