Francois Copie

Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators.

We experimentally investigate the interplay of Turing (modulational) and Faraday (parametric) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance, switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model.

Modulation instability in amplitude modulated dispersion oscillating fibers

We investigate theoretically and experimentally the modulation instability process in a dispersion oscillating fiber characterized by an amplitude modulation of its group velocity dispersion. We developed an analytical model that allows us to calculate the parametric gain in these fibers and to predict the position of the quasi-phase matched modulation instability sidelobes. The two fundamental frequencies characterizing the dispersion profile lead to the splitting of the original multiple sidelobes generated in basic sinusoidally varying dispersion oscillating fibers. These theoretical predictions are confirmed by experiments.

Parametric instabilities in modulated fiber ring cavities

We investigate modulational instability in inhomogeneous passive cavities modeled by the Ikeda map. The cavity boundary conditions and the modulation of the fiber dispersion force the system to develop parametric instabilities, which lead to the generation of simple, as well as period-doubled, temporal patterns. The analytical results obtained by means of the Floquet theory are validated through numerical solution of the Ikeda map, and the limitations of the mean-field Lugiato-Lefever model are highlighted.

Dynamics of Turing and Faraday instabilities in a longitudinally modulated fiber-ring cavity

We experimentally investigate the round-trip-to-round-trip dynamics of the modulation instability spectrum in a passive fiber-ring cavity presenting an inhomogeneous dispersion profile. By implementing a real-time spectroscopy technique, we are able to record successive single-shot spectra, which display the evolution of the system toward a stationary state. We find that the two instability regimes (Turing and Faraday) that compete in this kind of inhomogeneous cavity not only differ by their characteristic frequency but also by their dynamical behavior. The dynamic transition between those two regimes of instability is also presented.

Shock wave generation triggered by a weak background in optical fibers

We experimentally report the observation of dispersive shock waves from a short pulse superimposed onto a small continuous wave background in optical fibers. We show that the background allows us to strongly enhance the extension and contrast of the oscillatory wave train inherent to the dispersive shock. More than seven periods of oscillations with high contrast are observed experimentally and confirmed with numerical simulations. The dynamics of the process are simply explained from spectro-temporal representations.

Modulation instability in the weak dispersion regime of a dispersion modulated passive fiber-ring cavity

We present a theoretical and experimental study of the modulation instability process in a dispersion oscillating passive fiber-ring resonator in the low dispersion region. Generally, the modulation of the dispersion along the cavity length is responsible for the emergence of a regime characterised by multiple parametric resonances (or Faraday instabilities). We show that, under weak dispersion conditions, a huge number of Faraday sidebands can grow under the influence of fourth order dispersion. We specifically designed a piecewise uniform fiber-ring cavity and report on experiments that confirm our theoretical predictions. We recorded the dynamics of this system revealing strong interactions between the different sidebands in agreement with numerical simulations.

Modulation instability in dispersion oscillating fibers

In this review we present recent theoretical and experimental progress on modulation instability and parametric amplification processes in dispersion oscillating fibers. These optical fibers are characterized by longitudinal periodic variations of their outer diameter engineered over the meter-long scale, which provides an additional degree of freedom to the system and leads to the generation of multiple MI sideband pairs. The main results published in single-pass configurations and in passive cavities are summarized in this review.

Non-destructive phase and intensity distributed measurements of the nonlinear stage of modulation instability in optical fibers

We report a novel experimental setup to perform distributed characterization in intensity and phase of the nonlinear stage of modulation instability by means of a non-invasive experimental setup : a heterodyne time domain reflectometer.

Observation of period-doubling dynamics of modulation instability in uniform and dispersion oscillating fiber-ring cavities

We provide a direct observation of a period-doubling phenomenon associated to the modulation instability in both uniform and dispersion oscillating passive fiber ring cavities. This has been done by performing roundtrip-to-roundtrip measurements of the temporal pattern generated through the instability.

Modulation instability in the weak dispersion regime of dispersion oscillating fiber-ring cavities

Uniform passive fiber-ring cavities are macroscopic devices which are known to exhibit dissipative modulation instability (MI) when driven in the rather large dispersion regime [1]. In a previous study we showed that in this regime, a simple modulation of the dispersion along the length of the ring cavity is responsible for the appearance of a new domain of parametric instability, related to Faraday instabilities [2], which has been confirmed experimentally [3]. In the present work we study experimentally a modulated cavity but pumped in the vicinity of one of its zero-dispersion wavelength (ZDW). In this case we show that, like in simple propagation [4], higher order dispersion terms up to ß4 have to be taken into account. In our case, broad MI spectra are generated, composed of a large number of quasi-phase-matched sidebands.