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Soviet Journal of Quantum Electronics

Properties of photon echo formed by traveling and standing wave pulses

A. I. Alekseev, Askhat M Basharov

Published Jan 31, 1981• 0 citations
Publisher

Abstract

A theoretical study is made of the photon echo which appears in a rarefied gaseous medium as a result of successive action of traveling and standing wave pulses, polarized linearly at an angle ψ. This photon echo represents a superposition of two opposite traveling waves, one of which has the polarization of a standing wave pulse, the other has a linear polarization which depends on ψ and on the parameters of a resonant atomic transition. Similar polarization features are exhibited also by coherent radiation from a resonant medium subjected to steady-state fields of the traveling and standing waves separated by some distance in space. The possibility of obtaining a characteristic narrow resonance is discussed.

DOI
10.1070/qe1981v011n01abeh005353

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arXiv:1205.5381•Journal of Physics B Atomic Molecular and Optical Physics•Oct 24, 2012•5 citations
A theoretical study is made of the photon echo which appears in a rarefied gaseous medium as a result of successive action of traveling and standing wave pulses, polarized linearly at an angle ψ. This photon echo represents a superposition of two opposite traveling waves, one of which has the polarization of a standing wave pulse, the other has a linear polarization which depends on ψ and on the parameters of a resonant atomic transition. Similar polarization features are exhibited also by coherent radiation from a resonant medium subjected to steady-state fields of the traveling and standing waves separated by some distance in space. The possibility of obtaining a characteristic narrow resonance is discussed.
A calculation is presented to describe the response of an atomic system subjected to two strong standing wave field pulses separated in time. One finds a sequence of output pulses following the input ones, reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing wave fields can prove advantageous for exploring the effects of small angle scattering on both level populations and atomic coherences. (Author)
A calculation is presented to describe the response of an atomic system subjected to two strong standing-wave field pulses separated in time. One finds a sequence of output pulses following input pulses which is reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented, and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing-wave fields can prove advantageous for exploring the effects of small-angle scattering on both level populations and atomic coherences.
The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous SF6{\mathrm{F}}_{6}F6​ excited by pulses of CO2{\mathrm{O}}_{2}O2​ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (PPP and RRR branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions (QQQ branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.
The polarization properties of the photon echo generated by two linearly polarized pulses of resonant radiation at the (6s6p)3 P 1 ↔ (6s 2)1 S 0 transition of 174Yb are investigated. A complicated polarization behavior of the photon echo versus an angle between the polarization vectors of the excitation pulses is revealed in a mixture of ytterbium vapor with inert gas. For the angles ranging from 0° to 75°, a conventional echo with its linear polarization coinciding with the second excitation pulse dominates and the echo amplitude decreases with an increasing angle. For the angles ranging from 75° to 89°, the photon echo is elliptically polarized. Finally, for an angle of 90°, the conventional echo disappears and the collision echo becomes linearly polarized along the first excitation pulse.
The polarization properties of photon echoes in strong magnetic field, when the action of this field during the time of propagation of the exciting pulses and the echo signal through the resonant gaseous medium cannot be neglected, are studied theoretically. The photon echo polarization in strong magnetic field cannot be described by the polarization vector but rather by the polarization matrix. The degree of the photon echo polarization decreases with the increase of the magnetic field strength. The dependence of the photon echo intensity on the magnetic field strength was also analyzed numerically. In strong magnetic field the fast oscillations of this intensity appear to be damping and modulated by the slower ones. The spectrum of these oscillations depend also on the spectra of the exciting pulses, so that in case of small area of the first exciting pulse its temporal shape may be reconstructed from the oscillations of the echo intensity versus the magnetic field strength.
The stimulated photon echo formed by the sequence of three laser excitation pulses in gaseous medium on the transition with the angular momentum change 0-1 is considered with an account of elastic depolarizing collisions. The polarization properties of this echo may be potentially interesting for the purposes of data processing. It is shown, that with the polarization of the first pulse orthogonal to that of the second and third pulses the appearance of the echo signal will be entirely determined by the action of collisions. The existence of this echo is determined by the difference in the alignment and the orientation relaxation rates of the excited level.