Optical nonlocal meta-grating computing spatiotemporal differentiation

Abstract Optical analog computation could accelerate massively parallel operation without costly analog-to-digital conversion and promise more energy efficiency than their electronic counterparts. Although many novel optical computation features in spatial domain have been discovered across nanophotonic structures, more appealing and challenging spatiotemporal computation is seldom reported to optically process single-shot spatiotemporal wavepacket and characterize space-time dynamics in various ultrafast phenomena, because direct analog computation with extremely short time of picoseconds or femtoseconds is currently beyond the capability of state-of-the-art electronic instruments. Here, we demonstrate optical spatiotemporal differentiation computation for single-shot ultrafast wavepacket through space-time coupling between spatial and temporal differentiations. Realized by a mirror-symmetry-breaking nonlocal meta-grating, our spatiotemporal differentiator possesses a transfer function with linear dependence on spatial wavevector and temporal frequency, leading to first-order differentiations differentiation with experimental resolutions of ~14 μm (space) and ~260 fs (time). Because both orthogonal differentiations are correlated with an out-of-phase delay, this differentiator can manipulate space-time-related physical quantities, e.g., creating spatiotemporal phase singularities with transverse orbital angular momentum of light and detecting extremely high transverse velocities (at the level of the speed of light) of shifting intensity centroids in tilted-font pulses, which endow emerging space-time optics with fundamental computation blocks.