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IEEE Journal of Quantum Electronics

Frequency conversion involving Raman-like processes above the ionization threshold

Yves Gontier, M. Trahin

Published Jul 1, 1982• 21 citations
Publisher

Abstract

Resonant and nonresonant frequency conversion probabilities for processes taking place above and below the ionization threshold in hydrogen are compared. The frequency of the emitted radiation is different from any characteristic frequencies of the medium and cannot be resonantly reabsorbed. It is shown how particular resonances can enhance emission processes while keeping unchanged the losses coming from lowest order ionization.

DOI
10.1109/jqe.1982.1071666

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Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of $N$, where $N$ is the number of intense photons absorbed or emitted during the transition. For larger values of $N$ the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.

Physical Review A•Jan 1, 1973•12 citations
Resonant and nonresonant frequency conversion probabilities for processes taking place above and below the ionization threshold in hydrogen are compared. The frequency of the emitted radiation is different from any characteristic frequencies of the medium and cannot be resonantly reabsorbed. It is shown how particular resonances can enhance emission processes while keeping unchanged the losses coming from lowest order ionization.
An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.
The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.
When a radiation field of frequency ω1 interacts with atoms, etch of which has a transition frequency ω b a =(E b -E a )/\hbar, with ω1-ω b a =Δ≠0, nonresonant absorption can take place with probability P 1 inversely proportional to Δ 2 (a pressure broadening). When another radiation field of frequency ω2, such that ω1+ω2=2 ω b a , interacts simultaneously with the gas a resonant two-photon absorption can take place in addition to the nonresonant absorption. The probability of this two-photon absorption process, P 2, is found to be inversely proportional to Δ 4. If \varOmega=| <n-1|E|n ><b| µ|a >| is the Rabi frequency of the transition, it is found that P 2/(P 1(Δ)+P 1(-Δ)) is given by 12{ \varOmega(-Δ)\varOmega(-Δ)}2/{Δ 2(\varOmega(-Δ)2+\varOmega(Δ)2)}.
Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of NNN, where NNN is the number of intense photons absorbed or emitted during the transition. For larger values of NNN the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.