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.
Fig. 1. Expereimental setup for inducing
photonic lattices. Below: (a) Schematics of one-dimensional lattice
generation in a photorefractive crystal by using interference of two laser
beams, and light intensity patterns formed by a (b) one- and (c)
two-dimensional optical lattices on the crystal output face.
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.
Fig. 2; Left: Excitation schemes for
discrete solitons (top) inside a total internal reflection gap and gap
solitons (bottom) in a Bragg reflection gap. Right: Experimental intensity
profiles of two discrete solitons, centered on or between induced waveguides
(top) and a gap soliton (bottom). Shaded areas show minima of the induced
refractive index grating.
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.
Fig. 3; Schematics of the light intensity
distribution in an optical vortex soliton (a) in a bulk nonlinear crystal,
(b) in a two-dimensional “square” photonic lattice. Arrows show the
directions of the energy flow. Panel (c) shows a non-trivial asymmetric
vortex predicted to exist in the spectral gaps. Last panel shows the
characteristic four-peak intensity distribution of the discrete soliton in
the total internal reflection gap, observed in our experiments.
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Controlled generation and steering of spatial gap solitons
D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar,
Phys. Rev. Lett. 93, 083905-4 (2004).
[Full-text PDF (357 Kb)]
Asymmetric vortex solitons in nonlinear periodic lattices
T. J. Alexander, A. A. Sukhorukov, and Yu. S. Kivshar,
Phys. Rev. Lett. 93, 063901-4 (2004).
[Full-text PDF (877 Kb)]
Observation of discrete vortex solitons in optically induced photonic lattices
D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. G. Chen,
Phys. Rev. Lett. 92, 123903-4 (2004).
[Full-text PDF (735 Kb)]
Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices
A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Yu. S. Kivshar,
Phys. Rev. Lett. 92, 093901-4 (2004).
[Full-text PDF (726 Kb)]
Soliton stripes in two-dimensional nonlinear photonic lattices
D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen,
Opt. Lett. 29, 486-488 (2004).
[Full-text PDF (498 Kb)]
Observation of transverse instabilities in optically induced lattices
D. Neshev, A. A. Sukhorukov, Yu. S. Kivshar, and W. Krolikowski,
Opt. Lett. 29, 259-261 (2004).
[Full-text PDF (296 Kb)]
Spatial solitons in optically induced gratings
D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski,
Opt. Lett. 28, 710-712 (2003).
[Full-text PDF (723 Kb)]
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