Singular optics empowered by engineered optical materials

The rapid development of optical technologies, such as optical manipulation, data processing, sensing, microscopy, and communications, necessitates new degrees of freedom to sculpt optical beams in space and time beyond conventionally used spatially homogenous amplitude, phase, and polarization. Structuring light in space and time has been indeed shown to open new opportunities for both applied and fundamental science of light. Rapid progress in nanophotonics has opened up new ways of "engineering" ultra-compact, versatile optical nanostructures, such as optical two-dimensional metasurfaces or three-dimensional metamaterials that facilitate new ways of optical beam shaping and manipulation. Here, we review recent progress in the field of structured light-matter interactions with a focus on all-dielectric nanostructures. First, we introduce the concept of singular optics and then discuss several other families of spatially and temporally structured light beams. Next, we summarize recent progress in the design and optimization of photonic platforms, and then we outline some new phenomena enabled by the synergy of structured light and structured materials. Finally, we outline promising directions for applications of structured light beams and their interactions with engineered nanostructures.