Jason W. Fleischer

Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices

Nonlinear periodic lattices occur in a large variety of systems, such as biological molecules, nonlinear optical waveguides, solid-state systems and Bose–Einstein condensates. The underlying dynamics in these systems is dominated by the interplay between tunnelling between adjacent potential wells and nonlinearity. A balance between these two effects can result in a self-localized state: a lattice or ‘discrete’ soliton. Direct observation of lattice solitons has so far been limited to one-dimensional systems, namely in arrays of nonlinear optical waveguides. However, many fundamental features are expected to occur in higher dimensions, such as vortex lattice solitons, bright lattice solitons that carry angular momentum, and three-dimensional collisions between lattice solitons. Here, we report the experimental observation of two-dimensional (2D) lattice solitons. We use optical induction, the interference of two or more plane waves in a photosensitive material, to create a 2D photonic lattice in which the solitons form. Our results pave the way for the realization of a variety of nonlinear localization phenomena in photonic lattices and crystals. Finally, our observation directly relates to the proposed lattice solitons in Bose–Einstein condensates, which can be observed in optically induced periodic potentials.

Dispersive superfluid-like shock waves in nonlinear optics

We experimentally demonstrate dispersive optical shock waves in ID and 21), characterize their nonlinear properties, and observe the complex interactions when two such shocks collide.

Wave and defect dynamics in nonlinear photonic quasicrystals

Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery and initial theoretical analysis. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Blochs theorem. New and unique features such as fractal-like band structures and ‘phason’ degrees of freedom are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps, generic pattern-forming systems as in parametrically excited surface waves, liquid quasicrystals, and the more familiar atomic quasicrystals.

Spatial photonics in nonlinear waveguide arrays

The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.

Brillouin-zone spectroscopy of nonlinear photonic lattices

We present a novel experimental technique for Brillouin-zone spectroscopy of photonic lattices with and without defects. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion.

Observation of vortex-ring “discrete” solitons in 2D photonic lattices

We present the experimental observation of both on-site and off-site vortex ring solitons of unity topological charge in a nonlinear photonic lattice, along with a theoretical study of their propagation dynamics and stability

Observation of random-phase lattice solitons

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or ‘discrete’) solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.

Dispersive shock waves with nonlocal nonlinearity

We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.

Information transfer via cascaded collisions of vector solitons

We demonstrate experimentally the transport of information from one vector (Manakov-like) spatial soliton to another via collisions with a third, intermediate soliton.

Observation of All-Optical Bump-on-Tail Instability

We demonstrate an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially coherent spatial beams. For weak wave coupling, we observe momentum transfer with no variation in intensity. For strong wave coupling, modulations appear in intensity and evidence appears for wave (Langmuir) collapse at large scales. Borrowing plasma language, these limits represent regimes of weak and strong spatial optical turbulence. In both limits, the internal spectral energy redistribution is observed by recording and reconstructing a hologram of the evolving dynamics. The results are universal and can appear in any wave-kinetic system with short-wave-long-wave coupling.