IEEE Journal of Quantum Electronics

Photon-echo behavior in the presence of extreme inhomogeneous broadening

Nozomu Takeuchi

Published Jun 1, 1975• 9 citations

Abstract

Analysis of photon-echo behavior using single-mode excitation is given. It is shown that in the presence of extreme inhomogeneous broadening, the excitation with long pulses may display a complicated echo shape. Two typical cases are treated, one in which the pulses have equal length, and the other in which the pulses have equal electric-field strength. These show a large difference in echo behavior, especially for large excitation pulse areas.

DOI: 10.1109/jqe.1975.1068612

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IEEE Journal of Quantum Electronics

Photon-echo behavior in the presence of extreme inhomogeneous broadening

Nozomu Takeuchi

Published Jun 1, 1975• 9 citations

Publisher

Abstract

DOI: 10.1109/jqe.1975.1068612

Related papers

Photon echo at the excitation of a medium by extremely short and resonant pulses

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Physical ReviewMar 10, 1969150 citations

Angular echo spectroscopy of optically dense media

Olga M. Fedotova, Oleg Kh Khasanov, T. V. Smirnova

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEDec 29, 19990 citations

Photon echoes, observed recently in ruby and in

{\mathrm{NH}}_{2}

D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.

{\mathrm{F}}_{6}

excited by pulses of C

{\mathrm{O}}_{2}

laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (

P

and

R

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 (

Q

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.