# Experimental demonstration of spatiotemporal analog computation in ultrafast optics

## TL;DR

Researchers demonstrated a new optical device that can perform complex calculations on ultrafast light pulses, enabling faster and simpler measurements of light properties.

## Contribution

The first experimental realization of an optical spatiotemporal differentiator for analog computation on ultrafast optical pulses.

## Key findings

- The spatiotemporal differentiator achieves resolutions of 14 μm in space and 260 fs in time.
- A parabolic relationship between wavepacket velocity and differentiation intensity simplifies velocity detection.

## Abstract

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.