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SATURATION ASPECTS OF TWO-PHOTON SPECTROSCOPY OF $Na_{2}$ MOLECULES

J. P. Woerdman, Martin F. H. Schuurmans

Published Jan 1, 1978• 0 citations
OpenAlex

Abstract

We report on the saturation behavior of the $Na_{2}$ two-photon transition at 602.17 $^nm^{1,2}$ This transition has a dominant near-resonant intermediate level; the off-resonance $\\Delta$ is of the order of the Doppler width $\\Delta \\nu_{D}$. The dominant contribution to the Doppler-free two-photon line then cornea from two velocity packets of molecules which are Doppler-shifted into resonance. This results in some novel experimentally confirmed aspect, of the two-photon absorption: (i) the ratio of the amplitudes of the Doppler-free and Doppler-broadened two-photon lines is much larger than in the case $\\Delta \\gg \\Delta \\nu_{D}$, and (ii) the Doppler-free line saturates much stronger than the Doppler-broadened line. The resonant velocity packets of molecules are dominantly saturated on the ground-to-intermediate-level transition. The saturation power density is $\\sim 0.5 W/cm^{2}$; this value is consistent with a recent measurement of the Franck-Condon factors $involved^{3}$

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
SATURATION ASPECTS OF TWO-PHOTON SPECTROSCOPY OF Na2Na_{2}Na2​ MOLECULES
We report on the saturation behavior of the Na2Na_{2}Na2​ two-photon transition at 602.17 nm1,2^nm^{1,2}nm1,2 This transition has a dominant near-resonant intermediate level; the off-resonance Delta\\DeltaDelta is of the order of the Doppler width DeltanuD\\Delta \\nu_{D}DeltanuD​. The dominant contribution to the Doppler-free two-photon line then cornea from two velocity packets of molecules which are Doppler-shifted into resonance. This results in some novel experimentally confirmed aspect, of the two-photon absorption: (i) the ratio of the amplitudes of the Doppler-free and Doppler-broadened two-photon lines is much larger than in the case DeltaggDeltanuD\\Delta \\gg \\Delta \\nu_{D}DeltaggDeltanuD​, and (ii) the Doppler-free line saturates much stronger than the Doppler-broadened line. The resonant velocity packets of molecules are dominantly saturated on the ground-to-intermediate-level transition. The saturation power density is sim0.5W/cm2\\sim 0.5 W/cm^{2}sim0.5W/cm2; this value is consistent with a recent measurement of the Franck-Condon factors involved3involved^{3}involved3
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
Several paths to populate the final state of the 2-photon transition have been analyzed in this paper. It is pointed out that the contributions by the two packets of molecules with particular velocities to the Lorentzian peak will gradually dominate over the line shape as the offset of the intermediate state reduces. With more intense laser beams, the population of the two packets of molecules in the final state tends to be saturated, which causes the decrease of the peak ratio. By using the equations of motion for the density matrix, it has been proved theoretically that the actual population of the intermediate state results in the deformed line shape. We tried two methods to eliminate the Doppler-broadening backgrounds of the 2-photon transitions and enhanced the spectral resolution. The results discussed in this paper might promise their applications to the study of molecular high-lying states.
Discusses the theory of Doppler-free two-photon transitions. The theory is worked out for the case of one arbitrarily strong field and one weak field. The Doppler limit is assumed. These simplifications allow the authors to discuss the experimental manifestations of various parameters. They consider power shifts and broadening the number of resonant peaks and their positions. The general case of an off-resonant intermediate state and the single-frequency case with a resonant intermediate state are discussed. The former is found to lead to a power shift, whereas the latter is unshifted in a certain region. In addition the resonant case gives an enhancement without an appreciable increase in width.
We generalize the two-photon probe-absorption coefficient to include any amount of Doppler broadening and an arbitrarily intense saturator wave. By analytically performing integrals over a Lorentzian velocity distribution we are able to examine the transition from homogeneous broadening to extreme Doppler broadening for both zero and nonzero Stark shifts. For Doppler widths much larger than the saturator Rabi flopping frequency, the probe-absorption spectrum approaches a Doppler-free Lorentzian with width equal to the homogeneous linewidth and center displaced by the dynamic Stark shift.
We consider in this paper the Doppler-broadened absorption by two-level molecules of a gas from a weak traveling electromagnetic plane wave in the presence of an oppositely traveling strong plane wave at the same frequency. Here the absorption spectrum exhibits a dip that broadens and deepens as the gas is increasingly saturated by the strong wave. This saturation effect has been employed in the recent experiments on the fine structure of atomic hydrogen performed by H\"ansch, Shahin, and Schawlow (HSS). The form, linewidth, and strength of saturation dips in the fine-structure lines are studied for experimental parameters appropriate to the hydrogen experiment. In addition, saturation line-shape curves are calculated for experimental situations in which the strengths of the stronger field give rise to stronger or weaker saturation of the gas medium and varying degrees of Doppler broadening exist. The calculation of shape of the saturation dip and absorption curves for a Doppler-broadened gas of two-level atoms is made exactly; in effect, the strong field is treated as arbitrarily strong by avoiding a perturbation-theory treatment in favor of the exact solutions for a driven two-level system. The general behavior found is in accord with intuition and experimental observations by HSS. There is an optimum saturation power which gives a prominent dip and beyond which the dip suffers "power broadening."
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.