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Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light provide novel opportunities for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as magnet-free nonreciprocity and active tunability. Here, we introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics. This includes the design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, frequency conversion, active photonic structures exhibiting lasing from topologically protected modes, and many-body quantum topological phases of light. We also chart future research directions discussing device applications such as mode stabilization in lasers, parametric amplifiers protected against feedback, and ultrafast optical switches employing topological waveguides.

We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the interaction of optical absorption and wave interference and corresponds to moving a zero of the elastic S matrix onto the real wave vector axis. It is thus the time-reversed process of lasing at threshold. The effect is demonstrated in a simple Si slab geometry illuminated in the 500-900 nm range. Coherent perfect absorbers act as linear, absorptive interferometers, which may be useful as detectors, transducers, and switches.

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Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on onedimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to experimentally implement a four-dimensional (4D) topological lattice. The lattice dimensionality is established by circuit connections, and not by mapping to a lower-dimensional system. On the lattice’s three-dimensional surface, we observe topological surface states that are associated with a nonzero second Chern number but vanishing first Chern numbers. The 4D lattice belongs to symmetry class AI, which refers to time-reversal-invariant and spinless systems with no special spatial symmetry. Class AI is topologically trivial in one to three spatial dimensions, so 4D is the lowest possible dimension for achieving a topological insulator in this class. This work paves the way to the use of electric circuits for exploring high-dimensional topological models.

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 interand intra-surface band transitions. NPG Asia Materials (2017) 9, e425; doi:10.1038/am.2017.149; published online 25 August 2017 INTRODUCTIONThe fields of metamaterials and plasmonics have seen an extraordinary evolution in recent years, from the initial theoretical predictions of artificial negative refractive indices and cloaking 1,2 to the experimental realization of photonic metadevices with various functionalities that can be engineered and obtained on demand. 3,4 However, the practical implementations of plasmonic and metamaterial devices have long been hampered by energy dissipation in plasmonic media, especially in the visible to ultraviolet (UV) range, where even the best plasmonic metals (such as gold, silver and aluminum) suffer from strong dissipation due to interband electronic transitions and Drude losses. 5 This has inspired a search for alternative low-loss plasmonic materials for optical devices operating at high frequencies. 6,7 Candidates that are currently being investigated include highly doped semiconductors, metallic alloys, nitrides and oxides 8 and, more recently, twodimensional materials and topological insulator (TI) materials.TIs represent a new quantum phase of matter, which originates from the topological character of the bulk electronic bands in certain materials. The strong spin-orbit coupling in such materials leads to a band inversion and the appearance of Dirac surface states in the band gap. These topological surface states are chiral and protected from back-scattering by time-reversal symmetry. As a consequence, charge carriers from topologically protected surface states can carry current and are free to move parallel to the surface. Thus, TIs are ideal candidates to realize exotic plasmonic phenomena. Localized plasmons have recently been observed in TIs at THz frequencies (in Bi 2 Se 3 ) 9,10 as well as visible-to-UV frequencies (in single crystal

We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the type solved by the SALT algorithm. This mapping yields excellent agreement with more computationally demanding N-level time domain solutions for the steady state.