arXiv subjects

Alain M. Dikandé

Publications and source records attributed to Alain M. Dikandé.

15 recordsLinked to original sources

arXiv2025

On a hyperbolic Duffing oscillator with linear damping and periodic forcing

The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in theoretical investigations of dynamical properties of systems with parity-conserving symmetry, where a double-well substrate connects two metastable states separated by a barrier. Physical systems of interest include nonlinear feedback-controlled mass-spring-damper oscillators, active hysteresis circuits (e.g. memristors), protein chains prone to hydrogen bond-mediated conformational transitions, centro-symmetric crystals and so on. In this work we consider a Duffing-type oscillator with a double-well potential represented by a hyperbolic function of mass position. The hyperbolic double-well potential has two degenerate minima that can be smoothly tuned by varying a deformability parameter, leaving unchanged the barrier height. We investigate solutions of the equation of motion in the absence and presence of damping and forcing. In the absence of perturbations numerical solutions lead to a periodic train of anharmonic oscillations featuring a crystal of pulse solitons of sech types. However, when the hyperbolic double-well potential is inverted, analytical solutions can be obtained which turn out to be kink-soliton crystals described by Jacobi elliptic functions. When damping and forcing are taken into consideration, the system dynamics can transit from periodic to chaotic phases or vice-versa via period-doubling or period-halving bifurcations, by simply varying the deformability parameter. The Poincaré map of the proposed model carries the well-known characteristic signatures of chaos presursors of the standard Duffing model, which happens to be just a particular case of the bistable oscillator model with the hyperbolic double-well potential.

nlin.CD↗

arXiv2021

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé-Kofané double-well potentials

We consider a one-dimensional system of interacting particles, in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of shape deformability on the order of transition in quantum tunneling in the bistable system, and on the possible existence of exact solutions to the transfer-integral operator associated with the partition function of the system. The bistable potential is represented by a class composed of three families of parametrized double-well potentials, whose minima and barrier height can be tuned distinctly. It is found that the extra degree of freedom, introduced by the shape deformability parameter, favors a first-order transition in quantum tunneling, in addition to the second-order transition predicted with the $ϕ^4$ model. This first-order transition in quantum tunneling, which is consistent with Chudnovsky's conjecture of the influence of the shape of the potential barrier on the order of thermally-assisted transitions in bistable systems, is shown to occur at a critical value of the shape-deformability parameter which is the same for the three families of parametrized double-well potentials. Concerning the statistical mechanics of the system, the associate partition function is mapped onto a spectral problem by means of the transfer-integral formalism. The condition that the partition function can be exactly integrable, is determined by a criterion enabling exact eigenvalues and eigenfunctions for the transfer-integral operator. Analytical expressions of some of these exact eigenvalues and eigenfunctions are given, and the corresponding ground-state wavefunctions are used to compute the probability density which is relevant for calculations of thermodynamic quantities such as the correlation functions and the correlation lengths.

cond-mat.stat-mech↗

arXiv2021

Femtosecond laser inscriptions in Kerr nonlinear transparent media: dynamics in the presence of K-photon absorptions, radiative recombinations and electron diffusions

Femtosecond lasers interacting with Kerr nonlinear optical materials, propagate in form of filaments due to the balance of beam diffraction by self-focusing induced by the Kerr nonlinearity. Femtosecond laser filamentation is a universal phenomenon that belongs to a general class of processes proper to ultrashort lasers processing systems, associated with the competition between nonlinearity and dispersion also known to promote optical solitons. The present work considers a model describing femtosecond laser inscriptions in a transparent medium with Kerr nonlinearity. Upon inscription, the laser stores energy in the optical material which induces an electron plasma. The model consists of a cubic complex Ginzburg-Landau equation, in which an additional K-order nonlinear term takes into account K-photon absorption processes. The complex Ginzburg-Landau equation is coupled to a time first-order nonlinear ordinary differential equation, accounting for time evolution of the plasma density. The main objective of the study is to examine effects of the competition between multi-photon absorptions, radiative recombination and electron diffusion processes, on temporal profiles of the laser amplitude as well as of the plasma density. From numerical simulations, it is found that when the photon number (i.e. K) contributing to multiphoton ionization is large enough, taking the electron diffusion processes into account favours periodic structures in temporal profiles both of the laser and the plasma density. The pulse repetition rate in the optical soliton train is increased with increase of the electron diffusion coefficient, while the plasma density is a train of multi-periodic anharmonic wave patterns.

