Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally adopted in optical material modeling. The growing interest in plasmonic, polaritonic, and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials—metamaterials and metasurfaces—can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In metasurfaces, in particular, nonlocality engineering has emerged as a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials and metamaterials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward—toward new scientific discoveries and technological advancements.

Here, we show that space-time modulations provide an exciting route to realize complex nonreciprocal couplings, and, in particular, the elusive axion response. We develop an analytical formalism to homogenize anisotropic space-time crystals in the long wavelength limit. It is found that space-time crystals with suitable glide-rotation symmetry can have a giant axion-type response, several orders of magnitude larger than in natural materials. The nonreciprocal axion response may have interesting applications in optics, for example, in electromagnetic isolation, and in addition may enable exciting forms of light-wave interactions.

The optical isolation functionality is of key importance in many photonic systems. However, a robust optical isolation is rather challenging to obtain due to the weak nonreciprocal response of conventional materials. Here, we theoretically explore novel solutions to obtain one-way propagation of circularly polarized light using materials with a spontaneous nonreciprocal response combined with chiral metamaterials. Furthermore, we investigate the opportunity of using standard anisotropic nonreciprocal materials (e.g., ferrites or bismuth iron garnet) to obtain the optical isolation of circularly polarized light.

We study the propagation of electromagnetic waves in layered photonic crystals formed by materials with a spontaneous nonreciprocal response, such as Tellegen (axion) media or topological insulators. Surprisingly, it is proven that stratified Tellegen photonic crystals that break simultaneously the space inversion and time-reversal symmetries have always symmetric dispersion diagrams. Interestingly, we show that by combining chiral and nonreciprocal materials the photonic band diagrams can exhibit a spectral asymmetry such that $\omega \left(\mathbf{k}\right)\ne \omega \left(-\mathbf{k}\right)$. Furthermore, it is demonstrated that in some conditions two juxtaposed Tellegen medium layers have an electromagnetic response analogous to that of a biased ferrite slab.

Here, we show that isorefractive spacetime crystals with a travelling‐wave modulation may mimic rigorously the response of moving material systems. Unlike generic spacetime crystals, which are characterized by a bi‐anisotropic coupling in the co‐moving frame, isorefractive crystals exhibit an observer‐independent response, resulting in isotropic constitutive relations devoid of any bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss the impact of considering either a Galilean or a Lorentz transformation in the homogenization of spacetime crystals, showing that the effective response is independent of the considered transformation.

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with few modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break down and the Chern topology becomes ill defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be noninteger notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large $\mathbf{k}$.