Fig. 3: Simulated and experimental results of different-order DLs.

a Transverse displacement of wave packet ∆n after a single driving period versus phase modulation amplitude ∆ϕ. b Simulated pulse intensity evolutions in one driving period with total step M = 120. (i) and (ii) correspond to directional transports with ∆ϕ = 0 and 3.8, respectively. (iii) and (iv) correspond to the 1st- and 5th-order DLs, respectively. c Measured pulse intensity evolutions. (i)-(iv) correspond to the simulated results in b(i)-b(iv). d Mean-square displacement 〈n2(m)〉 with respect to step m for 1st- and 5th-order DLs. The inset figure shows the maximum mean-square displacement 〈n2(m)〉max versus the order of DL.