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Soviet Journal of Quantum Electronics

Two-photon absorption of ultrashort pulses in a gas

E. V. Baklanov, V. P. Chebotaev

Published Oct 31, 1977• 19 citations
Publisher

Abstract

Two-photon absorption of a continuous train of ultrashort pulses in a gas gives rise to resonances when the sum of the frequencies of two locked modes coincides with the transition frequency in the gas. It is shown that the width of these resonances is not governed by the pulse duration but by the width of the twophoton transition. Resonance intensities are of the same order of magnitude as in the single-frequency regime at the same power level. It is worth noting an important feature of the use of ultrashort pulses in studies of two-photon resonances due to the 1S-2S transition in the hydrogen atom: there is a strong increase in the efficiency of conversion of dye laser radiation to the ultraviolet range.

DOI
10.1070/qe1977v007n10abeh012851

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Two-photon absorption of a continuous train of ultrashort pulses in a gas gives rise to resonances when the sum of the frequencies of two locked modes coincides with the transition frequency in the gas. It is shown that the width of these resonances is not governed by the pulse duration but by the width of the twophoton transition. Resonance intensities are of the same order of magnitude as in the single-frequency regime at the same power level. It is worth noting an important feature of the use of ultrashort pulses in studies of two-photon resonances due to the 1S-2S transition in the hydrogen atom: there is a strong increase in the efficiency of conversion of dye laser radiation to the ultraviolet range.
We investigate the excitation of an atom or molecule via two-photon absorption induced by an ultrashort laser pulse in the perturbative intensity regime. We show that the probability for a resonant transition, i.e., with an intermediate state within the spectral width of the pulse, can be reduced to zero by pulses having a $\ensuremath{\theta}$-phase step at a certain detuning $\ensuremath{\delta}\ensuremath{\omega}$ from the central frequency. Our theoretical predictions are confirmed by numerical calculations for the $4s\ensuremath{\rightarrow}4d$ transition in the potassium atom.
Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.
The problem of two-photon interaction of atoms with the field of two standing-wave pulses is solved. It is shown that the transit broadening of the line caused by a finite pulse duration and finite transit time of atoms through the light beam is eliminated. On focusing the field a transverse velocity selection of atoms occurs that lends to a decrease of the quadratic Doppler shift of the frequency. A new value of the amplitude of the induced 1S--2S two-photon transition of hydration is obtained that is used for the calculation of the signals. The resonance amplitude in hydrogen proves to be larger for existing pulsed radiation sources than that in continuous excitation by the field.
Resonant and near-resonant two-photon excitations with ultrashort laser pulses of forbidden atomic transitions give access to a wide class of nonlinear-optical processes such as two-photon absorption, stimulated Raman scattering, four-wave sum- and difference-frequency mixing. The latter has proofed to be a powerful tool for efficient femtosecond pulse generation in the VUV-spectral range [1]. Nevertheless, up to now only few experimental results have been obtained which allow the direct observation of the coherent dynamics in two-photon induced radiation-matter interactions (see experimental papers [2-5] and monograph [6]).
A study is made of the evolution of ultrashort pulses of interrogation and generated fields, traveling across a medium after a pump pulse under two-photon resonance conditions. It is shown that, in spite of the absence of overlap of the pulses in space and time, the generated wave becomes phase-locked. The area theorem is obtained for the process in question. It is found that at large distances the second pulse should give rise to a subpulse of the interrogation field and a proportional subpulse whose area tends to zero or to 2π. This conclusion about the formation of subpulses and their limiting areas applies also in the two-photon interaction case. A report is given of an estimate of the threshold intensities of an interrogation pulse in cesium and sodium vapors. The maximum conversion efficiency is found as a function of the pump energy, parameters of the investigated medium, and frequencies of the interacting fields. It is shown that an overall conversion efficiency close to 100% can be obtained when the intensities of the pump and interrogation fields are within the capabilities of the currently available lasers.
Our recent studies of methods for obtaining ultrashort light pulses and analysis of the impact of ultrashort optical pulses on classical and quantum micro-objects with the identification of the determining role of the degree of unipolarity of pulses (maximum for strictly unipolar pulses) in the efficiency of direct laser acceleration of charged particles and excitation of atoms and molecules have been reviewed. Special attention has been paid to the coherent mode locking regime in lasers, which is implemented when the laser pulse duration is less than the relaxation time of the working transition in media with resonance amplification and absorption (laser analog of the phenomenon of self-induced transparency). Experimental data on coherent mode locking in a titanium-sapphire laser with a cell with rubidium vapor at self-induced transparency in rubidium have been presented. The interaction of ultrashort pulses in resonant media has also been analyzed.