Hospitalization dynamics during the first COVID-19 pandemic wave: SIR modelling compared to Belgium, France, Italy, Switzerland and New York City data

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

Large Q factor with very small Whispering Gallery Modes resonators

Efficient micro-resonators simultaneously require a large quality factor $Q$ and a small volume $V$. However, the former is ultimately limited by bending losses, the unavoidable radiation of energy of a wave upon changing direction of propagation. Such bending losses increase exponentially as $V$ decreases and eventually result in a drop of $Q$. Therefore, circular cavities are generally designed with radii that are much larger than the optical wavelength. The same leakage of energy by radiation limits the sharpness of bends in photonic integrated circuits. In this article, we present a way to reduce bending losses in circular micro-resonators. The proposed scheme consists of one or more external dielectric rings that are concentric with the cavity. These rings alter the field outside the cavity where radial oscillations set in, and thus control the far field radiation. As a result, the $Q$ factor can be increased by several orders of magnitude while keeping a small cavity volume

A new model for passive mode-looking in a semiconductor laser

We propose a new model for passive mode-locking that is a set of ordinary delay differential equations. We assume the ring cavity geometry and a 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 found that stable mode-locking can exist even when the non-lasing state between pulses becomes unstable

The \theta-formulation of the 2D elastica -- Buckling and boundary layer theory

The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a particularly easy boundary layer analysis in the limit of weak bending stiffness. Within this parameterization, boundary layers are located at inflexion points, where $\theta$ is extremum, and they connect regions of low and large curvature. A simple composite solution is derived without resorting to elliptic functions and integrals. This approximation can be used as an elementary building block to describe complex shapes. Applying this theory to the study of an elastic ring under uniform pressure and subject to a set of point forces, we discover a snapping instability. This instability is confirmed by numerical simulations. Finally, we carry out experiments and find good agreement of the theory with the experimental shape of the deformed elastica.Comment: associated ANIMATIONS and MATHEMATICA FILES available at https://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/355924/Holding

Bragg localized structures in a passive cavity with transverse refractive index modulation

We consider a passive nonlinear optical cavity containing a photonic crystal inside it. The cavity is driven by a superposition of the two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate existence of resting and moving transversely localized structures of light in this system

Intermittent chaos for ergodic light trapping in a photonic fiber plate

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.Peer ReviewedPostprint (published version

Control and removing of modulational instabilities in low dispersion photonic crystal fiber cavities

Taking up to fourth order dispersion effects into account, we show that fiber resonators become stable for large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for arbitrary small but nonzero fourth order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and opens the way to experimental implementation

A model for the break-up of a tuft of fibers

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 break-up of a tuft. The results show good agreement with experiment and indicate where a fiber is most likely to fracture based on the density of fiber end-points

Mode-splitting in a microring resonator for self-referenced biosensing

Self-referenced biosensing based on mode-splitting on a microring resonator is experimentally demonstrated. A Bragg grating integrated on the surface of the ring provides coupling between the clockwise and counterclockwise travelling modes of the pristine ring resonator lifting their degeneracy. The amount of mode-splitting is directly related to the reflectivity of the grating and it is only affected by structurally modifying the grating. Environmental perturbations to the surroundings of the gratings, such as temperature and bulk refractive index variations, have a minor effect on the amount of mode-splitting. This principle allows the realization of a self-referenced sensing scheme based on the detection of variations of the mode-splitting induced by structural changes to the grating. In this work, a polymethyl methacrylate (PMMA) Bragg grating is integrated onto a ring resonator in Al2O3. It is shown both theoretically and experimentally that the amount of splitting of a resonance varies minimally under temperature or bulk refractive index perturbations. However, the structural change of attaching a layer of biomolecules inside the grating does affect its reflectivity and the amount of mode splitting present. This result represents the first proof-of-concept demonstration of an integrated mode-splitting biosensor insensitive to temperature and refractive index variations of the liquid matrix where the molecules to be detected are embedded. The reported results pave the road towards the realization of truly self-referenced biosensors