Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community.

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Spatial coherence quantifies spatial field correlations over time, and is one of the fundamental properties of light. Here we investigate the spatial coherence of highly multimode lasers in the regime of short time scales. Counter intuitively, we show that in this regime, the temporal (longitudinal) modes play a crucial role in spatial coherence reduction. To evaluate the spatial coherence we measured the temporal dynamics of speckle fields generated by a highly multimode laser with over 10 5 lasing spatial (transverse) modes, and examined the dependence of speckle contrast on the exposure time of the detecting device. We show that in the regime of short time scale, the spatial and temporal modes interact to form spatio-temporal supermodes, such that the spatial degrees of freedom are encoded onto the temporal modes. As a result, the speckle contrast depends on the number of temporal modes, and the degree of spatial coherence is reduced and the speckle contrast is suppressed. In the regime of long times scale, the supermodes are no longer a valid representation of the laser modal structure. Consequently, the spatial coherence is independent of the temporal modes, and the classical result, where the speckle contrast is suppressed as the number of spatial modes, is obtained. Due to this new spatio-temporal mechanism, highly multimode lasers can be used for speckle suppression in high-speed full-field imaging applications, as we demonstrate here for imaging of a fast moving object.