Low-frequency Laser Field Research Articles

Low-energy electron-He scattering in a low-frequency laser field

A method for calculating the laser-assisted, electron-potential scattering differential cross section that is based on the Floquet-Lippmann-Schwinger equation is presented. The method is applied to the laser-assisted, low-energy electron-helium scattering in a ${\mathrm{CO}}_{2}$ laser field, in the static no-exchange approximation, for the scattering geometry in which the polarization vector of the laser field is parallel to the direction of the incident electron. We compare our results with the low-frequency approximation of Kroll and Watson [Phys. Rev. A 8, 804 (1973)] and find, overall, reasonable agreement. An alternative derivation of the Kroll and Watson low-frequency approximation, starting from the Floquet-Lippmann-Schwinger equation, is given in an appendix.

Diffraction electron-atom scattering in an intense low-frequency laser field

An explanation of discrepancies between predictions of the Kroll-Watson theory and cross sections measured in the Wallbank-Holmes experiments on electron-atom scattering in the presence of a powerful low-frequency laser field is presented. Our model calculations for helium and argon as target atoms come out to be in good agreement with experimental results; i.e., obtained cross sections are by many orders of magnitude larger than those predicted by the Kroll-Watson theory. A mechanism responsible for such a substantial increase of the calculated cross sections is found to be due to the diffraction scattering of electrons by atomic obstacles. {copyright} {ital 1997} {ital The American Physical Society}

Off-shell low-frequency approximation for potential scattering in a strong laser field: eikonal versus [1,1] Padé approximation

Analytical and numerical results for the T-matrix and the total cross section for scattering by a Yukawa potential in a strong low-frequency laser field are presented. They are based on our recently derived off-shell low-frequency approximation. The conditions under which the results by Daniele and co-workers can be applied are analysed. Expressions for the T-matrix and for the total cross section for scattering in a laser field in the eikonal approximation are derived. The total cross section is presented in the form of an eikonal multiple scattering series as a product of two factors. One of these factors only depends on the type of the scattering potential, while the other depends on the parameters of the scattered particle and the laser field. The results obtained are in good agreement with our earlier findings derived by using the [1,1] Padé approximation.

Methods for the measurement of the duration of high-harmonic pulses

We present two methods for measuring the duration of ultrashort high-harmonic pulses produced by an intense laser pulse propagating in an atomic gas. Both methods rely on the nonlinearity of ionization of atomic gases by optical laser pulses. In the first method, the same medium is used for the dual purpose of generating and measuring the high harmonics. The second method uses atomic photoionization in an intense low-frequency laser field to produce the optical analog of a ``streak camera'' capable of subfemtosecond resolution.

Tunnel ionization of H_{2} in a low-frequency laser field: A wave-packet approach

The dynamics of multielectron dissociative ionization (MEDI) of ${\mathrm{H}}_{2}$ in an intense IR laser pulse are investigated using a wave-packet propagation scheme. The electron tunneling processes corresponding to the successive ionizations of ${\mathrm{H}}_{2}$ are expressed in terms of field-free Born-Oppenheimer (BO) potential energy surfaces (PES) by transforming the tunnel shape resonance picture into a Feshbach resonance problem. This transformation is achieved by defining a new, time-dependent electronic basis in which the bound electrons are still described by field-free BO electronic states while the ionized ones are described by Airy functions. In the adiabatic, quasistatic approximation, these functions describe free electrons under the influence of the instantaneous electric field of the laser and such an ionized electron can have a negative total energy. As a consequence, when dressed by the continuous ejected electron energy, the BO PES of an ionic channel can be brought into resonance with states of the parent species. This construction gives a picture in which wave packets are to be propagated on a continuum of coupled electronic manifolds. A reduction of the wave-packet propagation scheme to an effective five-channel problem has been obtained for the description of the first dissociative ionization process in ${\mathrm{H}}_{2}$ by using Fano's formalism [U. Fano, Phys. Rev. 124, 1866 (1961)] to analytically diagonalize the infinite, continuous interaction potential matrix and by using the properties of Fano's solutions. With this algorithm, the effect that continuous ionization of ${\mathrm{H}}_{2}$ has on the dissociation dynamics of the ${\mathrm{H}}_{2}^{+}$ ion has been investigated. In comparison with results that would be obtained if the first ionization of ${\mathrm{H}}_{2}$ was impulsive, the wave-packet dynamics of the ${\mathrm{H}}_{2}^{+}$ ion prepared continuously by tunnel ionization are markedly nonadiabatic. The continuous ionization appears to give rise to a population in the dissociative continuum that is localized at small internuclear distances throughout the action of the laser pulse, and is released only when the laser pulse is over, yielding a complex fragment kinetic energy spectrum. Comparison with available experimental data is made.

Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field.

We generalize the recently formulated theory of high-order harmonic generation by low-frequency laser fields to the case of high-order sum and difference frequency mixing in a two-color field of noncommensurate frequencies in the optical-infrared regime. Our theoretical description includes both the single-atom response and propagation. We observe a different behavior of the sum and difference frequency mixing processes, in the single-atom response as well as in the propagation results. The results of our calculations including propagation compare very well with recent experimental observations.

Field-ionization rates of the hydrogen molecular ion

We calculate the quasienergies and wavefunctions of the hydrogen molecular ion perturbed by a strong external electric field. Results are obtained for static-field ionization rates of the lowest dressed states. The nonlinear Stark shifts are also calculated for weak and strong fields for a range of internuclear separations. Charge and current densities are obtained and used to explain the ionization resonance structure. The ionization currents are found to be very sensitive to field strength and internuclear distance. There is evidence of critical distances that indicate the validity of Coulomb explosion models and electron localization. However, for this system, the results do not agree well with simple over-barrier models of electron release. Multiphoton ionization rates of low-frequency intense laser fields are estimated by cycle averaging.

High-order harmonic generation in a bichromatic elliptically polarized laser field

The quantum theory of high-order harmonic generation by a low-frequency laser field is generalized to the case of a bichromatic elliptically polarized laser field. The quasiclassical cutoff law is analyzed. Numerical results for a linearly polarized bichromatic laser field are presented and analyzed for different laser field frequencies, intensities, and relative phases. Harmonic intensity is many orders of magnitude higher in the bichromatic case than in the monochromatic one, but the cutoff is shifted toward the lower harmonics. The plateau height can be controlled by changing the relative phase of the fields. A qualitative agreement with the recent experiments is shown. \textcopyright{} 1996 The American Physical Society.

Spatial asymmetry in the photofragmentation of diatomic molecules using coherent control.

A calculation of the spatial distribution of ion emission in the phase-controlled, two-color photodissociation of diatomic molecules in intense, low-frequency laser fields is presented. Using atomic orbitals, we determine the time average of the electronic charge distribution at the critical internuclear separation, the point at which electron localization occurs. We find qualitative agreement with a recent experiment with ${\mathrm{HD}}^{+}$, which shows asymmetry in the counterintuitive direction. We predict that ${\mathrm{H}}_{2}^{+}$ and lower frequencies will give even better agreement. \textcopyright{} 1996 The American Physical Society.

Collective field effects in electron - atom scattering in a low-frequency laser field

Several recent papers have examined the theory of electron - atom scattering in a low-frequency laser field. Only one of these papers obtained rough agreement with the size of the experimental cross section through the identification of a novel physical process: collective field effects. The purpose of this paper is to demonstrate that an error in the formulation led to an overestimate of the interaction potential by five orders of magnitude. The experimental results cannot be explained by collective field effects.

Theory of high-order harmonic generation by an elliptically polarized laser field.

We generalize a recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L'Huillier et al., Phys. Rev. A 48, R3433 (1993)] to the case of an elliptically polarized light. Our theoretical description includes both the single-atom response and propagation. Phase matching significantly modifies the results obtained in the single-atom response. The results of our calculations, including propagation for both the intensity and polarization properties of harmonics as a function of laser ellipticity, compare very well with recent experimental observations. \textcopyright{} 1996 The American Physical Society.

Low-energy electron - argon scattering in a low-frequency laser field

We have used several non-perturbative Floquet methods to calculate the differential and total cross sections for electron scattering from argon in a laser field. One method utilizes the mixed-gauge R-matrix technique to calculate the scattering cross section. A diabatic approximation adopted from molecular applications is also applied to this low-frequency limit. Results are compared with the well known Kroll - Watson approximation. We find that all three theoretical treatments agree well with each other but do not agree with some experimental results. Possible explanations for the discrepancy between the calculations and experiments are examined.

A classical and semiclassical study of electron - atom collisions in the presence of mono- and bichromatic low-frequency laser fields

Laser-assisted electron - atom collisions are studied using classical mechanics and short- and long-ranged model potentials for the electron - atom interaction. The classical energy transfer is compared with the values predicted by the soft-photon approximation and the differences are related to an adiabaticity parameter, which indicates the ratio of the time scales involved. Radiation of arbitrary polarization and the case of the combination of a laser fundamental and its first or second harmonic are also considered.

Phase of the atomic polarization in high-order harmonic generation.

A recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L'Huillier et al., Phys. Rev. A 48, R3433 (1993)] allows us to study the phase of the induced atomic dipole moment. We show that this phase exhibits a piecewise-linear dependence on the laser intensity. This dependence can be interpreted in quasiclassical terms, and is related to the action acquired by the electron during its motion in the laser field. The value of the phase, however, is also affected by the quantum effects of tunneling, diffusion, and interference. The phase of the dipole moment considerably influences the conversion efficiency, as well as the coherence properties, of the harmonics generated in macroscopic media.

THEORY OF BARRIER-SUPPRESSION IONIZATION OF ATOMS

The theoretical description of the ionization of an atom (ion) by external electromagnetic radiation up to now concerned two alternative situations; multiphoton ionization and tunneling ionization. For both cases the formulas describing the ionization probability when the intensity of the laser field is not too strong are well known. However, if the field is strong, then there exists a new channel; the so-called barrier-suppression (or above-barrier) ionization of the atom. How does this process occur? It is obvious that barrier-suppression ionization and sub-barrier tunneling ionization by low-frequency laser field transform smoothly into one another as the field strength F is varied near the value of the barrier-suppression field F BSI . This paper contains a review of various theoretical approaches developed during the last few years, especially analytical considerations. Some new semi-analytical expressions for ionization rates, energy and angular distributions of ejected electrons are also derived.

Inelastic fast-electron-hydrogen-atom collision in a laser field.

The laser-assisted electron-impact excitation of 2s and 2p dressed states of hydrogen is studied. The interaction of a linearly polarized laser field with the colliding system is treated by the nonperturbative Floquet theory, while the interaction of the fast incident electron with the target atom is treated in the first Born approximation. The nonresonant collision in a low-intensity, low-frequency laser field is dominated by the process with no exchanged photon with the field, while at larger intensities the collision accompanied by the exchange of real or virtual photons is much more important. For the stimulated bremsstrahlung, the 1s\ensuremath{\rightarrow}2s transition is strongly influenced by the resonant coupling between the final 2s and the intermediate 3p states. In the resonant cases, where laser frequency matches a transition frequency between the initial or final and an intermediate state, the collisions with the largest cross section are those in which the projectile induces a dipole transition in the atom.

Two-color multiphoton ionization of atoms using high-order harmonic radiation.

Laser-assisted single-photon ionization of an atomic system can be observed in the simultaneous presence of a strong low-frequency laser field and of one of its (weaker) high-order harmonics. Typical photoelectron spectra associated to such two-color processes are simulated via the numerical solution of the time-dependent Schr\"odinger equation, for a hydrogen atom in the presence of both fields. We address the question of the interplay between this laser-assisted process and above-threshold ionization. Our results show that new sets of two-color experiments can be performed at moderate laser intensities easily attainable by currently operated sources.

On-shell and off-shell low-frequency approximations for potential scattering in a strong laser field-optical theorem and sum rule

We present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-frequency laser field. Presented results, based on recently derived expressions for the off- and on-shell low-frequency T matrices are beyond the first Born approximation results of Daniele et al. (1986) for scattering on the Yukawa potential in a laser field. An analytical expression for the total cross section is obtained using the (1,1) Pade approximant to the off-shell low-frequency T matrix. This result explicitly shows departure from the sum rule and it is analysed as function of the laser field intensity and polarization angle. If the laser field is so strong that the laser field induced scattering particle impulse eA0 is comparable with the initial impulse pi this departure has a maximum. For an ultra-strong laser field (eA0>>pi) the total cross section is small in comparison with the field-free section, i.e. the influence of the scattering potential is weak. The results for different values of the screening radius are also presented and it is observed that the departure from the sum rule is larger for long-range potentials (when the interplay between the potential and the intense radiation field is important). The departure is strong for small values of the polarization angle ( Theta i<20 degrees ) and weak for 45 degrees < Theta i<135.

Theory of high-harmonic generation by low-frequency laser fields.

We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law ${\mathit{I}}_{\mathit{p}}$+3.17${\mathit{U}}_{\mathit{p}}$, where ${\mathit{I}}_{\mathit{p}}$ is the atomic ionization potential and ${\mathit{U}}_{\mathit{p}}$ is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

Inelastic electron-atom scattering in the presence of an elliptically polarized low-frequency laser field

The Kroll-Watson theory has previously been extended to scattering by an atomic target. The theory and its extension were both done for a linearly polarized laser. The theory is extended to general polarization with the surprising result that off-shell information on the scattering process enters at the level of omega 1. It does not appear for linear polarization. The result depends upon no approximations other than an expansion in powers of omega . The connection to existing experiments and previous theory is described.