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.

Quasicrystals are aperiodic structures with rotational symmetries forbidden to conventional periodic crystals; examples of quasicrystals can be found in aluminum alloys, polymers, and even ancient Islamic art. Here, we present direct experimental observation of disorder-enhanced wave transport in quasicrystals, which contrasts directly with the characteristic suppression of transport by disorder. Our experiments are carried out in photonic quasicrystals, where we find that increasing disorder leads to enhanced expansion of the beam propagating through the medium. By further increasing the disorder, we observe that the beam progresses through a regime of diffusive-like transport until it finally transitions to Anderson localization and the suppression of transport. We study this fundamental phenomenon and elucidate its origins by relating it to the basic properties of quasicrystalline media in the presence of disorder.

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.