**11** Publications

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Infect Dis Model 2021 3;6:398-404. Epub 2021 Feb 3.

Optique Nonlinéaire Théorique, Université libre de Bruxelles (U.L.B.), CP 231, Belgium.

Using the classical Susceptible-Infected-Recovered epidemiological model, an analytical formula is derived for the number of beds occupied by Covid-19 patients. The analytical curve is fitted to data in Belgium, France, New York City and Switzerland, with a correlation coefficient exceeding 98.8%, suggesting that finer models are unnecessary with such macroscopic data. The fitting is used to extract estimates of the doubling time in the ascending phase of the epidemic, the mean recovery time and, for those who require medical intervention, the mean hospitalization time. Large variations can be observed among different outbreaks.

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http://dx.doi.org/10.1016/j.idm.2021.01.006 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7857065 | PMC |

February 2021

Chaos 2020 Nov;30(11):113114

Optique Non-linéaire Théorique, Université Libre de Bruxelles, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium.

We consider the KdV equation on a circle and its Lie-Poisson reconstruction, which is reminiscent of an equation of motion for fluid particles. For periodic waves, the stroboscopic reconstructed motion is governed by an iterated map whose Poincaré rotation number yields the drift velocity. We show that this number has a geometric origin: it is the sum of a dynamical phase, a Berry phase, and an "anomalous phase." The last two quantities are universal: they are solely due to the underlying Virasoro group structure. The Berry phase, in particular, was previously described by Oblak [J. High Energy Phys. 10, 114 (2017)] for two-dimensional conformal field theories and follows from adiabatic deformations produced by the propagating wave. We illustrate these general results with cnoidal waves, for which all phases can be evaluated in closed form thanks to a uniformizing map that we derive. Along the way, we encounter "orbital bifurcations" occurring when a wave becomes non-uniformizable: there exists a resonance wedge, in the cnoidal parameter space, where particle motion is locked to the wave, while no such locking occurs outside of the wedge.

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http://dx.doi.org/10.1063/5.0021892 | DOI Listing |

November 2020

Opt Express 2019 Nov;27(24):34997-35011

Whispering gallery mode resonators hold great promises as very sensitive detectors, with a wide range of applications, notably as biosensors. However, in order to monitor the fine variations in their resonances, a costly and bulky apparatus is required, which confines the use of these efficient tools within specialised labs. Here, we consider a micro-ring resonator that is completely covered by a Bragg grating and propose to functionalize it only over a quarter of its perimeter. As target molecules progressively bind to the active region of the resonator, some particular resonances near the edge of the band gap undergo monotonous frequency splitting. Such a splitting, within the GHz range, can be monitored by conventional electronics and, hence, does not require finely tunable lasers or spectrometers. Meanwhile, the ultrahigh sensitivity that is characteristic of whispering gallery mode resonators is maintained. This robust and sensitive self-heterodyne detection scheme may pave the way to portable whispering-gallery-mode-based detectors, and in particular to point-of-care diagnostic tools.

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http://dx.doi.org/10.1364/OE.27.034997 | DOI Listing |

November 2019

Phys Rev E 2019 Aug;100(2-1):022132

Département de Physique, Université libre de Bruxelles (U.L.B.), CP 223, Belgium.

We study the model of growing filament against a wall proposed by Peskin, Odell, and Oster [Biophys. J. 65, 316 (1993)BIOJAU0006-349510.1016/S0006-3495(93)81035-X] using the ratio of chemical to diffusion timescales as a small expansion parameter. A detailed multiple-scale analysis allows us to fully describe the spatiotemporal evolution toward a steady-state distribution for the wall-tip distance, including chemical effects, in very good agreement with numerical simulations. Implications on the quasistatic approximation, where the force on the wall is allowed to vary slowly in time, are discussed. A corrected force-velocity relationship together with explicit expressions of the relevant timescales are provided.

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http://dx.doi.org/10.1103/PhysRevE.100.022132 | DOI Listing |

August 2019

Light Sci Appl 2016 Dec 30;5(12):e16216. Epub 2016 Dec 30.

ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain.

Extracting the light trapped in a waveguide, or the opposite effect of trapping light in a thin region and guiding it perpendicular to its incident propagation direction, is essential for optimal energetic performance in illumination, display or light harvesting devices. Here we demonstrate that the paradoxical goal of letting as much light in or out while maintaining the wave effectively trapped can be achieved with a periodic array of interpenetrated fibers forming a photonic fiber plate. Photons entering perpendicular to that plate may be trapped in an intermittent chaotic trajectory, leading to an optically ergodic system. We fabricated such a photonic fiber plate and showed that for a solar cell incorporated on one of the plate surfaces, light absorption is greatly enhanced. Confirming this, we found the unexpected result that a more chaotic photon trajectory reduces the production of photon scattering entropy.

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http://dx.doi.org/10.1038/lsa.2016.216 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6059888 | PMC |

December 2016

Opt Express 2016 Dec;24(25):28204-28220

We derive formulas for whispering gallery mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a Wentzel-Kramers-Brillouin (WKB) treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.

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http://dx.doi.org/10.1364/OE.24.028204 | DOI Listing |

December 2016

Phys Rev Lett 2011 Aug 9;107(7):073902. Epub 2011 Aug 9.

ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, Barcelona, Spain.

We demonstrate coherent optical coupling between molecular and plasmon resonances that are well separated in energy. In the presence of metallic nanoparticles, the second harmonic spectrum of organic dyes no longer peaks at the absorption wavelength but is instead blueshifted by 25 nm towards the localized plasmon resonance. The phase of the light generated by the dyes displays a large modulation across the plasmon resonance and no change across the molecular one. The second harmonic signal contributed by the nanoparticles, which is peaked at the plasmon frequency when no molecules are present, similarly displays a shift towards the molecular resonance in their presence. A model based on the interplay of the nonlinear optical near fields is able to account for these observations.

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http://dx.doi.org/10.1103/PhysRevLett.107.073902 | DOI Listing |

August 2011

Phys Rev E Stat Nonlin Soft Matter Phys 2006 Oct 10;74(4 Pt 1):041806. Epub 2006 Oct 10.

BP Institute for Multiphase Flow, University of Cambridge, Madingley Road, Cambridge, CB3 0EZ, United Kingdom.

A simple model for the forces acting on a single fiber as it is withdrawn from a tangled fiber assembly is proposed. Particular emphasis is placed on understanding the dynamics of the reptating fiber with respect to the entanglement of fibers within the tuft. The resulting two-parameter model captures the qualitative features of experimental simulation. The model is extended to describe the breakup of a tuft. The results show good agreement with experiment and indicate where a tuft is most likely to fracture based on the density of fiber endpoints.

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http://dx.doi.org/10.1103/PhysRevE.74.041806 | DOI Listing |

October 2006

Opt Lett 2006 Feb;31(4):495-7

Service d'Optique et Acoustique, Université Libre de Bruxelles, CP194/5, 50, Avenue F. D. Roosevelt, B-1050 Bruxelles, Belgium.

We consider a double-pass ring cavity with nonlinear incoherent optical feedback and analyze its response when it is driven by a continuous laser beam. This particular cavity is equivalent, in the temporal domain, to a simple spatial-pattern-generating system made from a Kerr slice and a feedback mirror. After formulating the evolution equations, we investigate the behavior of small-amplitude solutions and obtain an expression for the round-trip gains. We then explore the important effect of dispersion in the nonlinear medium. Finally, we show that stable modes are possible by solving numerically the full nonlinear equations.

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http://dx.doi.org/10.1364/ol.31.000495 | DOI Listing |

February 2006

Phys Rev E Stat Nonlin Soft Matter Phys 2005 Aug 17;72(2 Pt 2):026607. Epub 2005 Aug 17.

Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq, France.

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.

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http://dx.doi.org/10.1103/PhysRevE.72.026607 | DOI Listing |

August 2005

Opt Lett 2004 Jun;29(11):1221-3

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany.

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.

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http://dx.doi.org/10.1364/ol.29.001221 | DOI Listing |

June 2004