General expressions are derived and investigated for the degree of polarization of electrons as a result of resonant two-photon ionization of unpolarized atoms having the S state as the ground state. The exciting and ionizing electromagnetic fields have arbitrary degrees of polarization and directions of propagation. It is shown that in cases where the matrix elements of P → S transitions from the resonant state to the continuum predominante over the matrix elements of P → D transitions, completely polarized photoelectrons may be obtained. These cases are found for sodium and potassium atoms.
Two independently tunable, linearly polarized dye lasers are counterpropagated through a heat pipe containing sodium vapor. The frequency of the first laser ${\ensuremath{\omega}}_{1}$ is incremented through both 3
p2P1/2,3/2 fine-structure levels while the second laser ${\ensuremath{\omega}}_{2}$ is scanned through the energy increment necessary to reach ns
2S1/2 and
nd2D3/2,5/2 levels (n=5--35). Following excitation, ionization occurs through chemi-ionizing collisions. The polarization (defined as the ionization intensity measured when the two planes of polarization of the laser beams are parallel minus the intensity when perpendicular divided by the sum of the intensities) P=(
I?-${I}_{\ensuremath{\perp}}$)/(
I?+${I}_{\ensuremath{\perp}}$) goes from +1 to -1 as ${\ensuremath{\omega}}_{1}$ is tuned between the 3
p2P1/2,3/2 fine-structure levels. This novel polarization effect is shown to be due to an interference between the two pathways to the ns
2S1/2 levels. Upon exciting the unresolved nd
2D3/2,5/2 levels, the polarization is very close to zero when ${\ensuremath{\omega}}_{1}$ is at or near the 3p
2P3/2,1/2 levels. A simple few-level atom theory reproduces the experimental observations except for the case when both lasers are in resonance.
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3
2S1/2,F=2--3
2P3/2,F=3 transition. The intensity profile of the deflected beam was measured at different laser power levels and for different laser polarizations. Calculations using a constant force derived from a two-level atom yield deflections which are too large. The results of more realistic simulation calculations agree very well with the measured deflection. Those calculations incorporate the atomic-beam spatial and velocity distributions as well as the laser frequency distribution and polarization state. Optical pumping, loss of atoms to the nonresonant F=1 ground state, and Doppler shifting of the atoms out of resonance are all considered, as also are the statistics and angular distributions of the spontaneous photons.
Polarization rotation effects in atomic sodium vapor are studied both experimentally and theoretically. Two pulsed dye laser beams propagate collinearly through a cell containing sodium vapor. The direction of polarization of a linearly polarized dye laser beam of frequency ${\ensuremath{\omega}}_{1}$ is found to be rotated by a circularly polarized beam of frequency ${\ensuremath{\omega}}_{2}$. This rotation is due to the difference in refractive index at ${\ensuremath{\omega}}_{1}$ for right and left circularly polarized light which is produced by the circularly polarized beam. When ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ is tuned near the $3S\ensuremath{-}5S$ two-photon transition of atomic sodium, this difference is primarily due to the dispersion associated with the two-photon transition. Other sources of polarization rotation which were identified include (i) real transfers of population to excited atomic levels due to collisionally induced transitions and (ii) optically induced atomic energy-level shifts. The theory includes both the effects of two-photon dispersion and optically induced energy shifts. The application of the two-photon polarization rotation effect as a fast, optically controlled shutter or modulator and as a sensitive detection technique for two-photon spectroscopy are briefly discussed.
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
nl state, the theoretically allowed maximum value of their ratio is
23. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.