physics.optics↗

arXiv2021

Thermal lensing-induced soliton molecules in beta-phase Gallium Oxide

In recent years, beta gallium oxide (beta-\ce{Ga2O3}) has become the most investigated isomorph of gallium oxide polymorphs, due to the great potential it represents for applications in optoelectronics and photonics for solar technology, particularly in blind ultraviolet photodetector solar cells (SBUV) designs. To optimize its use in these applications, and to identify possible new features, knowledge of its fundamental properties is relevant. In this respect, optical, thermal and electronic properties of beta-\ce{Ga2O3} have been studied expriementally, providing evidence of a wide-band inorganic and transparent semiconductor with a Kerr nonlinearity. Thermo-optical properties of the material, probed in SBUV sensing experiments, have highlighted a sizable heat diffusion characterized by a temperature gradient along the path of optical beams, quadratic in beam position and promoting a refractive-index change with temperature. The experimentally observed Kerr nonlinearity together with the thermally induced birefringence, point unambiguously to a possible formation of soliton molecules during propagation of high-intensity fields in beta-\ce{Ga2O3}. To put this conjecture on a firm ground we propose a theoretical analysis, based on the cubic nonlinear Schroedinger equation in 1+1 spatial dimension, in which thermal lensing creates an effective potential quadratic in the coordinate of beam position. Using the non-isospectral inverse-scattering transform method, the exact one-soliton solution to the propagation equation is obtained. This solution features a bound state of entangled pulses forming a soliton molecule, in which pulses are more or less entangled depending on characteristic parameters of the system.

cond-mat.mtrl-sci↗

arXiv2021

Elliptic solitons in optical fiber media

We examine the evolution of a time-varying perturbation signal pumped into a mono-mode fiber in the anomalous dispersion regime. We analytically establish that the perturbation evolves into a conservative pattern of periodic pulses which structures and profiles share close similarity with the so-called soliton-crystal states recently observed in fiber media [see e.g. A. Haboucha et al., Phys. Rev. A\textbf{78}, 043806 (2008); D. Y. Tang et al., Phys. Rev. Lett. \textbf{101}, 153904 (2008); F. Amrani et al., Opt. Express \textbf{19}, 13134 (2011)]. We derive mathematically and generate numerically a crystal of solitons using time division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons which can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.

nlin.PS↗

arXiv2021

Laser dynamics in nonlinear transparent media with electron plasma generation: effects of electron-hole radiative recombinations

The performance of optical devices manufactured via laser micromachining on nonlinear transparent materials, relies usually on three main factors which are the characteristic laser parameters (i.e. the laser power, pulse duration and pulse repetition rate), characteristic properties of host materials (e.g. their chromatic dispersions, optical nonlinearities or self-focusing features, etc.) and the relative importance of physical processes such as the avalanche impact ionization, multiphoton ionization and electron-hole radiative recombination processes. These factors act in conjunction to impose the regime of laser operation, in particular their competition determines the appropriate laser operation regime. In this work a theoretical study is proposed to explore the effects of the competition between multiphoton absorption, plasma ionization and electron-hole radiative recombination processes, on the laser dynamics in transparent materials with Kerr nonlinearity. The study rests on a model consisting of a K-order nonlinear complex Ginzburg-Landau equation, coupled to a first-order equation describing time variation of the electron plasma density. An analysis of stability of continuous waves, following the modulational-instability approach, reveals that the combination of multiphoton absorption and electron-hole radiative recombination processes can be detrimental or favorable to continuous-wave operation, depending on the group-velocity dispersion of the host medium. Numerical simulations of the model equations in the full nonlinear regime, reveal the eixstence of pulse trains the amplitudes of which are enhanced by the radiative recombination processes. Numerical results for the density of the induced electron plasma feature two distinct regimes of time evolution, depending on the strength of the electron-hole radiative recombination processes.

nlin.PS↗

arXiv2020

Kink-antikink scattering-induced breathing bound states and oscillons in a parametrized $ϕ^4$ model

