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Physical Review A

Resonant two-photon transition to the continuum from an initialJ=0 state using elliptically polarized light

Banani Datta, Santanu Bhattacharyya

Published Dec 1, 1994• 0 citations

Abstract

We have studied the transition probabilities and the photofragment energy and angular distributions in a resonant two-photon transition to the continuum with an elliptically polarized radiation field. The general formalism applies both to ionization of atoms within the framework of a single-electron model and the dissociation of diatomic molecules with the involvement of \ensuremath{\Sigma} states only. Detailed calculations for an initial J=0 state give the observable quantities as functions of detuning, intensity, and the polarization parameter for several combinations of the system parameters such as bound-bound and bound-continuum couplings and the Fano q parameter. For sufficiently intense fields the Raman-like coupling between the two coherently excited magnetic sublevels of the resonant J=1 state (one of which can be decoupled from the ground state by a linear transformation) causes a significant enhancement of the transition probability near the Fano minimum obtained for linearly or circularly polarized fields. The evolution of the photofragment kinetic-energy distribution changes with the ellipticity parameter of the radiation. The angular distribution becomes intensity dependent for general ellipticity parameters; the shapes of the resultant distribution in different space-fixed planes are discussed.

DOI: 10.1103/physreva.50.5064

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We have studied the transition probabilities and the photofragment energy and angular distributions in a resonant two-photon transition to the continuum with an elliptically polarized radiation field. The general formalism applies both to ionization of atoms within the framework of a single-electron model and the dissociation of diatomic molecules with the involvement of \ensuremath{\Sigma} states only. Detailed calculations for an initial J=0 state give the observable quantities as functions of detuning, intensity, and the polarization parameter for several combinations of the system parameters such as bound-bound and bound-continuum couplings and the Fano q parameter. For sufficiently intense fields the Raman-like coupling between the two coherently excited magnetic sublevels of the resonant J=1 state (one of which can be decoupled from the ground state by a linear transformation) causes a significant enhancement of the transition probability near the Fano minimum obtained for linearly or circularly polarized fields. The evolution of the photofragment kinetic-energy distribution changes with the ellipticity parameter of the radiation. The angular distribution becomes intensity dependent for general ellipticity parameters; the shapes of the resultant distribution in different space-fixed planes are discussed.

The polarization dependence of resonant two-photon dissociation characteristics has been investigated for

{\mathrm{HD}}^{+}

excited from the ground state by two fields of different frequencies. The change in dissociation probability with field intensity and the dissociation line shape have been shown in the case of a single intermediate resonance for all possible combinations of polarizations. The photofragment energy spectra and the branching ratio between two possible continuum-energy states have been investigated for these polarization states when two intermediate resonances are present.

The three-dimensional angular distribution of electrons in two-photon ionization of atoms by an elliptically polarized laser beam, from an initial state with arbitrary angular momentum J i , is expressed in terms of six frequency-dependent invariant atomic parameters. The specific effect of the field polarization on the angular distribution (the elliptic dichroism, ED) is discussed for the general case of elliptic polarization. The necessary conditions for a non-zero ED are established and its physical origin is explained. The general theory is illustrated by a simple analytical calculation for the -potential model. Numerical calculations of the angular distribution parameters for H and Cs atoms are also performed and the dependence of ED magnitude on the atomic quantum numbers and the photon frequency is discussed for different frequencies.

A general approach to the problem of spontaneous transfer of light-induced anisotropy in the scheme of Raman scattering of resonance elliptically polarized light is developed. Depending on the type of the field-excited ( a )↔( b ) transition, the stationary distribution of atoms over the sublevels of the final level ( c ) coupled with the excited level only by the ( b )→( c ) spontaneous transition is either isotropic and does not depend on field parameters or anisotropic. In the latter case, the anisotropy is determined by both field polarization and (at fairly large level momentum values) field detuning and intensity.

Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers

n

,

l

, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary

\mathrm{nl}

state, the theoretically allowed maximum value of their ratio is

\frac{3}{2}

. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.

We report in detail our complete characterization of atomic photoionization via a single measurement, namely, that of the two-photon photoelectron angular distribution using elliptically polarized light. Through these measurements we are able to determine the atomic parameters necessary to unambiguously describe two-photon ionization of atomic rubidium. These parameters include relative cross sections for photoionization into various outgoing channels as well as the phase difference between the continuum S and D partial waves. We present a derivation of the angular distribution with arbitrarily polarized light in terms of these cross sections and phases, demonstrate the advantages of using elliptically polarized light, discuss details of the experiment, and report the results of our measurements in this paper. While measured phase differences are in excellent agreement with expected values over the entire range of photoelectron kinetic energy of our measurements from 0 to 0.5 eV, ratios of cross sections for photoionization into the two D channels are anomalous, suggesting unexpected fine structure effects in these continua.

We report in detail our complete characterization of atomic photoionization via a single measurement, namely, that of the two-photon photoelectron angular distribution using elliptically polarized light. Through these measurements we are able to determine the atomic parameters necessary to unambiguously describe two-photon ionization of atomic rubidium. These parameters include relative cross sections for photoionization into various outgoing channels as well as the phase difference between the continuum S and D partial waves. We present a derivation of the angular distribution with arbitrarily polarized light in terms of these cross sections and phases, demonstrate the advantages of using elliptically polarized light, discuss details of the experiment, and report the results of our measurements in this paper. While measured phase differences are in excellent agreement with expected values over the entire range of photoelectron kinetic energy of our measurements from 0 to 0.5 eV, ratios of cross sections for photoionization into the two D channels are anomalous, suggesting unexpected fine structure effects in these continua.