A hallmark feature of topological insulators is robust edge transport that is impervious to scattering at defects and lattice disorder. We demonstrate a topological system, using a photonic platform, in which the existence of the topological phase is brought about by optical nonlinearity. The lattice structure remains topologically trivial in the linear regime, but as the optical power is increased above a certain power threshold, the system is driven into the topologically nontrivial regime. This transition is marked by the transient emergence of a protected unidirectional transport channel along the edge of the structure. Our work studies topological properties of matter in the nonlinear regime, providing a possible route for the development of compact devices that harness topological features in an on-demand fashion.

We predict that the interplay between the spin-orbit coupling, stemming from the transverse electric--transverse magnetic energy splitting, and the Zeeman effect in semiconductor microcavities supporting exciton-polariton quasiparticles, results in the appearance of unidirectional linear topological edge states when the top microcavity mirror is patterned to form a truncated dislocated Lieb lattice of cylindrical pillars. Periodic nonlinear edge states are found to emerge from the linear ones. They are strongly localized across the interface and they are remarkably robust in comparison to their counterparts in honeycomb lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move steadily along the lattice edge.

Waveguiding structures made of anisotropic media support bound states in the continuum (BICs) that arise when the radiation channel of otherwise semileaky modes is suppressed. Hitherto, only structures with optical axes aligned in symmetric orientations inside the waveguide plane, where BICs appear as lines in the momentum-frequency dispersion diagram, have been considered. Here we address settings where such symmetry is broken and unveil a number of fundamental different features. Weak and strong symmetry-breaking regimes are identified, corresponding to azimuthal and polar optical axes orientation asymmetries, respectively. The azimuthal symmetry breaking is found to still preserve the existence loci of BICs in the momentum-frequency dispersion diagram as lines. However, all possible BICs become interferometric, while the polarization separable states that occur in symmetric settings cease to exist. The polar symmetry breaking has stronger effects and transforms the BICs' existence loci from lines to points, which correspond to full-vector states that exist at discrete values of the optical axis orientation for a given wavelength. Such transformation results in fundamental changes in the topological properties of the radiated field around the BICs.

We address the inhibition of tunnelling in polariton condensates confined in a potential landscape created by a honeycomb array of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. The coupling rate between the microcavity pillars can be strongly impacted even by weak out-of-phase temporal modulations of the depths of the corresponding potential wells. When such a modulation is implemented in truncated honeycomb arrays that realize a polariton topological insulator, which supports unidirectional edge states in the presence of spin-orbit coupling and Zeeman splitting, it allows controlling the velocity of the states. The origin of the phenomenon is the dynamical modulation with a proper frequency, which notably changes the dispersion of the system and the group velocity of edge states. We show that such a control is possible for modulation frequencies close to resonances for inhibition of tunnelling in a two-well configuration. Edge states considerably slow down, and even stop completely, when the modulation frequency approaches a resonant value, while above such frequency splitting of the edge states into wavepackets moving with different velocities occurs.

Topological insulators are unique devices supporting unidirectional edge states at their interfaces. Due to topological protection, such edge states persist in the presence of disorder and do not experience backscattering upon interaction with defects. Despite the topological protection and the fact that such states at the opposite edges of an insulator carry opposite currents, a physical mechanism exists allowing topological excitations propagating at opposite edges to be resonantly coupled. Such a mechanism uses weak periodic temporal modulations of the system parameters and does not affect the internal symmetry and topology of the system. This mechanism is illustrated in truncated honeycomb arrays of microcavity pillars, where topological insulation is possible for polaritons under the combined action of spin–orbit coupling and Zeeman splitting in the external magnetic field. The temporal modulation of the potential leads to a periodic switching between topological states with the same Bloch momentum, but located at the opposite edges. The switching rate is found to increase for narrower ribbon structures and for larger modulation depth, though it is changing nonmonotonically with the Bloch momentum of the input edge state. These results provide a promising realization of a coupling device based on topologically protected states.

This viewpoint relates to an article by B A Malomed, D Mihalache, F Wise, and L Torner (2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53–R72) and was published as part of a series of viewpoints celebrating 50 of the most influential papers published in the Journal of Physics series, which is celebrating its 50th anniversary.