Recent studies have emphasized the important role that a shape deformability of scalar-field models pertaining to the same class with the standard $ϕ^4$ field, can play in controlling the production of a specific type of breathing bound states so-called oscillons. In the context of cosmology, the built-in mechanism of oscillons suggests that they can affect the standard picture of scalar ultra-light dark matter. In the present work kink scatterings are investigated in a parametrized model of bistable system admitting the classical $ϕ^4$ field as an asymptotic limit, with focus on the formation of long-lived low-amplitude almost harmonic oscillations of the scalar field around a vacuum. The parametrized model is characterized by a double-well potential with a shape-deformation parameter that changes only the steepness of the potential walls, and hence the flatness of the hump of the potential barrier, leaving unaffected the two degenerate minima and the barrier height. It is found that the variation of the deformability parameter promotes several additional vibrational modes in the kink-phonon scattering potential, leading to suppression of the two-bounce windows in kink-antikink scatterings and the production of oscillons. Numerical results suggest that the anharmonicity of the potential barrier, characterized by a flat barrier hump, is the main determinant factor for the production of oscillons in double-well systems.

hep-th↗

arXiv2020

Exciton-polariton solitons in a semiconductor microwire of finite size

Exciton-polariton solitons are strongly nonlinear quasiparticles composed of coupled exciton-photon states due to the interaction of light with matter. In semiconductor microcavity systems such as semiconductor micro and nanowires, polaritons are characterized by a negative mass which when combined with the repulsive nonlinear exciton-exciton interaction, leads to the generation of bright polariton solitons. In this work we investigate the dynamics of bright exciton-polariton solitons in a finite-size microcavity waveguide, for which radiative losses are assumed balanced by the external pumping. An exact bright-soliton solution to the model equations of motion, consisting of a periodic train of polariton pulses, is obtained in terms of Jacobi elliptic functions. Exact analytical expressions corresponding to the energies of both photonic and excitonic components of the pulse train are found. Results suggest that the size (i.e. the length) of a microwire waveguide plays a relevant role in obtaining a quantitative estimate of the energy that could be conveyed by polariton solitons propagating in the medium.

cond-mat.mes-hall↗

arXiv2019

Soliton lattices originating from excitons interacting with high-intensity fields in finite molecular crystals

The effects of long-range intermolecular interactions on characteristic features of soliton bound states, consisting of localized excitons and polaritons in molecular crystals interacting with a high-intensity optical field, are investigated. Analytical solutions to the resulting modified nonlinear Schrödinger equation are obtained in terms of elliptic-type bright- and dark-soliton structures, which are assumed to correspond to periodic trains of pulse solitons and kink solitons respectively. Long-range intermolecular interactions are shown to renormalize the exciton-polariton interaction strength, hence generating a significantly huge increase in amplitudes of the bright solitons but a decrease in amplitudes of dark solitons. Results suggest that long-range intermolecular interactions hold relevant roles, both qualitatively and quantitatively, in the formation of amplitude and phase modulated strongly nonlinear exciton-polariton solitary-wave patterns, as well as in the energy transfer along molecular crystals interacting with high-intensity optical fields.

physics.optics↗

arXiv2019

Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability

Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption that soliton combs are self-organized ensemble of co-propagating coherently entangled states of light, and depending on the group-velocity dispersion they can result from space-division multiplexing of single-bright and single-dark solitons. Their analytical and numerical reconstruction schemes are discussed, while a linear-stability analysis leads to a $2\times 2$ Lamé eigenvalue problem whose boundstate spectrum is composed of a Goldstone-type translation mode and stable internal modes, as well as unstable decaying modes and growing modes. A power-spectral analysis of the three distinct possible soliton crystals enables us probe their inner structures in the frequency domain, and unveil the existence of structural defects in their power spectra.

physics.optics↗

arXiv2018

Solitons in a discrete model of chiral liquid crystals with competing interactions

Chiral liquid crystals exhibit in-plane spontaneous polarizations, however in their smectic phase the primary order parameter is a tilt vector associated with molecular rotations around the long molecular axis parallel to the director. The molecular rotations lead to several distinct phases among which a domain-wall texture with a periodic-kink soliton profile. In this study the formation of domain walls in smectic chiral liquid crystals is analyzed, with emphasis on the competition between ising-type symmetric and antisymmetric nearest-neighbor interactions, and an in-plane electric field. It is found that antisymmetric intermolecular interactions, which are of chiral origin, increase the width of kink structures in the domain wall at moderate intensity of the $y$ component of the electric field. Increasing the $x$ component of the electric field creates unstable condition for soliton formation irrespective of magnitudes of the symmetric and chiral intermolecular interactions. Stability condition for single-kink domain-wall structures in the discrete molecular chain, is discussed by estimating the Peierls stress experienced by the single-kink soliton. Results suggest that chirality lowers the Peierls-Nabarro barrier, hence increasing the lifetime of single-kink structures in the discrete medium.

