Fig. 1: PGB in the temporal synthetic dimension.
From: Tera-sample-per-second arbitrary waveform generation in a synthetic dimension
a Photonic Galton board (PGB). The pegs (gray rounded rectangles) of each row have a tunable coupling ratio (the number in the gray rounded rectangles, corresponding to the coupling ratio), thus they can be made to control the number of photons (beads, orange circles) going to the left or right. T1 and T2 are the time delays of the left and right paths, respectively. At the bottom of the PGB, the temporal distribution of the photons is formed, which is a temporally sampled arbitrary waveform whose shape and sampling interval are determined by the pegs with tunable coupling ratio and path length difference, respectively. b The PGB implemented by fiber optics. An ultra-short optical pulse containing multiple photons from a mode-locked laser (MLL) is inputted into the long loop (blue line) through an optical coupler (OC1). The long loop and the short one (red line) are mutually coupled by a beam splitter (BS). Each loop contains an acousto-optic modulator (AOM1 or AOM2) for controlling the gain and loss of the optical pulses recirculating in the loops. After the seed pulse recirculates in the two loops for more round trips, a sequence of pulses is generated from each loop. By detecting and combining the optical pulse sequences at a detection unit (DU), a temporally sampled arbitrary waveform is generated. c Establishment of the temporal synthetic dimension. The blue and red arrowed lines indicate the pulses traveling in the long and short loops, respectively. The BS is depicted as a gray rectangle and the AOMs in the long and short loop are depicted as orange and green circles, respectively. The n-th pulse in the m-th round trip with an electric field um,n in the long loop and vm,n in the short loop is coupled to its nearest neighbor sites u(v)m+1,n+1 and v(u)m+1,n in the next round trip, respectively. As the pulses recirculate and couple in the two loops, a synthetic temporal dimension, pulse position n, is synthesized. PD photodetector, OSC oscilloscope, ACO optical autocorrelator.
