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Journal of the Optical Society of America B

Analytic solutions of the Maxwell–Bloch equations for high photon-echo efficiency of multiple pulse sequences

Leung Tsang, Carrie S. Cornish, William Randall Babbitt

Published Feb 1, 2003• 17 citations
Publisher

Abstract

We derive a method for predicting the efficiency of stimulated photon echoes in optically thick media. Analytic solutions to the Maxwell–Bloch equations are derived for multiple pulse sequences in which the pulses are either temporally brief or have a low pulse area. This method retains the temporal and spatial information of the recalled waveform, and it provides a nonintensive computational method for determining the recall efficiency of stimulated photon echoes. The case considered is when the medium is optically thick and the recall efficiency is high, but with minimal distortion of the data. The results are in good agreement with a full space, time, and frequency numerical integration of the Maxwell–Bloch equations.

DOI
10.1364/josab.20.000379

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We derive a method for predicting the efficiency of stimulated photon echoes in optically thick media. Analytic solutions to the Maxwell–Bloch equations are derived for multiple pulse sequences in which the pulses are either temporally brief or have a low pulse area. This method retains the temporal and spatial information of the recalled waveform, and it provides a nonintensive computational method for determining the recall efficiency of stimulated photon echoes. The case considered is when the medium is optically thick and the recall efficiency is high, but with minimal distortion of the data. The results are in good agreement with a full space, time, and frequency numerical integration of the Maxwell–Bloch equations.
We have found that highly efficient waveform recall is possible in coherent transient systems in which the storage is optically thick. Coherent transients may be used in a variety of information storage and processing applications with advantages over traditional electronic methods. However, it is believed that a serious problem in application of photon echoes in practical systems is the relatively low efficiency of the process. We show in our numerical studies that waveform recall efficiencies greater than unity can be achieved in absorbing media with appropriate choice of absorption length and brief pulse area, even for very weak data pulses. We also present our preliminary experimental results in Barium vapor in which efficiencies of 50% were obtained for both the stimulated and two-pulse photon echoes.
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.
Important applications in optical information storage and processing based on photon echo have been developed.An accurate and effective numerical method to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium will be introduced.Two-pulse photon echo is calculated then photon echo and multiple-pulse photon echoes are stimulated in optical thin(thick) media by using the method,and the physical properties of those echoes are analyzed.The results show that the approach to storage and retrieval of light using multiple-pulse photon echoes based on stimulated photon echo is an effective mode.
We have studied the effect of generative-pulse amplitude, spatial profile, and temporal character as well as medium optical thickness on the power of photon and stimulated echoes. Working in atomic Yb vapor, photon echoes are observed that, absent material relaxation, are more powerful than the first generative pulse, thereby exceeding typically expected photon-echo powers by approximately two orders of magnitude. Factors crucial to the generation of powerful echoes identified through Maxwell-Bloch simulation are experimentally confirmed.