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Soviet Journal of Quantum Electronics

Influence of diffraction on formation of photon echo signals

Sergey M. Zakharov, Yu D Lysak, Edward A. Manykin

Published Apr 30, 1987• 0 citations
Publisher

Abstract

A theoretical analysis is made of the formation of photon echo signals under one-photon resonance conditions when a medium is excited by light pulses with a finite transverse aperture. Basic equations are formulated and a method of solving these within the limits of perturbation theory using Green's functions is indicated. An analysis is made of some analytic solutions. An expression is derived to describe the spatial profile of the photon echo signal under diffraction conditions.

DOI
10.1070/qe1987v017n04abeh008626

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A theoretical analysis is made of the formation of photon echo signals under one-photon resonance conditions when a medium is excited by light pulses with a finite transverse aperture. Basic equations are formulated and a method of solving these within the limits of perturbation theory using Green's functions is indicated. An analysis is made of some analytic solutions. An expression is derived to describe the spatial profile of the photon echo signal under diffraction conditions.
In this chapter, we provide a review of early theoretical studies on the photon echo in gases. We derive the basic equations, which will be employed in this monograph for the theoretical description of electromagnetic processes in gas media. For the elementary case when the angular momenta J b , and J a of the upper ( b ) and lower ( a ) resonant levels are equal to 1 and 0, respectively, we analyze the formation of photon echo and stimulated photon echo signals in the case of an inhomogeneously broadened spectral line corresponding to an optically allowed b → a transition. We discuss characteristic parameters involved in the theory of photon echo in gas 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 semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
An analysis is made of the influence of the phase matching conditions on the four-photon scattering spectrum at a one-photon resonance under various focusing conditions. An analytic expression is obtained for the phase matching integral in the limiting cases of hard focusing and strong absorption in a medium with the cubic nonlinearity. A study is made of the influence of one-photon resonances on the form of the spectrum of four-photon scattering by excited and preionisation states of atoms. Calculations are reported of the four-photon scattering spectra in which allowance is made for the interference of the resonant and nonresonant components of the third-order nonlinear susceptibility. A method for the normalisation of the experimental four-photon scattering spectra under one-photon resonance conditions is proposed; this method allows for the distortions associated with the influence of the phase mismatch and of one-photon absorption.