The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} ${10}^{9}$ larger than the case of equal-frequency photons with no loss in resolution.The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} ${10}^{9}$ larger than the case of equal-frequency photons with no loss in resolution.

Physical Review AAug 1, 1976149 citations

Two-photon absorption without Doppler broadening

M. D. Levenson

IEEE Journal of Quantum ElectronicsSep 1, 19740 citations

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

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

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 $involved^{3}$ 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 $involved^{3}$

Jan 1, 19780 citations

{10}^{9}

larger than the case of equal-frequency photons with no loss in resolution.

SATURATION ASPECTS OF TWO-PHOTON SPECTROSCOPY OF

Na_{2}

MOLECULES

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}