The approximation method introduced by Keldysh is revised and extended. The technique is applicable to the photodetachment by a plane-wave field of an electron bound by a short-range potential. The approximation is to neglect the effect of the binding potential as compared to the field effects on the final state of the detached electron. By choice of a different gauge than that used by Keldysh, the formalism becomes very simple and tractable. A general basis for the formalism is developed, and it is then applied to find transition probabilities for any order of interaction for both linearly and circularly polarized plane-wave fields. The low-intensity, first-order limit and the high-intensity, high-order limit yield the correct results. Two intensity parameters are identified. The fundamental one is $z=\frac{{e}^{2}{a}^{2}}{4m\ensuremath{\omega}}$, where $a$ is the magnitude of the vector potential (in radiation gauge) of the field of circular frequency $\ensuremath{\omega}$. The second parameter is ${z}_{1}=\frac{2z\ensuremath{\omega}}{{E}_{B}}$, where ${E}_{B}$ is binding energy, and it becomes important only in the asymptotic case. With the assumption that the field leaves the neutral atomic core relatively unaffected, the formalism is applied to the example of the negative hydrogen ion irradiated by circularly or linearly polarized 10.6-\ensuremath{\mu}m radiation. Photodetachment angular distributions and total transition probabilities are examined for explicit intensity effects. It is found that total transition probability $W$ is not sensitive to intensity since $\frac{d(logW)}{d}$ ($logz$) retains low-intensity straight-line behavior up to quite high values of $z$. An important intensity effect is the major significance of higher-than-lowest-order terms when $z$ is large, especially for circular polarization. A sensitive indicator of intensity is the ratio of photodetachment probabilities in circularly and linearly polarized fields, which increases sharply with intensity. An investigation of the convergence of perturbation expansions gives the upper limit $zl[\frac{{E}_{B}}{\ensuremath{\omega}}]\ensuremath{-}\frac{{E}_{B}}{\ensuremath{\omega}}$, where the square bracket means "smallest integer containing" the quantity in brackets. This limit is $zl0.59$ for ${\mathrm{H}}^{\ensuremath{-}}$ in 10.6-\ensuremath{\mu}m radiation. The failure of perturbation theory is not necessarily manifest in qualitative ways. For example, it is not apparent in total photoelectron yield as a function of intensity.

Effect of an intense electromagnetic field on a weakly bound system

Angle-resolved photoelectron spectroscopy has been performed for more than 70 years in various guises, but recently its potential to help solve in detail problems in the photoionization dynamics and intramolecular dynamics of gas-phase molecules has been recognized. One key development has been the design of experiments in appropriate geometries to extract information that pertains to the molecular frame, another has been the development of imaging spectrometers, and a third is the use of ultrafast lasers to cause photoionization. In this review, which is aimed at experimentalists, simple expressions for photoelectron angular distributions (PADs) in various experimental geometries are given and their applications explained.

Photoelectron angular distributions.

We evaluate the maximum allowed value of the ratio between the total $N$-photon ionization rates for circularly and linearly polarized incident light. It appears that this maximum increases very rapidly with $N$.

Circular versus Linear Polarization in Multiphoton Ionization

Multiphoton ionization of rare gases by a tunable-wavelength 30-psec laser pulse at 1.06 μm

The quasistationary quasienergy state approach (QQES) is applied to the analysis of partial (n-photon) decay rates and angular distributions (ADs) of photoelectrons produced by an elliptically polarized laser field. The problem is formulated for a weakly bound electron with an energy E0 in the threedimensional δ-model potential (which approximates the short-range potential of a negative ion) interacting with a strong monochromatic laser field having an electric vector F (ωt) .T he resu lts presented cover weak (perturbative), strong (nonperturbative), and superstrong field regimes as well as a wide interval of frequencies ω extending from the tunnelling (¯ hω �| E0|) and multiphoton (¯ ω |E0|). For a weak laser field, exact equations for the normalization factor and for the Fourier coefficients of the QQES wavefunction at the origin (|r |→ 0) (that are key elements of the QQES approach for a δ-model potential) as well as for the detachment amplitudes are analysed analytically using both standard Rayleigh– Schr¨ odinger perturbation theory (PT) in the intensity, I ,o f the lase rfi eld and Brillouin–Wigner PT expansions involving the exact (complex) quasienergy � . The lowest-order perturbative results for the n-photon ADs are presented in analytic form, and the parametrization of ADs in terms of polarization- and angular-independent atomic parameters is discussed for the general case of elliptical polarization. The major emphasis is on the analysis of an ellipticity induced distortion of three-dimensional ADs and, especially, on the elliptic dichroism (ED) effect, i.e. the dependence of the photoelectron yield in a fixed direction n on the sign of the ellipticity (or on the helicity) of a laser field. The dominant role of binding potential effects for a correct description of ED and threshold effects is demonstrated, and the intimate relationship between atomic ED factors and scattering phases o ft hedetached electron is established for multiphoton detachment, including the above-threshold case.

/pdf/multiphoton-detachment-of-a-negative-ion-by-an-elliptically-172uinfvwc.pdf

Multiphoton detachment of a negative ion by an elliptically polarized, monochromatic laser field

We present a theoretical interpretation of an effect recently observed in two- and three-photon ionization of Cs. We show that the total cross sections for two- and three-photon ionization of a one-electron atom depend on the polarization of the incident light. Expressions are derived for the ratio of the cross section for circularly polarized light to that for linearly polarized, and their maximum values are obtained.

Effect of Light Polarization on Multiphoton Ionization of Atoms

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Effect of Light Polarization on Multiphoton Ionization of Atoms