Abdelkader Makhoute

Light polarization effects in laser-assisted (e,2e) collisions in helium

The influence of laser polarization on the triple differential cross section (TDCS) for electron impact ionization of helium is analysed in the asymmetric coplanar geometry. The interaction of the laser field with the incident, and scattered electrons is treated non-perturbatively by using Volkov waves, while that of the ejected electron moving in the combined field of the residual ion He+ and of the laser is obtained by using the ansatz formulated by Joachain et al (1988 Phys. Rev. Lett. 61 165) for the case of atomic hydrogen. The remaining interactions are treated by using first-order perturbation theory. Detailed calculations of the scattering amplitudes are performed for a helium target. We discuss the influence of the laser polarization on TDCS as a function of the angle of ejection of the slow electron for selected choices of the laser frequency and number of photons exchanged between the external field and the electron-helium system.

On the second Born approximation for laser-assisted electron-atom collisions

The differential cross section for electron-hydrogen atom collisions in the presence of a CO2 laser field is analysed as a function of the incident electron energy. We show that the criticism of the second Born treatment of elastic scattering and excitation by fast electrons is unjustified for various geometrical configurations. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion.

Effects of laser polarization in laser-assisted electron-helium inelastic collisions: a Sturmian approach

The influence of linearly and circularly polarized laser fields on the dynamics of fast electron-impact excitation in atomic helium is discussed. A detailed analysis is made in the excitation of 2 1S, 3 1S and 3 1D dressed states of helium target. By using a semiperturbative treatment with the Sturmian basis expansion, we take into account the target atom distortion induced by a laser field. Important differences appear between the angular distributions depending on the different states of polarization, in particular the circular polarization presents an experimental interest. We give new features (intermediate resonances) for both polarizations, concerning the n = 2 states of helium for emission and the n = 3 for the absorption, in terms of laser frequency. Qualitative differences from the case of laser-assisted elastic collisions have been found.

The second Born approximation in laser-assisted (e, 2e) collisions in hydrogen

The second Born approximation has been used to calculate the triple differential cross sections for electron-impact ionization of atomic hydrogen in the presence of a linearly polarized laser field. The interaction of the laser field with the unbound electrons is treated in a nonperturbative way by the use of Volkov waves. We have used the wave function proposed by Joachain et al (1988 Phys. Rev. Lett. 61 165) for the ejected electron moving in the combined field of the residual photon and of the laser. We present a more precise treatment of the small-energy region of the incident electron by performing the calculation of the second Born term in this energy region. Detailed calculations of the scattering amplitudes are evaluated by using the Sturmian basis expansion. The second-order Born amplitude is capable of giving a reasonable correction to the first Born approximation model in studying laser-assisted (e, 2e) problems in the low energy range.

The kinetics of the atomic relaxation induced by laser noise

We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two- and a three-level system, while the statistical fluctuations of the laser field are described by a pre-Gaussian model. The interaction of the laser-target is treated nonperturbatively by using the calculation method based on the Hermitian Floquet theory. Our aim consists in studying the kinetics of atomic relaxation induced by laser noise. In the resonant case with electric field strengths small with respect to the atomic unit electric strength, the present nonperturbative results are in agreement with those obtained within the rotating wave approximation of Eberly et al and Wodkiewicz et al for an atom modelled by a two-level system. We discuss some examples which demonstrate the destruction of atomic coherence by the noise, the regime of relaxation to the equilibrium state and the optical analogue of motional narrowing. We also give new results for two- and three-level systems, and for a strong laser field at exact resonance, in the case of phase, amplitude noises. The case of fluctuation due to collisions is also discussed. Our numerical results indicate that ionization effects, in the presence of laser noise, can lead to important modifications of the populations for strong laser-atom interactions. The changes in the ionization rates generated by the noise are also investigated.

Electron impact ionisation of helium-like ions

We present in this paper a theoretical study of the single ionisation by electron impact of positive ions belonging to the helium isoelectronic sequence. Using the Coulomb-Born approximation, we obtain the cross sections for the ionisation of these ions from the ground state and from the metastable states 21S and 23S. Our theoretical results are in good agreement with the available experimental data.

Weakly nonlinear analysis and localized structures in nonlinear cavities with metamaterials

We consider an optical ring cavity filled with a metamaterial and with a Kerr medium. The cavity is driven by a coherent radiation beam. The modelling of this device leads to the well known Lugiato-Lefever equation with high order diffraction. We show that this effect alters in depth the space-time dynamics of this device. A weakly nonlinear analysis in the vicinity of the first threshold associated with the Turing instability is performed. This analysis allows us to determine the parameter regime where transition from super- to sub-critical bifurcation occurs. When the modulational instability appears subcritically, we show that bright localized structures of light may be generated in two-dimensional setting. Close to the second threshold associated with the Turing instability, dark localized structures are generated and their snaking bifurcation diagram is constructed.

Electron-impact elastic scattering of helium in the presence of a laser field: non perturbative approach

We report a detailed analysis of electron-helium scattering in the presence of a laser field; focusing on the elastic process of helium atoms from the ground state 11 S. The process under investigation is dealt with a nonperturbative approach using the Volkov wave function to describe the incident and scattered electrons, while the laser–target interaction is treated by using the Floquet method. The interaction of the incident electron with the atomic target is treated within the first Born approximation. Our results are perfectly consistent with the experimental data of DeHarak et al and with the Kroll–Watson approximation results for both one and two photon emission. We have investigated the effect of nonresonant and near resonant laser field on the electron–helium elastic collision process. It was found that the differential cross section is sensitive to the intensity and the frequency of the laser field. In the case of a non resonant laser field, dressing effects are important at small scattering angles. For a near-resonant laser photon energy, those effects are strongly reduced in the forward direction.

Periodic and Localized Structures in a Photonic Crystal Fiber Resonator

We consider a photonic crystal fiber resonator , driven by a coherent beam. The threshold for appearance of dark localized structures is estimated analytically and numerically by using a weakly nonlinear analysis in the vicinity of the modulational instability threshold. The nonlinear analysis allows to determine the parameter regime where the transition from supercritical to subcritical modulational instability takes place. This transition determines the threshold associated with the formation of dark cavity solitons. Numerical simulations of the governing model equation are in good agreement with the analytical results.

Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials

We consider an optical ring cavity filled with a metamaterial and with a Kerr medium. The cavity is driven by a coherent radiation beam. The modelling of this device leads to the well known Lugiato-Lefever equation with high order diffraction term. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction effect allows us to stabilise dark localised structures in this device. These structures consist of dips or holes in the transverse profile of the intracavity field and do not exist without high-order diffraction effects. We show that high order diffraction effects alter in depth the space-time dynamics of this device. A weakly nonlinear analysis in the vicinity of the first threshold associated with the Turing instability is performed. This analysis allows us to determine the parameter regime where the transition from super- to sub-critical bifurcation occurs. When the modulational instability appears subcritically, we show that bright localised structures of light may be generated in two-dimensional setting. Close to the second threshold associated with the Turing instability, dark localised structures are generated.