We perform nonperturbative calculations of resonant multiwave mixing of two high-intensity laser beams of different frequencies both for a general three-level system and for the 3
2S1/2--3
2P1/2 electronic resonance of the sodium atom. Our calculations proceed by direct numerical integration of the density-matrix equations and subsequent Fourier analysis of the calculated time-dependent density-matrix elements. We examine the case where two nearly degenerate input beams are each detuned many collisional linewidths from electronic resonance, and the frequency difference between the input beams is tuned through a ground-state resonance. Unlike previous high-intensity analyses, each input beam can be resonant with numerous transitions simultaneously; for a three-level system, we refer to this as an ``M-type'' system, in analogy with \ensuremath{\Lambda}- and V-type systems. Calculated four-, six-, and eight-wave-mixing spectra exhibit subharmonic resonances of the type observed experimentally by Trebino and Rahn [Opt. Lett. 12, 912 (1987)]. The three-level system is studied to gain insight into the physics of these subharmonic resonances. For more quantitative comparison with experiment, we use a model that includes the 16 Zeeman and hyperfine states in the 3
2S1/2 and the 3
2P1/2 levels, and accounts for arbitrary linear polarization of the input laser radiation. The relative intensities of the resonance features in the calculated multiwave-mixing spectra show good agreement with experiment. These resonance features broaden and shift as laser intensity increases, as predicted for four-wave-mixing processes in previous, less general high-intensity analyses. Both theory and experiment also show additional resonant features in the eight-wave-mixing spectra that appear at very high intensity.
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.
The nonlinear response of sodium vapor with a laser tuned near the 4D two-photon resonance is investigated over a large range of sodium concentrations and pump intensities with emphasis on the influence of coherent cancellation effects on the induced polarizations and the primary mechanism for the generation of the new frequencies. Over a wide range of circumstances, the response of the medium is dominated by parametric four-wave mixing as compared to amplified spontaneous emission or stimulated electronic hyper-Raman scattering. Secondary four-wave-mixing fields are generated by stimulated Raman scattering of one parametric four-wave-mixing field and a coupling of these fields with the driving laser field. A sharp onset of saturation of the parametric four-wave-mixing signals with sodium number density and a transition from a quadratic to a linear power dependence is observed. Both effects are explained in terms of the two-photon cancellation effect.
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.
A polarization-rotation effect is demonstrated which utilizes the dispersion associated with $3S\ensuremath{-}5S$ two-photon transitions in sodium vapor. A linearly polarized beam at ${\ensuremath{\nu}}_{1}$ is rotated by a circularly polarized beam at ${\ensuremath{\nu}}_{2}$ when ${\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{2}$ is near the two-photon transition frequency. When combined with a polarizer a rapid optical shutter is obtained.