cond-mat.soft↗

arXiv2018

Exciton-polariton soliton wavetrains in molecular crystals with dispersive long-range intermolecular interactions

The peculiar crystal structure of one-dimensional molecular solids originates from packing of an array of molecules in which intermolecular interactions are dominantly dispersive, including hydrogen-bond, van der Waals and London-type forces. These forces are usually relatively weaker than covalent and ionic bondings such that long-range intermolecular interactions should play important role in dispersion properties of molecular crystals such as polymers and biomolecular chain structures. In this work the effects of long but finite-range intermolecular interactions on single-exciton dispersion energy, and hence on characteristic parameters of periodic soliton trains associated with bound exciton-polariton states in one-dimensional molecular crystals interacting with an electromagnetic field, are investigated. Long-range interactions are shown to quantitatively modify the exciton-polariton soliton amplitudes, width and velocity as a result of shrinkage of the single-exciton energy spectrum. The soliton structures of interest are nonlinear wavetrains, consisting of periodically ordered single-pulse (i.e. bright) or single-kink (i.e. dark) solitons with equal separation between the constituent single-soliton modes. Periodic soliton structures are relevant and best suited for finite-size chain systems, where periodic boundary conditions rule the generation of nonlinear wave profiles. Generally they are of weaker nonlinearity compared to their single-soliton constituents as well established within the framework of their generation via the process of modulational instability

cond-mat.mes-hall↗

arXiv2004

Long-range dispersion and spatial diffusion of fault waves in the Burridge-Knopoff earthquake model

The Burridge-Knopoff model of earthquakes has recently gained increased interest for the consistency of the predicted energy released by sismic faults, with the Gutenberg-Richter scaling law. The present work suggests an improvement of this model to account for long-range dispersions and large spatial diffusion of sismic faults. An enhancement of the threshold speed of shock waves driven by translated fault fronts is pointed out and shown to result from the interactions between components of the system situated far aways them and others. Due to the enhanced threshold speed, size of the sismic fault gets increased but a control effect can still be gained from tunable dispersion extent irrespective of the total length of the system. To the viewpoint of the Burridge-Knopoff block-lattice model, this last consideration introduces the possibility of sizable but finite interactions among infinitely aligned massive blocks. Implications on the fault wave propagation are examined by numerical simulations of the improved nonlinear partial differential equation.

nlin.PS↗

arXiv2004

Nonlinear optical responses and gap-soliton lattices in layered dielectric materials

A new approach to the nonlinear reponse of a multiplayer structure consisting of alternating dielectric materials with intensity-dependent dielectric constants is considered in both analytical and numerical viewpoints. The nonlinear feedback of the structure gives rise to an artificial potential acting as a mean-field feedback on each single dielectric material due to other layers. For superlattices resulting from a regular periodic arrangement of an infinite number of single dielectric layers, it is shown that an analytical expression of this mean-field feedback can be obtained and waveshapes of the associate gap solitons are derived. The case of a multilayer with dispersive interlayer interactions is considered numerically and leads to strongly localized gap solitons. Implicatons of the artificial soliton structure as for possible theoretical modelling of soliton-compression phenomena are discussed.

nlin.PS↗

arXiv2004

Quasi-continuum approximation to the Nonlinear Schrödinger equation with Long-range dispersions

The long-wavelength, weak-dispersion limit of the discrete nonlinear Schrödinger equation with long-range dispersion is analytically considered. This continuum approximation is carried out irrespective of the dispersion range and hence can be assumed exact in the weak dispersion regime. For nonlinear Schrödinger equations showing finite dispersion extents, the long-range parameter is still a relevant control parameter allowing to tune the dispersion from short-range to long-range regimes with respect to the dispersion extent. The long-range Kac-Baker potential becomes unappropriate in this context owing to an "edge anomaly" consisting of vanishing maximum dispersion frequency and group velocity(and in turn soliton width) in the "Debye" limit. An improved Kac-Baker potential is then considered which gives rise to a non-zero maximum frequency, and allows for soliton excitations with finite widths in the nonlinear Schrödinger system subjected to the long-range but finite-extent dispersion.

nlin.PS↗