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Physical Review A

Laser-induced detachment processes in an electric field

Bo Gao, Anthony F. Starace

Published Nov 1, 1990• 26 citations
Publisher

Abstract

An analytic momentum-space wave function for an electron in both laser and static uniform electric fields is presented. It is used to obtain analytic multiphoton detachment cross sections in a static, uniform electric field which include effects of static-field-induced electron-photon interactions. These general results are not restricted to weak laser intensities or to weak static-field strengths and depend only on (a) the electric dipole approximation and (b) the approximation that final-state electron-atom interactions are ignored. Four specific predictions of our general formulas for the most interesting case of linearly polarized light polarized along the static-field direction are presented for weakly bound electrons initially in an s state. First, the effects of a weak static electric field on N-photon detachment cross sections near threshold are shown to be described by two modulation factors, one for odd N and one for even N, which depend only on a scaled energy. Second, for photodetachment in a static electric field, effects of static-field-induced electron-photon interactions are demonstrated. Third, the lifetime against field ionization is presented. Fourth, the cross section for electric-field-induced stimulated emission is presented. Numerical results for the latter three effects are presented for the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion. The simpler case of circularly polarized light directed along the static-electric-field direction is treated briefly. In particular, we show for this case that the static- and laser-field effects are uncoupled and that the near-threshold, weak static-electric-field modulation factors for the N-photon detachment cross sections are dependent on N.

DOI
10.1103/physreva.42.5580

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Multiphoton detachment of halogen negative ions with elliptically polarized light

Christophe Blondel, F. Dulieu, Christian Delsart

Multiphoton excitation with elliptically polarized light brings out more information in the photodetachment or photoionization processes than linearly polarized light. This information can be reached by recording photoelectron angular distributions for several values of the ellipticity angle, and fitting the whole set of data with an analytic formula. We give here the appropriate formula, valid for any number N of exciting photons, with the assumptions of (1) an initially even and momentumless (J equals 0) atom or ion and (2) that after excitation of an electron, the residual core be left in an odd state. These are the conditions met by multiphoton detachment from halogen negative ions. With elliptically polarized light of (lambda) equals 1064.2 nm, we have measured the angular distributions of three-photon detached electrons from the ion I-, and four-photon detached electrons from Cl- and F-. The experimental results are quantitatively analyzed and commented on.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 6, 1996•0 citations
An analytic momentum-space wave function for an electron in both laser and static uniform electric fields is presented. It is used to obtain analytic multiphoton detachment cross sections in a static, uniform electric field which include effects of static-field-induced electron-photon interactions. These general results are not restricted to weak laser intensities or to weak static-field strengths and depend only on (a) the electric dipole approximation and (b) the approximation that final-state electron-atom interactions are ignored. Four specific predictions of our general formulas for the most interesting case of linearly polarized light polarized along the static-field direction are presented for weakly bound electrons initially in an s state. First, the effects of a weak static electric field on N-photon detachment cross sections near threshold are shown to be described by two modulation factors, one for odd N and one for even N, which depend only on a scaled energy. Second, for photodetachment in a static electric field, effects of static-field-induced electron-photon interactions are demonstrated. Third, the lifetime against field ionization is presented. Fourth, the cross section for electric-field-induced stimulated emission is presented. Numerical results for the latter three effects are presented for the H\ensuremath−{\mathrm{H}}^{\mathrm{\ensuremath{-}}}H\ensuremath− ion. The simpler case of circularly polarized light directed along the static-electric-field direction is treated briefly. In particular, we show for this case that the static- and laser-field effects are uncoupled and that the near-threshold, weak static-electric-field modulation factors for the N-photon detachment cross sections are dependent on N.
We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green's function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.
Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of ${\mathrm{H}}^{\ensuremath{-}}$ in both laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order $(\ensuremath{\sim}{I}^{2})$ in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate (S(S(S-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner's threshold law for a short-range potential is discussed.
Photodetachment from negative ions in a static electric field has been studied using ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$. These experiments were done with greater precision than previous studies and allow a quantitative comparison of data with theory. A 10-keV ion beam was sent through a region with fields of up to 1.5 kV/cm applied parallel to the beam velocity. A pulsed dye-laser beam, perpendicular to the ion beam, photoneutralized the ions. The relative cross sections were measured by detecting the resulting fast neutral atoms. Detachment below threshold and oscillations on the cross section above threshold were observed near the ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ threshold at 16 269.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and near the ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ threshold at 29 138.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The phase of the oscillations in the data is in good agreement with predictions for s-wave photodetachment in a static electric field, but the amplitude of the oscillations is found to be slightly reduced.
In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.
Exact calculations of the photoionization cross sections of ground-state H in the presence of an external electric field are presented. The oscillations obtained above the zero-field ionization limit for $\ensuremath{\pi}$ polarization do not arise from specific properties of m=0m=0m=0 states, but from cancellation effects in the oscillator strengths due to the symmetry properties of the wave functions and of the light. The dependence of the cross section upon the light polarization is thoroughly explained and agrees with recent experiments on Rb.
Multiphoton excitation with elliptically polarized light brings out more information in the photodetachment or photoionization processes than linearly polarized light. This information can be reached by recording photoelectron angular distributions for several values of the ellipticity angle, and fitting the whole set of data with an analytic formula. We give here the appropriate formula, valid for any number N of exciting photons, with the assumptions of (1) an initially even and momentumless (J equals 0) atom or ion and (2) that after excitation of an electron, the residual core be left in an odd state. These are the conditions met by multiphoton detachment from halogen negative ions. With elliptically polarized light of (lambda) equals 1064.2 nm, we have measured the angular distributions of three-photon detached electrons from the ion I-, and four-photon detached electrons from Cl- and F-. The experimental results are quantitatively analyzed and commented on.