Fig. 1. System schematic, side, and top views. Set of wave guides evenly spaced in the x direction but randomly spaced along the y axis. Wave guides take periodic trajectories in space and have periodic thickness modulations. Shape is exaggerated for illustration.

Fig. 2. Reversing Anderson localization: light propagation. Wave propagation in nearest-neighbor coupled wave guides described by Eq. (7), with four choices of driving fields. (A) An undriven, disordered lattice with random nearest-neighbor couplings. The beam width remains limited, as expected for Anderson localization. (B) The same lattice, driven by a uniform amplitude AC electric field with an amplitude designed to induce DL for ω=6; that is, for an ϵi which depends linearly on the site index, such that we would expect DL if not for disorder. (C) The same lattice, driven by an appropriately tailored time-periodic spatially nonuniform field. The nature of the driving field was determined to make the lattice behave as an effectively disorder-free lattice with uniform couplings, using numerical optimization. The beam exhibits discrete diffraction, as expected. We note the wave expansion seen here is indeed extremely similar to the one exhibited in a uniform lattice (not shown here, as it is practically identical), up to the effect of higher order corrections after much longer propagation times. (D) The same lattice, driven with a random driving field. The wave packet exhibits diffusive behavior, which is inconsistent with the behavior of both Anderson localization and a regular wave guide array.

Fig. 3. Reversing Anderson localization: couplings. (Left panel) Black dots represent the couplings in the original undriven system in Eq. (6), with random γi∈[0.2, 1]. Red dots represent the couplings in the effective Hamiltonian in Eq. (8), which are produced when we drive the system as Eq. (2) with appropriate parameters (V,ϵ). (Right panel) To calculate the appropriate driving parameters, we impose V=0 and use numerical optimization to calculate ϵi, shown here as a black line. Figure 2 verifies that these choices of driving parameters have the expected effect on light propagation through the wave guide array. The significant linear component (scale on right vertical axis) is responsible for uniform changes in the coupling coefficient; this produces a time-dependent electric field, similar to that of DL. To better exhibit the tailored spatial dependence required to undo Anderson localization, we indicate the smaller nonlinear component of the driving field in red (scale on left vertical axis).

Fig. 4. Inducing DL. (Left panel) This undriven irregular wave guide array has a coupling that changes as a cosine of the index number, which leads to a complex diffraction of a single site excitation. (Right panel) Using a tailored spatially nonuniform driving, we obtain notable suppression of the wave function spreading. The driving profile is produced in the same method as before; the target Hamiltonian is completely decoupled.