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Nonlinear propagation of waves in periodic media has long been a focus of strong interest. The physics of this phenomenon is common for a variety of systems, including excitations in biological molecules, electrons in solid-state matter, ultracold atoms in optical standing waves, and light waves in nonlinear media with periodic modulation of the refractive index. Only in optics, however, the
effects associated with this phenomenon can be directly observed and examined in close details. A strong motivation for work in this area comes from the analogy between the behaviour of light in periodic photonic structures and electrons in
superconductors. This analogy suggests the possibility of replacing electronic
components with novel types of photonic devices where light propagation is fully controlled in engineered micro-structures. Nonlinearity adds a possibility to
control propagation of light purely optically, i.e. with light itself. Such
all-optical devices may form foundation of future high-bandwidth, ultrafast
communications and computing technologies.
In practice, development of new schemes for controlling light in periodic
structures is hindered by difficulties that arise in fabrication of materials
with both periodicity on the optical wavelength scale and strong nonlinearity
accessible at low laser powers. In a joint effort between the Nonlinear Physics
Centre and Laser Physics Centre, we circumvented these difficulties and
implemented a “quick and simple” way to produce reconfigurable periodic
structures with strong nonlinearity. We induce periodic modulation of the
refractive index in a highly nonlinear photorefractive crystal by using a
periodic interference pattern of several broad laser beams [Fig. 1] and
employing a natural ability of the crystal to respond to light by changing its
refractive index. The resulting periodic refractive index profile acts as a
regular array of optical waveguides for any probe beam entering the crystal.
Because this array is “written” by laser light, we call it an
optically-induced lattice. Our experimental set-up [Fig. 1] allows for
unprecedented flexibility and dynamical tunability of the optically-induced
photonic lattices. The modulation depth of the refractive index is controlled by
the external electric field applied to the crystal, lattice periodicity and
dimensionality – by changing the geometry and number of interfering beams.
Periodic structure of the optical refractive index induces a band-gap structure of spectrum for the propagating optical waves. The existence of gaps implies that optical waves with certain wave-vectors cannot propagate through the structure due to either total internal or Bragg reflection. The dynamics of any probe laser beam propagation in a nonlinear optically-induced lattice is therefore dominated by an interplay between nonlinearity of the medium and scattering from the periodic structure. Our group conducts theoretical and experimental studies of the key aspects of light propagation in nonlinear photonic lattices, and recently we demonstrated a number of novel remarkable phenomena, including formation and steering of discrete and gap solitons, and trapping and stabilization of a discrete vortex.
Discrete lattice solitons are self-trapped, spatially localized and non-diffracting beams of light that, due to self-focusing nonlinearity of the crystal, can be trapped in the total internal reflection gap of the periodic structure. Their intensity profile is only slightly modulated by the lattice, and their excitation in the lattice is a threshold effect depending on the level of the input laser power [Fig. 2]. In contrast, gap solitons are nonlinear beams that can be trapped inside Bragg reflection gaps of the optical lattice. Their excitation is non-trivial as it requires zero transverse velocity relative of the lattice and careful selection of the wave-vector corresponding to the particular spectral region inside the gap. Both requirements were satisfied in our successful (and first in its kind) experiment on generation of immobile gap solitons in one-dimensional optical lattices by using a twin-beam excitation scheme [Fig. 2]. In addition, this experiment confirmed our theoretical prediction of anomalous steering behaviour of gap solitons, which can be fully explored and exploited for the purpose of light control in optical lattices. Mobility and interaction properties of lattice solitons are strongly affected by the lattice, and are under our further investigation.
Two-dimensional optically induced lattices enabled us to study propagation and localization of beams with complex topological structure, such as optical vortices. Optical vortices are beams of light with quantized circulation of energy, carrying a phase singularity. The intensity of light at the vortex core is always zero, and in a nonlinear medium vortices can be spatially localized as vortex solitons [Fig. 3(a)]. Remarkably, vortex solitons “survive” in the lattice, where their intensity profile is strongly modulated, but a directional flow of energy is preserved [Fig. 3(b)]. We demonstrated the experimental generation of a discrete vortex soliton in a photorefractive crystal [last panel in Fig. 3]. Unlike the vortex propagating in a bulk self-focusing medium, where it quickly disintegrates, the discrete vortex is stabilized by the lattice. More recently, we discovered that lattices may support a novel class of asymmetric vortex solitons with no counterparts in homogeneous media [Fig. 3(c)]. Experimental observation of the broad class of asymmetric vortices in photonic lattices is underway.
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