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Acta Scientiarum Naturalium Universitatis Sunyatseni

Numerical Solution and Applications of Photon Echo

Longzhao Lu, Cheng Li, Xiangyang Yu

Published Mar 25, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
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.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.
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.