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Fractals, shapes comprised of self-similar parts, are not merely prescribed linear structures. A wide class of fractals can also arise from the rich dynamics inherent to nonlinear optics.

Incoherent optical spatial solitons are self-trapped beams with a multimodal structure that varies randomly in time. All incoherent solitons observed so far have been supported by nonlinearities with slow response times. Here, Segev and colleagues demonstrate such solitons in nonlinear media with fast (essentially instantaneous) response times and show that new physical features appear.

An experimental realization of a photonic topological insulator is reported that consists of helical waveguides arranged in a honeycomb lattice; the helicity provides a symmetry-breaking effect, leading to optical states that are topologically protected against scattering by disorder.

Self-accelerating beams are attractive for light-matter interaction applications but their propagation has been limited by absorption. Here, Schley et al.demonstrate self-healing in shape-maintaining, accelerating beams where the central peak intensity is preserved despite losses and apply these beams to particle manipulation.

Branched flow of light is experimentally observed inside a thin soap membrane, where smooth variations of the membrane thickness transform the light beam into branched filaments of enhanced intensity that keep dividing as the waves propagate.

The propagation of light in photonic crystals with a honeycomb structure mirrors the behaviour of charges in graphene, therefore allowing for the investigation of electronic properties that cannot otherwise be accessed in graphene itself. This approach is now used to predict unexpected edge states that localize in the bearded edges of hexagonal lattices.

An increase in diffusion beyond the ballistic-transport regime is now demonstrated. This so-called hyper-transport is observed in an optical experiment, but it might also be evident in other systems with time-varying disorder.

Interacting optical wavepackets in the presence of a thermal optical nonlinearity are described by the same mathematics as the gravitational self-interaction of quantum wavepackets, providing a way of emulating gravitational phenomena in the lab.

Magnetic effects are fundamentally weak at optical frequencies. Now, by applying inhomogeneous strain in photonic band structures of a honeycomb lattice of waveguides, scientists show experimentally and theoretically that it is possible to induce a pseudomagnetic field at optical frequencies. The field yields 'photonic Landau levels', which suggests the possibility of achieving greater field enhancements and slow-light effects in aperiodic photonic crystal structures than those available in periodic structures.

Non-classical correlations between two photons in the near-field regime give rise to entanglement in their total angular momentum, leading to a completely different structure of quantum correlations of photon pairs.

Time-reflected waves are a critical feature of time-crystals, yet their properties are historically difficult to measure. Here, the authors experimentally demonstrate time-reflected electromagnetic waves including direct evidence of their phase conjugate nature.

Imaging through linear media is straightforward, but light beams propagating through nonlinear media become heavily distorted, rendering all usual imaging techniques practically useless. Now, scientists have found a way to recover images transmitted through nonlinear media — by using back-propagation simulations.

Confirmation of localization effects in a true Anderson lattice of a perturbed periodic potential is achieved by using a photonic lattice on which random fluctuations are imposed. Nonlinear, self-focussing effects are also observed.

A photonic equivalent of a quasicrystal is created in which wave and defect dynamics can be made visible — for example, it is shown that a dislocation introduced in the photonic quasicrystal is healed by re-arrangements of the lattice.

A photonic system that shows behaviour similar to that of a violation of parity–time symmetry provides a convenient test bed to explore this and related phenomena. It could also lead to a new class of optical materials with exotic properties that exploit non-reciprocal light flow.

Wavefront shaping is typically carried out outside the medium within which the beam is propagating. Sheng et al.exploit concepts inspired by General Relativity for wavefront shaping within optical waveguide settings, constructing narrow collimated beams and shape-preserving beams accelerating on arbitrary trajectories

Features much smaller than the wavelength are not expected to have a significant impact on the transport of a wave. Here, the authors show that Anderson localization can dominate light transport in a one-dimensional disordered system, even when the disordered features are a thousand times smaller than the wavelength.

In measurements that employ phase retrieval algorithms, such as coherent diffraction imaging, reconstruction of one-dimensional signals is challenging due to ambiguity issues. Here, the authors demonstrate super-resolution coherent imaging of one-dimensional objects by utilizing sparsity prior information.

X-ray laser holds promise for deciphering three-dimensional structures of organic molecules, which constitutes a major goal in structural biology. Mutzafi et al.propose an algorithm to overcome the issue of laser-induced sample damage based on prior knowledge of the atoms that comprise the molecules.

By introducing a further modal dimension to transform a two-dimensional photonic waveguide array, a photonic topological insulator with protected topological surface states in three dimensions, enabled by a screw dislocation, is demonstrated.

Optical guiding by a synthetic gauge field is experimentally demonstrated through an array of evanescently coupled identical waveguides, opening the door to applications of artificial gauge fields in optical, microwave and acoustic systems and in cold atoms.

By engineering the electron wavefunction it is possible to create Aharonov–Bohm-like phases and relativistic effects such as length contraction and time dilation in a non-relativistic setting and in the absence of electromagnetic fields.

Exploiting Einstein’s theory of general relativity, the curved space associated with specially designed nanophotonic structures is shown to be able to manipulate light propagation.

Yaron Silberberg of the Weizmann Institute in Israel passed away in April. Here, some of his former students and friends remind us of who Yaron was: a creative researcher and a mentor without ego with major achievements in nonlinear optics, microscopy and quantum physics.

Vortex electron beams are generated using single electrons but their low beam-density is a limitation in electron microscopy. Here the authors propose a scheme for the realization of non-diffracting electron beams by shaping wavepackets of multiple electrons and including electron–electron interactions.

We study second harmonic generation in photonic time-crystals, and find conditions for which the process is highly enhanced, leading to efficient generation of higher-order harmonics.

A spatially oscillating two-dimensional waveguide array is used to realize a photonic topological insulator in synthetic dimensions with modal-space edge states, unidirectionality and robust topological protection.

A counter-intuitive state—known as a topological Anderson insulator—in which strong disorder leads to the formation of topologically protected rather than trivial states is realized in a photonic system.

The Anderson localization of light within disordered media has become a topic of great interest in recent years. Here the characterization of the effect and its related phenomena are reviewed, with a discussion on the role that nonlinearity and quantum correlated photons can play.