Experimental demonstration of spatiotemporal analog computation in ultrafast optics.

It is intractable to perform information processing and computation on single ultrafast optical pulses, within picoseconds or even femtoseconds. Here, we experimentally demonstrate an optical spatiotemporal differentiator, a mirror-symmetry-breaking dielectric metagrating, which performs analog computations of both spatial and temporal differentiations on single ultrafast optical wavepackets. The spatiotemporal differentiator is designed with a transfer function with linear dependence on spatial wavevector and temporal frequency and fabricated by using a double-exposure E-beam lithography process. We achieve the first-order spatiotemporal differentiation with experimental resolutions of approximately 14 μm (in space) and 260 fs (in time). Furthermore, we report a parabolic relationship between the transverse velocity of a front-tilted photonic wavepacket and the normalized intensity of its first-order spatiotemporal-differentiation wavepacket. This relationship allows direct measurement of the transverse velocity using only the normalized intensity, fundamentally simplifying velocity detection. These capabilities of optical spatiotemporal computation endow emerging space-time optics with fundamental computation blocks.