Liad Levi

Super-diffusion in optical realizations of Anderson localization

We discuss the dynamics of particles in one dimension in potentials that are random in both space and time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is suppressed by random fluctuations in the refractive index. If the refractive index fluctuates along the direction of the paraxial propagation of the beam, the localization is destroyed. We analyze this broken localization in terms of the spectral decomposition of the potential. When the potential has a discrete spectrum, the spread is controlled by the overlap of Chirikov resonances in phase space. As the number of Fourier components is increased, the resonances merge into a continuum, which is described by a Fokker–Planck equation. We express the diffusion coefficient in terms of the spectral intensity of the potential. For a general class of potentials that are commonly used in optics, the solutions to the Fokker–Planck equation exhibit anomalous diffusion in phase space, implying that when Anderson localization is broken by temporal fluctuations of the potential, the result is transport at a rate similar to a ballistic one or even faster. For a class of potentials which arise in some existing realizations of Anderson localization, atypical behavior is found.

Spontaneous pattern formation upon incoherent waves: from modulation-instability to steady-state.

We study the long-range propagation of incoherent light following the modulation instability (MI) process in non-instantaneous nonlinear Kerr-type media. We find that the system eventually reaches a steady-state characterized by a lower degree of coherence than in the initial state, with small fluctuations around a pronounced mean value. We find that the average values of the spatial correlation distance at steady-state and the fluctuations around it, which are obtained either through ensemble averaging, or by spatial averaging, or via temporal averaging, are all identical. This feature may be viewed as indication of ergodic behavior, which occurs in the long-time evolution following incoherent MI. Finally, we find that the steady-state properties of the system depend on the initial coherence but not on the nonlinearity strength, although the system evolves faster to steady-state as the strength of the nonlinearity is increased.

Self-phase modulation spectral broadening in two-dimensional spatial solitons: toward three-dimensional spatiotemporal pulse-train solitons

We demonstrate self-phase modulation (SPM) spectral broadening in two-dimensional solitons in homogeneous media using two different schemes. In the active mode, a train of pulses are collectively trapped and form a spatial soliton through a photorefractive, slowly responding, and electronically controlled self-focusing nonlinearity, and each pulse experiences spectral broadening by the fast SPM nonlinearity. In the passive mode, the pulse-train beam is guided in a waveguide that is optically induced by a continuous-wave thermal spatial soliton. The soliton formation increased the normalized spectral broadening factor from 0.5% up to 197%. This experiment presents significant progress toward the experimental demonstration of three-dimensional spatiotemporal pulse-train solitons.

Disorder-Enhanced Transport in Photonic Quasicrystals

We have learned how to construct ordered index-of-refraction-modulated structures that allow us to control the propagation of light. Initially, researchers were simply interested in fabrication; now they are exploring limitations in the structures.

Disorder-enhanced transport in photonic quasi-crystals: Anderson localization and delocalization

We demonstrate experimentally that disorder enhances transport of waves in Penrose-type photonic quasicrystals. Increasing disorder gives rise to a transition from “bumpy ride” to diffusive transport.

Wave-particle duality during hyper-transport of light in dynamic disorder

We present an analytic spectral wave theory describing the propagation of wavepackets in dynamically-evolving disordered potentials, in the hyper-transport regime. The results are examined in the context of Bohrs correspondence principle.

Spontaneous pattern formation upon incoherent waves: From modulation-instability to dynamic equilibrium

We study long-range propagation of spatially-incoherent light in non-instantaneous nonlinearities, and show that the system eventually reaches dynamic equilibrium, which depends only on the initial coherence, and not on the strength of the nonlinearity.

Spontaneous Pattern Formation upon Random Phase Waves: From Modulation-Instability to Dynamic Equilibrium

We show that MI is the driving force bringing spatially-incoherent light to an equilibrium state, while propagating through non-instantaneous nonlinearities. The equilibrium state depends only on the initial coherence, and not on the nonlinearity strength.