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.

Flatbands are receiving increasing theoretical and experimental attention in the field of photonics, in particular in the field of photonic lattices. Flatband photonic lattices consist of arrays of coupled waveguides or resonators where the peculiar lattice geometry results in at least one completely flat or dispersionless band in its photonic band structure. Although bearing a strong resemblance to structural slow light, this independent research direction is instead inspired by analogies with “frustrated” condensed matter systems. In this Perspective, we critically analyze the research carried out to date, discuss how this exotic physics may lead to novel photonic device applications, and chart promising future directions in theory and experiment.

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g. for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.

Flatband systems typically host “compact localized states” (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states. Such unconventional line states cannot be expressed as a linear combination of the previously observed boundary-independent bulk CLS but rather arise from the nontrivial real-space topology. The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as nonreciprocity and waveguiding protected against fabrication disorder. Moving forward, there is a pressing need to identify applications where topological designs can lead to useful improvements in device performance. Here, we review applications of topological photonics to ring resonator–based systems, including one‐ and two‐dimensional resonator arrays, and dynamically modulated resonators. We evaluate potential applications such as quantum light generation, disorder‐robust delay lines, and optical isolation, as well as future research directions and open problems that need to be addressed.