Rainbow Archimedean spiral emission from optical fibres.

We demonstrate a new practical approach for generating multicolour spiral-shaped beams. It makes use of a standard silica optical fibre, combined with a tilted input laser beam. The resulting breaking of the fibre axial symmetry leads to the propagation of a helical beam. The associated output far-field has a spiral shape, independently of the input laser power value. Whereas, with a high-power near-infrared femtosecond laser, a visible supercontinuum spiral emission is generated. With appropriate control of the input laser coupling conditions, the colours of the spiral spatially self-organize in a rainbow distribution. Our method is independent of the laser source wavelength and polarization. Therefore, standard optical fibres may be used for generating spiral beams in many applications, ranging from communications to optical tweezers and quantum optics.

Spatial Beam Self-Cleaning in Second-Harmonic Generation.

We experimentally demonstrate the spatial self-cleaning of a highly multimode optical beam, in the process of second-harmonic generation in a quadratic nonlinear potassium titanyl phosphate crystal. As the beam energy grows larger, the output beam from the crystal evolves from a highly speckled intensity pattern into a single, bell-shaped spot, sitting on a low energy background. We demonstrate that quadratic beam cleanup is accompanied by significant self-focusing of the fundamental beam, for both positive and negative signs of the linear phase mismatch close to the phase-matching condition.

On the asymptotic evolution of finite energy Airy wave functions.

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Nonlinear control of soliton pulse delay with asymmetric dual-core photonic crystal fibers.

Dual-core photonic crystal fiber nonlinear couplers permit the achievement of distortion-free power-controlled delay of picosecond pulses. The stable control of pulse time delay is achievable by means of resonance soliton solutions.

Multidimensional solitons in fiber arrays.

We demonstrate that nonlinear optical fiber arrays can support stable solitonlike pulses with finite energy. The bound state that we have found is localized both in time and in spatial domain in the direction perpendicular to the pulse propagation. Numerical studies support our analytical conclusions.

Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays.

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.

Modulational instability of continuous waves and one-dimensional temporal solitons in fiber arrays.

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.

Higher-order effects in bandwidth-limited soliton propagation in optical fibers.

By means of numerical studies and soliton perturbation theory we examine the effects of higher-order linear and nonlinear terms in bandwidth-limited amplified soliton propagation. We show that these effects are responsible for strong reductions of soliton-soliton interaction in such systems.

Spatiotemporal pulse dynamics in a periodic nonlinear waveguide.

We present analytical results, based on a variational approach, on the spatiotemporal evolution of a pulse in a nonlinear waveguide with a periodic refractive-index profile. Stationary pulses, along with their stability properties, are predicted and then compared with numerical simulations of the governing equation.

Analysis of switching phenomena in a dense medium of two-level atoms.

The switching characteristics of a dense medium of two-level atoms is studied analytically. Switching depends on the ratio of the Rabi frequency to the strength of the near-dipole-dipole interaction. When this ratio is nearly one, an exact solution is obtained. Other values of the parameter are studied by the use of asymptotic analysis, and the conditions for switching are determined from an analytic expression.

Switching dynamics of helical solitons in a periodically twisted birefringent fiber filter.

We discuss the conditions for the formation, switching, and spatial instability of solitary waves with helical evolution of the polarization in optical fibers with periodic birefringence.

Generation of solitons in a nonlinear periodic medium.

We derive a simple analytical expression for the modulational instability of two counterpropagating waves in a periodic nonlinear structure. Numerical studies reveal that the nonlinear development of this instability leads to time-recurrent energy storage in the form of steady solitons and to soliton train emission from both ends of the filter.

Nonlinear dynamics of induced modulational instability in a self-focusing slab waveguide with normal dispersion.

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.

Reflection and transmission of self-focused channels at nonlinear dielectric interfaces.

We show with an extensive numerical study that the global reflection and transmission properties of a finite-width optical self-focused channel incident at an oblique angle to an interface separating two self-focusing nonlinear media can be categorized into three distinct regimes of behavior as the incidence angle is varied through the angle for total internal reflection. The largest regime in parameter space is the nonlinear regime, where a channel undergoes either total internal reflection or transmission, in marked contrast to the well-known linear Snell's law behavior. The beam asymptotics in this latter region are quantitatively explained by a recent equivalent-particle theory.