Polychromatic dynamic localization in curved photonic lattices

Dynamic localization is the suppression of the broadening of a charged-particle wave packet as it moves along a periodic potential in an a.c. electric field1–3. The same effect occurs for optical beams in curved photonic lattices, where the lattice bending has the role of the driving field, and leads to the cancellation of diffraction4–8. Dynamic localization was also observed for Bose–Einstein condensates9, and could have a role in the spin dynamics of molecular magnets10. It has been predicated that dynamic localization will occur in multidimensional lattices at a series of resonances between lattice, particle and driving-field parameters1. However, only the first dynamic localization resonance in one-dimensional lattices has been observed in any physical system6–9. Here, we report on the experimental observation of higher-order and mixed dynamic localization resonances in both oneand two-dimensional photonic lattices. New features such as spectral broadening of the dynamic localization resonances and localization-induced transformation of the lattice symmetry are demonstrated. These phenomena could be used to shape polychromatic beams emitted by supercontinuum light sources11,12. In optics, the effect of an external electric field on the motion of charged particles in periodic potentials can be mimicked by the propagation of a laser beam in an array of curved waveguides13. A schematic diagram of a one-dimensional waveguide array is shown in Fig. 1a. In such a structure, light propagation is governed by coupling between the modes of neighbouring waveguides, similar to wave dynamics in discrete lattices14. Constant waveguide curvature corresponds to a d.c. field, and in this case the beam experiences Bloch oscillations13, which have also been observed in straight optical latticeswith transverselymodulated parameters15–18. Dynamic localization due to a.c. fields can then be observed in arrays of periodically curved optical waveguides with alternating curvature5,6,8. A zigzag bending leads to similar behaviour4, and arrays with optimized discontinuous waveguide curvature also enable us to compensate for the long-range coupling between the non-nearest waveguide modes7. In straight waveguide arrays, optical beams experience broadening due to discrete diffraction14, whereas in the regime of Bloch oscillations or dynamic localization a periodic reconstruction of the initial light distribution occurs. Whereas the effective d.c. driving field always leads to Bloch oscillations with a period proportional to the inverse driving amplitude, dynamic localization is a resonant effect that occurs only for certain relations between the a.c. field profiles and the wave-particle parameters. By adjusting the detuning from the dynamic localization resonance, it becomes possible to control the rate of wave transport. For light propagating in curved waveguide arrays, the detuning depends on the wavelength, and application