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Journal of Physics B Atomic and Molecular Physics

Non-stationary two-photon resonant third-harmonic generation

A V Ivanova, G G Melikyan

Published Feb 14, 1985• 2 citations
Publisher

Abstract

A theoretical model of resonant third-harmonic generation and two-photon induced fluorescence in a gas, based on the canonical variant of the method of averages, is presented. The effect of an intermediate metastable state on the kinetics and the lineshapes of these processes, where the metastable state lifetime is in excess of the pulse duration, is studied. The results are compared with the data on an experiment carried out by Wang and Davis (1975) in thallium vapour.

DOI
10.1088/0022-3700/18/3/030

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A theoretical model of resonant third-harmonic generation and two-photon induced fluorescence in a gas, based on the canonical variant of the method of averages, is presented. The effect of an intermediate metastable state on the kinetics and the lineshapes of these processes, where the metastable state lifetime is in excess of the pulse duration, is studied. The results are compared with the data on an experiment carried out by Wang and Davis (1975) in thallium vapour.
The effect of temporal coherent control on the two-photon resonant third-harmonic generation in the continuum of ionization of an atomic system is experimentally investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference in the third-harmonic generation, as a function of delay between pulses, is reported. The transition from a resonant to a nonresonant case is also shown. The results agree with the predictions of a recently published theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation that is much shorter than the pulse duration.
The effect of temporal coherent control on the two-photon-resonant third-harmonic generation and multiphoton ionization into the continuum states of an atomic system is experimentally and theoretically investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference as a function of the delay between the pulses is reported. The transition from the resonant to the nonresonant case is also shown. The obtained results agree with the prediction of a theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation, which is much shorter than the pulse duration.
Three-photon resonantly enhanced third harmonic generation in a collisionally self-broadened gas of two-level atoms, appropriately buffered to allow phase matching, achieves maximum output when the input frequency is sufficiently detuned from exact resonance to avoid excessive self-absorption of the third harmonic. For a given active gas density or laser detuning there exists a relation between the buffer gas density, active gas density and laser detuning which maximizes the third harmonic intensity. The optimal combination depends only on the physical characteristics of the tripling medium and the buffer gas. When the third harmonic is maximized the absorption coefficient alpha and the sample length L combine so that alpha L is of order unity. The characteristics of three-photon resonantly enhanced third harmonic generation in a buffered gas are analysed in detail.
We have observed fluorescence and ionization signals resulting from two-photon resonant excitation of thallium in an atomic beam. The output of a pulsed dye laser is used to excite the resonance between the ground state (6('2)P(,1/2)) and an excited n('2)P state of thallium. Both two-photon absorption and three-photon absorption occur simultaneously; the latter results in photoionization of the atom. The excited states populated by two-photon absorption decay via cascade fluorescence back to the ground state; one or more of these spectral components constitute our fluorescence signal. The lifetimes of the excited n('2)P states of thallium have been measured directly by observing the exponential decay of this fluorescence. Calculations are included to ascertain the time required for the fluorescence signal to reach within 2% of a simple exponential decay. This decay is a measure of the lifetime of the initial state, under the condition that none of the fluorescence components arise from states which are populated by cascade through longer-lived states. The lifetimes of the n('2)P(,1/2) and n('2)P(,3/2) states of thallium for n = 7 to 11 are determined in this manner and compared with the values deduced from semi-empirical calculations of oscillator strengths by various authors. For calculations employing the effects of core polarizability in the electron wavefunctions and in the transition matrix elements, the agreement is very good--to within our experimental uncertainty, which is typically(, )<5%. Our measurements are also compared to the four other known experimental values for such excited states of thallium. Some of these previous experiments and calculations were carried out in conjunction with parity non-conservation experiments in thallium. Our measurements may provide useful checks on the accuracy of some of the calculations performed in the evaluation of such experiments. The ionization and fluorescence signals are also studied under conditions of strong saturation of the two-photon resonance with the 7('2)P states. The manifestation of saturation in the ionization signal is a broadening of the excitation spectrum, which is found to greatly exceed that of the fluorescence signal. Furthermore, the ratio of the ionization signal to the fluorescence signal at the peak of the resonance is found to vary linearly at intensities below about 10('9) W/cm('2); this too saturates at higher intensities. Various models are employed to simulate the observed behavior, encompassing both rate equations as well as density matrix formulations. The numerical solutions to these models are compared with the observed behavior; the agreement is found to depend strongly on the assumed experi- mental conditions to which the ensemble of atoms is subjected.
We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.