Localized Faraday patterns under heterogeneous parametric excitation.

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

Kerr frequency combs and triangular spectra.

Nonlinear externally driven optical cavities are known to generate periodic patterns. They grow from the linearly unstable background states due to modulation instability. These periodic solutions are also known as Kerr frequency combs, which have a variety of applications in metrology. The stationary state of periodic wave trains can be explained theoretically only in weakly nonlinear regimes near the onset of the instability using the order parameter description. However, in both weakly and strongly nonlinear dissipative regimes, only numerical solutions can be found. No analytic solutions are known so far except for the homogeneous continuous wave solution. Here, we derive an analytical expression for the intracavity fully nonlinear dissipative periodic wave train profiles that provides good agreement with the results of numerical simulations. Our approach is based on empirical knowledge of the triangular shape of the frequency comb spectrum.

Nondestructive distributed measurement of supercontinuum generation along highly nonlinear optical fibers.

Supercontinuum generation (SCG) in optical fibers arises from the spectral broadening of an intense light, which results from the interplay of both linear and nonlinear optical effects. In this Letter, a nondestructive optical time domain reflectometry method is proposed for the first time, to the best of our knowledge, to measure the spatial (longitudinal) evolution of the SC induced along an optical fiber. The method was experimentally tested on highly nonlinear fibers. The experimental results are in a good agreement with the optical spectra measured at the fiber outputs.

Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities.

We study analytically, numerically, and experimentally the nonlinear symmetry breaking induced by broken reflection symmetry in an optical fiber system. In particular, we investigate the modulation instability regime and reveal the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures. Our theory explains early observations, and the predictions are in excellent agreement with our experimental findings.

Convection-induced stabilization of optical dissipative solitons.

In spatially extended convective systems, the reflection symmetry breaking induced by drift effects leads to a striking nonlinear effect that drastically affects the formation and stability of dissipative solitons in optical parametric oscillators. The phenomenon of nonlinear-induced convection dynamics is revealed using a model of the complex quintic Ginzburg-Landau equation with nonlinear gradient terms in it. Mechanisms leading to stabilization of dissipative solitons by convection are singled out. The predictions are in very good agreement with numerical solutions found from the governing equations of the optical parametric oscillators.

Rogue waves in a multistable system.

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.

All-fiber tunable optical delay line.

We present a tunable optical delay line based on the use of a single chirped fiber Bragg grating written into a standard single mode optical fiber. In the proposed scheme, the delay is induced through the Bragg grating differential group delay curve. This is achieved by launching orthogonally polarized optical pulses in both directions into the Bragg grating and by controlling its local birefringence. This bidirectional propagation allows to compensate the second-order dispersion. The setup is suitable to delay pulses with a spectral width just less than the grating reflection bandwidth, which is particularly useful in the context of forthcoming wavelength division multiplexing ultra-high bit rate lightwave systems. In this work, the performances of the setup are investigated using a pulsed laser delivering 6.3 ps Fourier transform limited pulses at 1548 nm. A maximum delay of 120 ps (about 20 times the pulse width) is reported experimentally.

Introduction: dissipative localized structures in extended systems.

Localized structures belong to the class of dissipative structures found far from equilibrium. Contributions from the most representative groups working on a various fields of natural science such as biology, chemistry, plant ecology, mathematics, optics, and laser physics are presented. The aim of this issue is to gather specialists from these fields towards a cross-fertilization among these active areas of research and thereby to present an overview of the state of art in the formation and the characterization of dissipative localized structures. Nonlinear optics and laser physics have an important part in this issue because of potential applications in information technology. In particular, localized structures could be used as "bits" for parallel information storage and processing.

Convection-induced nonlinear symmetry breaking in wave mixing.

We show that the combined action of diffraction and convection (walk-off) in wave mixing processes leads to a nonlinear symmetry breaking in the generated traveling waves. The dynamics near to threshold is reduced to a Ginzburg-Landau model, showing an original dependence of the nonlinear self-coupling term on the convection. Analytical expressions of the intensity and velocity of traveling waves emphasize the utmost importance of convection in this phenomenon. These predictions are in excellent agreement with the numerical solutions of the full dynamical model.

Modulated optical structures over a modulationally stable medium.

Evidence of modulated dissipative structures with an intrinsic wavelength in a nonlinear optical system devoid of Turing instability is given. They are found in the transverse field distribution of an optical cavity containing a liquid crystal light valve. Their existence is related to a transition from flat to modulated fronts connecting the unstable middle branch of a bistability cycle and either of the two stable uniform states. We first analyze the cavity in the limit of nascent bistability, where a modified Swift-Hohenberg equation is derived. This allows for a simple analytical expression of the threshold associated with the transition as well as the wavelength of the emerging structure. Numerical simulations show development of ring-shaped modulated fronts and confirm analytical predictions. We then turn to the full model and find the same transition, both analytically and numerically, proving that this transition in not limited to nascent bistability regimes.

Experimental evidence of absolute and convective instabilities in optics.

Experimental evidence of convective and absolute instabilities in a nonlinear optical system is given. In optics, the presence of spatial nonuniformities brings in additional complexity. Hence, signatures characterizing these two regimes are derived based on analytical and numerical investigations. The corresponding noise-sustained and dynamical patterns are observed experimentally in a liquid crystal layer subjected to a laser beam with tilted feedback.

Increasing spatial complexity toward near-resonant regimes of quadratic media.

Near-resonant conditions lead to a strong interaction between saddle node and modulational instabilities in diffractive optical frequency down-conversion systems. The study of such an interaction reveals a new type of stable phase-locked mixed-mode hexagonal structure below the lasing threshold. Without this interaction, hexagonal structures do not exist. The analytical expression of the threshold associated with these structures is derived. Numerical solutions of the governing equations are in close agreement with analytical predictions.