Efficient photon echoes in optically thick media

We present the results of analytical and numerical calculations of the amplitude and temporal shape of photon echoes produced in optically thick absorbing media. In particular, we are interested in echo output signals that mimic the temporal shape of one of the input pulses (the data pulse). Echo recall efficiencies of temporally structured data pulses exceeding unity can be obtained in optically thick media while preserving the information content of the data pulse. We find that the relationship between the maximum echo efficiency and the Beer's length at which that maximum is attained is nearly linear. This linear relation holds well beyond the optimal absorption length predicted by linear theory for both two-pulse photon echoes and three-pulse stimulated photon echoes. These results have significance in the development of optical coherent transient memory and processing systems, where previous calculations predicted recall efficiencies of only a few percent.