arXiv subjects

Alain M. Dikande

Publications and source records attributed to Alain M. Dikande.

23 records · Page 2Linked to original sources

arXiv2016

Matter-Wave Fields for Double-Slit Atom Interferometry: Variational Versus Exact Solitons

A major challenge in the theoretical modeling of double-slit interferometry involving matter-wave fields is the appropriate waveform to be assigned to this field. While all the studies carried out to date on this issue deal with variational fields, experiments suggest that the optical field is generated by splitting a single-hump Bose-Einstein condensate into two spatially and temporally entangled pulses indicating the possibility of fully controlling the subsequent motion of the two output pulses. To probe the consistency of variational and exact soliton solutions to the field equation, we solve the Gross-Pitaevskii equation with an optical potential barrier assumed to act as a beam splitter, while including gravity. The exact solution is compared with the two most common variational wavefunctions, namely, the Hermite-Gaussian and super-sech modes. From numerical simulations, evidence is given of the exact solution as being the most appropriate matter-wave structure that provides a coherent description of the generation and spatio-temporal evolution of matter-wave optical fields in a hypothetical implementation of double-slit atom interferometry

nlin.PS↗

arXiv2011

Thermal lensing-induced bifocusing of spatial solitons in Kerr-type optical media

Thermo-optical effects cause a bifocusing of incoming beams in optical media, due to the birefringence created by a thermal lens that can resolve the incoming beams into two-component signals of different polarizations. We propose a non-perturbative theoretical description of the process of formation of double-pulse solitons in Kerr optical media with a thermally-induced birefringence, based on solving simultaneously the heat equation and the propagation equation for a beam in a one-dimensional medium with uniform heat flux load. By means of a non-isospectral Inverse Scattering Transform assuming an initial solution with a pulse shape, a one-soliton solution to the wave equation is obtained that represents a double-pulse beam which characteristic properties depend strongly on the profile of heat spatial distribution.

nlin.PS↗

arXiv2010

Induced soliton ejection from a continuous-wave source waveguided by an optical pulse-soliton train

It has been established for some time that high-power pump can trap a probe beam of lower intensity that is simultaneously propagating in a Kerr-type optical medium, inducing a focusing of the probe with the emergence of modes displaying solitonic properties. To understand the mechanism by which such self-sustained modes are generated, and mainly the changes on probe spectrum induced by the cross-phase-modulation effect for an harmonic probe trapped by a multiplex of temporal pulses, a linear equation (for the probe) and a nonlinear Schrödinger equation (for the pump) both coupled by a cross-phase-modulation term, are considered simultaneously. In general the set of coupled probe-pump equations is not exactly tractable at any arbitrary value of the ratio of the cross-phase to the self-phase modulation strengths. However, for certain values of this ratio, the probe modulation wavector develops into $|n,l\textgreater$ {\it quantum states} involving $2n+1$ soliton-shaped eigenfunctions which spectral properties can be characterized unambiguously. Solutions of the probe equation give evidence that the competition between the self-phase and cross-phase modulations leads to a broadband spectrum, with the possibility of a quasi-continuum of soliton modes when the cross-phase-modulation coupling is strong enough.

physics.optics↗

arXiv2004

Numerical analysis of the existence and stability of nonlinear excitations in a parametric model of ferromagnetic chain

A parametrized spin model was recently introduced and intended for one-dimensional ferromagnets with a deformable Zeeman energy. This model is revisited and given more realistic interpretation in terms of a model for ferromagnetic systems with nonconvex anisotropies. A main virtue of the improved form is its exact reduction to the discrete Remoissenet-Peyrard model, i.e. a parametrized version of the Takeno-Homma's discrete sine-Gordon model. The spin-wave phase of the improved parametrized spin model is investigated assuming both harmonic and anharmonic excitations. Intrinsic-self-localized modes, regarded as zone-boundary breather spin waves, are pointed out by simulating the nonlinear difference equations describing the spin equilibrium positions in the chain, and are shown to exist irrespective of values of the model parameter. Domain-wall textures of the model are also numerically examined in terms of kink solitons and with regard to the parametrization.

nlin.PS↗

arXiv2000

Nonlinear coherent wavetrains and bifurcations in a class of deformable models for one-dimensional nonlinear discrete Klein-Gordon systems

The discrete static properties of a class of deformable double-well potential models are investigated. The Peierls-stress potential of the models is explicitely given. Numerical analysis of the equation of motion reveal different soliton wavetrain profiles, most of which are periodic. Soliton wavetrains are also found analytically in terms of continuum nonlinear periodic wavefunction solutions then called periodons. The periodon stability in a lattice phonon bath is discussed. Looking at bifurcation phenomena and routes to chaos for a representative model of this class, the return map is derived in terms of a two-dimensional, two-parameter map. This map appears to be area preserving, possesses three characteristic fixed points with one elliptic, and displays complex bifurcation diagrams with hopf-like singularities. The routes to chaos also show complexities all due to the interplay of two control parameters.

nlin.PS↗