Contagious photons: Laser dynamics and the susceptible-infected-recovered model.

We explore a complete analogy between the classic susceptible-infected-recovered epidemiological model with natural birth and death rates, and class-B laser equations. As a result, recently derived asymptotic formulas in the former context can be used to describe the switch-on intensity pulse of a laser suddenly brought well above the lasing threshold, as in active Q-switching. Conversely, the well-studied laser relaxation oscillations find a companion behavior in epidemiology, emphasizing nontrivial timescales. Finally, we discuss the possible correspondence between multistrain outbreaks and multimode lasing.

Effect of external tension on the wetting of an elastic sheet.

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle θ_{Y}. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with 0<θ_{Y}<π/2, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring θ_{Y}=0. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and "vesicle" solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λ_{BC}, and find that the shape of the drop is determined by the ratio A/λ_{BC}^{2}, where A is the area of the drop.

Speed of wave packets and the nonlinear Schrödinger equation.

The universal theory of weakly nonlinear wave packets given by the nonlinear Schrödinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple-scale analysis carried out beyond all orders reveals that a single soliton, bright or dark, can travel at a different speed than the group velocity. In an exponentially small but finite range of parameters, the envelope of the soliton is locked to the rapid oscillations of the carrier wave. Eventually, the dynamics is governed by an equation analogous to that of a pendulum, in which the center of mass of the soliton is subjected to a periodic potential. Consequently, the soliton speed is not constant and generally contains a periodic component. Furthermore, the interaction between two distant solitons can in principle be profoundly altered by the aforementioned effective periodic potential and we conjecture the existence of new bound states. These results are derived on a wide class of wave models and in such a general way that they are believed to be of universal validity.

Analytical theory of gain-switched laser pulses: From Lotka-Volterra slow-fast dynamics to passive Q switching.

Gain switching is a simple technique for generating short pulses through direct modulation of optical gain in lasers. Its mathematical description requires the connection between a slowly varying, low intensity solution and a short, high intensity solution. Previous studies constructed a complete pulse by patching these two partial solutions at an arbitrary point in the phase plane. Here, we develop an asymptotic theory in which slow and fast solutions are matched together through a third intermediate solution. The mathematical analysis of the laser problem benefits from a preliminary study of the Lotka-Volterra equations when the two competing populations exhibit different timescales. Since this particular limit has never been explored, we first analyze the Lotka-Volterra equations before applying the theory to the more complex laser equations. We show a significant effect of the transition layer on the pulse intensity. Last, we discuss the case of sustained laser pulses generated through the Q-switching technique and show how their description may benefit from our theory.

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.

Berry phases in the reconstructed KdV equation.

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.

Portable microresonator-based label-free detector: monotonous resonance splitting with particle adsorption.

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.

Steady-state and transient analysis of the Peskin-Odell-Oster Brownian ratchet model in the limit of large but finite diffusion.

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.

Dispersion relations and bending losses of cylindrical and spherical shells, slabs, and slot waveguides.

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.

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.

Large optical-frequency shift of molecular radiation via coherent coupling to an off-resonance plasmon.

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.

Model for the breakup 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 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.

Fast self-pulsing through nonlinear incoherent feedback.

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.

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.

Delay differential equations for mode-locked semiconductor lasers.

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.