We experimentally demonstrate degenerate, forward four-wave mixing effects in a self-defocusing photorefractive medium, in both one and two transverse dimensions. We observe the nonlinear evolution of new modes as a function of propagation distance, in both the near-field and far-field (Fourier space) regions.

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.

The holographic reconstruction of optically-induced objects typically assumes that the object is axially thin. Here, we demonstrate a simple approach that works for axially thick objects which evolve dynamically. Results are verified by reconstructing linear scattering experiments in a self-defocusing photorefractive crystal.

We consider the propagation of a partially coherent spatial beam in both self-focusing and self-defocusing nonlinear media. Using a Gaussian-Schell model, we derive an equation governing the width of highly incoherent beams as they propagate in both types of media and confirm its validity by using numerical simulations. Experiments performed in a biased photorefractive crystal match the predicted scaling.

We examine an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially incoherent spatial beams. Using a radiation transport approach, we develop plasmalike dispersion relations for perturbation modes and show that a positive gradient in the power spectrum can trigger instability. Theoretical considerations are confirmed by experiment and numerical simulation.

A novel all-solid Bragg fiber composed entirely of silica material is proposed in this paper. The core of this Bragg fiber is composed of conventional silica, and the cladding is formed by a set of alternating layers of up-doped and down-doped silica. This all-solid silica Bragg fiber is technically feasible and can simplify the fabrication technique. Dispersion properties of this silica Bragg fiber are investigated, and simulations show that zero dispersion wavelength lambda0 near 1.55 m with nonlinear coefficient gamma about 50 W-1km-1 can be obtained in silica Bragg fiber.

We study the over-focusing of spatial light beams due to self-focusing nonlinearity, in both local and nonlocal nonlinear media. Numerical simulation of both cases reveals a peaked profile, with a near-cusp at the center surrounded by exponentially-decaying tails, at a critical self-focusing power. The profile is a local effect, occurring as diffraction counteracts nonlinearity. Nonlocality, however, is needed to prevent modulation instability of the initial beam and to prevent catastrophic collapse in 2D. The peaked profile remains for weak nonlocality but disappears for wide nonlocal responses. Beyond the critical power for a peaked solution, or for longer propagation distances, competition between nonlinearity and diffraction causes oscillatory collapse-bounce behavior. The numerical results are confirmed by observing these dynamics in a self-focusing glass with a nonlocal, thermal response.

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.

We study the dynamics of phasons in a nonlinear photonic quasicrystal. The photonic quasicrystal is formed by optical induction, and its dynamics is initiated by allowing the light waves inducing the quasicrystal to nonlinearly interact with one another. We show quantitatively that, when phason strain is introduced in a controlled manner, it relaxes through the nonlinear interactions within the photonic quasicrystal. We establish experimentally that the relaxation rate of phason strain in the quasicrystal is substantially lower than the relaxation rate of phonon strain, as predicted for atomic quasicrystals. Finally, we monitor and identify individual 'atomic-scale' phason flips occurring in the photonic quasicrystal as its phason strain relaxes, as well as noise-induced phason fluctuations.

We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schrödinger equation.

We investigate modulational instability in normally dispersive highly birefringent fibers. By means of a technique based on a two-frequency pump field we are able to provide evidence for strong nonlinear dependence of the modulational instability spectra. This dependence manifests itself by the appearance of a nonlinear spectral gap in which modulational instability vanishes.

We examine the stationary propagation of a black solitary wave in a fiber laser or in a fiber transmission system with periodically distributed amplifiers and saturable absorbers that is governed by the Ginzburg-Landau equation. An analytical solution of the chirped black solitary wave to the Ginzburg-Landau equation that includes the nonlinear saturation effect is obtained for what we believe to be the first time. The stability analyses reveal that the stationary propagation of the chirped black solitary wave can be stable when the saturation effect of nonlinear gain or loss is taken into account, whereas the chirped black solitary-wave solution of the Ginzburg-Landau equation that does not include the nonlinear saturation of gain or loss is found to be unstable. The criterion for the stable or unstable propagation of the chirped black solitary wave in the presence of the nonlinear gain or loss saturation is presented. Also, it is shown that two identical chirped black solitary waves launched in parallel will attract each other and may develop into a bound state of two parallel chirped black solitary waves. This is in contrast to the behavior of conventional black solitons of an unperturbed system, in which the two black solitons launched in parallel repel each other and distance themselves during propagation.

Femtosecond space-time coupling effects in dispersive nonlinear media are investigated by a simple approximate method. The applicability of the method is verified by comparison with earlier numerical simulations. New results are presented for astigmatic beams as well as for negative dispersion. The position of the beam waist in the material changes the collapse threshold. For astigmatic beams, collapse is prevented for pulse durations shorter than a critical value.

We present a linear stability analysis of two-dimensional continuous waves and one-dimensional temporal solitons in nonlinear-optical fiber arrays. Guided by this analysis, we use numerical integrations of the governing equations to show that these arrays are all-optical switching devices. Light injected into the N-fiber array is temporally compressed and spatially localized into a few fibers on output.

An array of coupled nonlinear waveguides supports discrete soliton modes in which light is self-trapped in a few guides. We obtain an analytical description of these solitons and reveal that well-confined modes may be stably packed into the array. Power-controlled soliton steering may be achieved with linearly chirped solitons.

We show that optical shock-wave solutions are possible in nonlinear dispersive amplifying media that exhibit a frequency-dependent gain and background loss. These shock-wave domains exist at lasing threshold and are permitted in both the normal and the anomalous dispersive regions.

We study the propagation of two pulses with orthogonal linear polarizations in a nonlinear periodic dielectric structure with chi((3)) nonlinearity. Specifically, we derive the coupled nonlinear Schrödinger equations and find their solitary-wave solutions in a simple case. We show that two orthogonally polarized pulses can copropagate as a coupled gap soliton through a nonlinear periodic structure, while each pulse alone will be strongly reflected owing to the Bragg reflection. Based on the results, we present a new all-optical switching scheme and investigate its operational characteristics.

Simple, exact analytical solutions of Maxwell's equations are given for the TE-type self-guided modes of a medium that has a power-law dependence on intensity I(q) for the continuum values of q. An analytical criterion shows that such spatial solitons are stable for q < 2 only. Our derivation is novel in that solitons are borrowed from the known modes of the sech(2) profile (linear) waveguide, rather than by solving the nonlinear wave equation. The results reveal the change in soliton propagation as the nonlinear medium itself changes.

We analyze the transfer of energy between a continuous pump beam and space-time-modulated waves in a dispersive slab waveguide. With a self-focusing nonlinearity and propagation in the normal dispersion regime, a proper choice of the initial modulation frequencies permits a simple nonlinear dynamical description of this process.