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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical echo phenomenon in the system of two-level atoms beyond the mean field approximation

P. I. Khadzhi

Published May 10, 1996• 0 citations
Publisher

Abstract

The occurrence of optical echo phenomena in two-level media is analyzed beyond the mean field approximation. The polarization of the medium and the intensity of the echo signal depend in a complex way on both the areas of the pulses and on the area of the `material' field and the relation between (on the one hand) the photon densities of each pulse and (on the other) the density of two-level atoms (excitons) of the medium.

DOI
10.1117/12.239471

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The occurrence of optical echo phenomena in two-level media is analyzed beyond the mean field approximation. The polarization of the medium and the intensity of the echo signal depend in a complex way on both the areas of the pulses and on the area of the `material' field and the relation between (on the one hand) the photon densities of each pulse and (on the other) the density of two-level atoms (excitons) of the medium.
The authors derive analytical expressions for secondary echoes formed under the two-pulse excitation of the optically dense media developing McCall-Hahn area theorem for echo effects. They find that a series of self-reviving echo signals with a total area of 2$\ensuremath{\pi}$ or 0$\ensuremath{\pi}$ is excited and propagates deep in the media demonstrating strong non-linear nature of light-matter interaction at small changes of second pulse area. The pulse area approach paves the way for precise coherent spectroscopy, the study of different photon echoes and quantum control of light pulses in the optically dense media.
The effect of two-pulse photon echoes at the complicated action on a two-level medium with large inhomogeneous broadening of supremely short and quasiresonant pulses is investigated. Two versions of the action sequence of both pulses are considered. It is shown that the temporal properties of the echo signal are depended largely on the action order of indicated pulses. The effect of suppression of the optical echoes in the both cases at the action on a medium of the supremely short zeroth 'area' pulse is predicted. The qualitative procedure of definition of the complicated echoes spatial properties has been proposed and applied. It is shown that in indicated cases the diagrams of the echo signal intensity direction are not so peaked as in the case of common light echo.
The theoretical analysis on photon echoes is reported in a resonant multi-level system with level degeneracy, by a general consideration. With respect to the system possessing more than three-fold degeneracy, the intensity of photon echoes depends not only on the areas of the exciting optical pulses, but also on their polarization characteristics. In particular, it was found that some anomalous echoes change their intensities with the polarization directions of exciting optical pulses which have different frequencies from those of the echoes because of the coherent coupling of resonant transitions with common energy level and the interference effect of transitions through the degenerate sublevels. In the first half of this paper the general formulation on the multi-level system with arbitrary degeneracy is performed, and in the second half, the application of the general theory to some typical examples is also given.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.