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The removal of photons from certain quantum light sources produces so-called photon-subtracted states with enhanced mean photon numbers and intricate quantum correlations. Here, we propose an integrated photon-subtraction scheme that, contrary to previous approaches, is not heralded by photon correlation (coincidence) measurements. In this way, our technique exploits the “Welcher Weg” (“which way”) information problem, as it does not provide information about the modes from which the subtracted photons emanated. We show that this lack of information allows the generation of multiphoton states endowed with rich quantum correlations that strongly depend on the parity, evenness or oddness, of the number of subtracted photons. 

Abstract Optical resonators are structures that utilize wave interference and feedback to confine light in all three dimensions. Depending on the feedback mechanism, resonators can support either standing- or traveling-wave modes. Over the years, the distinction between these two different types of modes has become so prevalent that nowadays it is one of the main characteristics for classifying optical resonators. Here, we show that an intermediate link between these two rather different groups exists. In particular, we introduce a new class of photonic resonators that supports a hybrid optical mode, i.e. at one location along the resonator the electromagnetic fields associated with the mode feature a purely standing-wave pattern, while at a different location, the fields of the same mode represent a pure traveling wave. The proposed concept is general and can be implemented using chip-scale photonics as well as free-space optics. Moreover, it can be extended to other wave phenomena such as microwaves and acoustics. 

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.