Elliptical billiard-ball echo model

The billiard-ball echo model is expanded to include the effects of using sub-Doppler-linewidth lasers in photon-echo experiments. The simple heuristic model which emerges explains such echo phenomena in gases as the echo time width and the degradation of echo intensity with angling of the excitation pulses. We derive simple results in the small-pulsearea limit and give formal expressions for excitation pulses of arbitrary area.