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Optica Acta International Journal of Optics

Tri-level Echo in the Case of Exciting Pulses with Arbitrary Shapes

Igor V. Yevseyev, Valery M. Yermachenko, Решетов Владимир Александрович

Published Jun 1, 1983• 8 citations
Publisher

Abstract

In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.

DOI
10.1080/713821263

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Optics and Spectroscopy•Sep 1, 2006•7 citations
In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.
A theory is developed for the modified tri-level photon echo formed in gaseous media. Consideration is given to the cases when echo is generated both by atoms for molecules with zero nuclear spin and by atoms with non-zero nuclear spin. In the first case, it is shown that this particular kind of photon echo can be used to measure the relaxation characteristics of the multipole moments of the optically forbidden transition. On the basis of these considerations new experiments are suggested for the observation of the relaxation characteristics mentioned above. In the second case, formulae are obtained for the calculation of pre-exponential factors describing the dependence of the quantum beats of the intensity of the modified tri-level photon echo as a function of the time intervals between the exciting pulses. Values of the pre-exponential factors need to be known in order to correctly obtain spectroscopic information about an optically forbidden transition.
With regard to the depolarizing collisions the polarization properties of the photon echo formed by two exciting pulses linearly polarized at an angle ψ to each other with arbitrary values of their areas and arbitrary ratios of the durations and the time of reversible Doppler relaxation are obtained. The case of the small area of the first exciting pulse is examined. It is shown that the polarization properties of the photon echo can be described by equations obtained in the limit of small areas for both the first and the second exciting pulses up to the area of the second exciting pulse of the order of unity.
A technique for the derivation of the electric field strength of varieties of photon-echo signals formed by exciting pulses with smooth envelopes is developed. This technique is based on joint solution of the d'Alembert and Schrödinger equations. The matrix of the evolution operator is constructed, which permits a description of the state of an individual atom (molecule) resulting from the action of an arbitrary exciting pulse sequence. The special form of exciting pulses with smooth envelope considered here is, together with the model of rectangular exciting pulses, one of the models that permits an analytical solution when the areas of the exciting pulses are not small. As an example, the technique is applied to the calculation of the electric field strength of signals of the modified three-level photon echo and the three-level photon echo formed by exciting pulses with smooth envelopes. The signal characteristics of photon-echo varieties formed by rectangular and non-rectangular exciting pulses are compared. It is shown that if the spectral lines of the resonant transitions are broad then the shapes and the peaks of the echo signals depend essentially on the shapes of the exciting pulses. The appearance of the fine structure of the modified three-level photon-echo and three-level photon-echo signal shapes is predicted. The necessity of setting up experiments aimed at observing the theoretically predicted special features of these photon-echo varieties is pointed out.
The modified stimulated photon echo is proposed as a method for the investigation of elastic collisions of excited atoms with non-excited foreign gas atoms, which induce the redistribution of the excited atoms in Zeeman sublevels. Such collisions cause the difference in the population, orientation and alignment relaxation times of a resonant level. It is shown that the proper choice of mutual orientation of the exciting-light polarisation vectors makes it possible to determine the relaxation times for the population, orientation and alignment of a resonant level. It is found that the formulae, derived in the limit of exciting-pulse small areas, are the most attractive for spectroscopic purposes, as in this case the polarisation properties of the modified stimulated photon echo do not depend on the exciting-pulse shapes, nor on their areas. A detailed discussion of the experimental results of Hartmann and collaborators (1979) and of Keller and Le Gouet (1984), mainly concerned with the investigation of the modified stimulated photon echoes in gases, is carried out.
A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.