We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient diffraction control available in such nonconservative structures. The dynamics of light in such lattices crucially depends on the ratio of the switching length for the straight segments of each coupler and the longitudinal lattice period. Depending on the longitudinal period, one can achieve either beam rectification when the input light propagates at a fixed angle across the structure without diffractive broadening or dynamic localization when the initial intensity distribution is periodically restored after each longitudinal period. Importantly, the transition between these two different propagation regimes can be achieved by tuning only gain and losses acting in the system, provided that the PT symmetry remains unbroken. The impact of Kerr nonlinearity is also discussed.

We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.

The rectification of light beams in an optical ratchet is reported. This directed transport is implemented using a photonic mesh lattice consisting of sequences of directional couplers. In such a structure, we observe light propagation at an angle that is independent of the input direction of the injected beam.

We address stationary patterns in exciton-polariton condensates supported by a narrow external pump beam, and we discover that even in the absence of trapping potentials, such condensates may support stable localized stationary dissipative solutions (quasicompactons), whose field decays faster than exponentially or even vanishes everywhere outside the pump spot. More general conditions lead to dissipative solitons which may display bistability. The bistability in exciton-polariton condensates, which manifests itself in the simultaneous existence of two stable and one unstable localized solitons with different amplitudes, widths, and exciton-photon fractions under the same physical conditions, strongly depends on the width of the pump beam and is found to disappear for sufficiently narrow pump beams.

We report two-dimensional Anderson localization in waveguide arrays with effectively one-dimensional disorder. Although the disorder is highly anisotropic it induces strong localization along both array axes, in which the waveguide spacing is regular or disordered.

Three dimensional Light Bullets (3D-LBs) are the most symmetric solitary waves, being nonlinear optical wavepackets propagating without diffraction nor dispersion. Since their theoretical prediction, 3D-LB's have constituted a challenge in nonlinear science, due to the impossibility to avoid catastrophic collapse in conventional homogeneous nonlinear media. We have recently observed stable 3D-LBs in media with periodically modulated transverse refractive index profile. We found that higher order linear and nonlinear effects force the 3D-LBs to evolve along their propagation path and eventually decay. The evolution and decay mechanism entails spatiotemporal effects, which under certain conditions, leads to superluminally propagating wavepackets.

We experimentally and numerically investigate the propagation of light bullets (LBs) excited in two-dimensional fiber arrays. The combination of nonlinear self-frequency shift, wavelength dependence of the dispersion, and the interwaveguide coupling strength induce an adiabatic variation of the parameters of the LBs along their propagation paths, until they reach the limits of the regime of existence and decay. The relative strength of the various perturbative effects can partially be controlled by the array's geometry. The characterization of the LB dynamics is carried out by implementing a spatiotemporal, cross-correlating, and spectrally resolved imaging system with femtosecond resolution. The experimental results are in good agreement with the numerical data if higher-order nonlinear effects and the wavelength dependence of the dispersion and coupling are included. The observed wave packets are linked to the stationary solutions of the simplified nonlinear Schrodinger equation. Furthermore, the maximum possible range of existence of LBs in arrays of waveguides is discussed.

We investigate femtosecond spatiotemporal dynamics in waveguide arrays. Experiments use an ultrafast cross-correlator tracing the Light Bullet evolution. Simulations with higher-order effects underline the solitary nature of the observed wavepackets.

We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in two-dimensional geometries, in spite of their intrinsic catastrophic instability in the absence of the lattice. Solitons centered on saturable domains are always unstable.

We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable of trapping solitons launched close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with an increasing of the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.

We address the existence and properties of multipole solitons localized at a thermally insulating interface between uniform or layered thermal media and a linear dielectric. We find that in the case of uniform media, only surface multipoles with less than three poles can be stable. In contrast, we reveal that periodic alternation of the thermo-optic coefficient in layered thermal media makes possible the stabilization of higher-order multipoles.

We investigate the dynamics of spatio-temporal nonlinear localization in arrays of evanescently coupled silica fiber arrays. In contrast to continuous systems the formation of stable light bullets becomes possible.