A theoretical model for superradiant damping effect in inhomogeneously broadened media and its application to photon-echo problems are discussed. Only optically thin systems are considered, and all nonradiative relaxation mechanisms are neglected. Numerical calculations are performed for a very wide square inhomogeneous line shape and square applied pulses. It is shown that excitation of the system becomes increasingly difficult as the superradiant lifetime ${\tau }_s$ becomes comparable with $T_2^{*}$. The energy reradiated after the end of the exciting pulse is considerable for ${\tau }_s\approx T_2^{*}$ and for some applied pulse areas. Two-pulse sequences produce multiple echoes as the microscopic polarizations spontaneously rephase. The first-echo amplitude maximum is found to occur for first-applied-pulse areas increasingly above $\frac{1}{2}\pi$ as ${\tau }_s$ decreases. For a given first-pulse area, the echo intensities increase initially as ${\tau }_s$ decreases (negligible damping) and finally decrease and vanish (important damping). The ratio of the second- to first-echo amplitudes is found to be proportional to $\frac{T_2^{*}}{{\tau }_s}$ for small superradiance levels and to decrease when ${\tau }_s$ approaches $T_2^{*}$. An approximate estimate of this ratio is derived for the region of linearity in $\frac{T_2^{*}}{{\tau }_s}$.

• Received 23 October 1969

DOI:https://doi.org/10.1103/PhysRevA.1.1472