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Conference on Lasers and Electro-Optics

Efficient modeling of optical coherent transient processors

Tiejun Chang, Ming Tian, William Randall Babbitt

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. Fully coupled Maxwell-Bloch equations are required to adequately study the problem of coherent pulse propagation and stimulated photon echo processes, especially in optically thick media. The coupled Maxwell-Bloch equations for optical coherent transients (OCT) simulations have so far assumed a collinear configuration, where all the inputs and echoes propagate along the same direction. We present our own model.

DOI
10.1109/cleo.2002.1033630

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Summary form only given. Fully coupled Maxwell-Bloch equations are required to adequately study the problem of coherent pulse propagation and stimulated photon echo processes, especially in optically thick media. The coupled Maxwell-Bloch equations for optical coherent transients (OCT) simulations have so far assumed a collinear configuration, where all the inputs and echoes propagate along the same direction. We present our own model.
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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.
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 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.
In this paper we investigate the influence of optical density or superradiance on the photon echo decay using the coupled Maxwell–Bloch equations. Our theory applies to optically thick but dilute media, where the transition dipole–dipole interaction between nearby chromophores is negligible, but the far-field interaction is not. Corrections to the (normalized) echo decay in the optically thin limit, INe(tπ)=exp [−4tπ/T2] (tπ and T2 are the interpulse separation times and the coherence relaxation times, respectively), are found by expanding the polarization, excited state population and pulse electric fields in powers of ζ=αz, where α is the inverse Beer’s absorption length, and z is the coordinate along the pulse propagation axis. Numerical solutions for optically thick samples are also presented, and when ζ≫1 the normalized echo intensity is found to obey the simple analytic form: INe(tπ)=2 exp [−tπ/T1]−1, when tπ/T1<ln 2 and INe(tπ)=0 for longer times. (T1 is the population relaxation time.) In this limit the echo decay is independent of the coherence relaxation time T2, illustrating the profound effect intermolecular coupling may have on any nonlinear optical measurement. We show that at low temperatures, when T2=2T1, the echo decay rate increases as the optical density increases. However, for higher temperatures, when T2 is sufficiently shorter than 2T1, the opposite behavior results, that is, the echo decay rate decreases as the optical density increases.