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Optoelectronics Letters

Analytic solutions of Bloch equations with phase term for two-pulse photon echo by the phase modulation pulses

Xiurong Ma, Wenzhong Deng, Yunlong Shan

Published Jan 12, 2021• 0 citations
Publisher
DOI
10.1007/s11801-021-0008-7

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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.
The excitation of photon echo by noise pulses that are formed by modulation of the carrying frequency with Gauss noise is modeled. The modeling is based on optical Bloch equations the solution of which for noise pulse realizations is constructed by their stepwise approximation. In terms of the formalism of state transfer matrices, the two- and three-pulse excitation modes are analyzed. The complex envelopes of the primary and stimulated echo responses are determined. In the linear (low-level-signal) mode, the shape of the two-pulse echo corresponds to that of the time delayed and inverted noise pulse. The boundary of the linear mode, upon exceeding of which distortions of the shape of the noise pulse become noticeable, is determined. The shape of the stimulated (three-pulse) echo in the linear mode corresponds to that of the autocorrelation function of the noise pulse realization. Upon passage beyond the boundary of the linear mode, the shape of the three-pulse echo corresponds either to the cross-correlation function of distorted noise pulses (with different intensities) or to the autocorrelation function of distorted pulses (with the same intensities). The modeled photon echo excitation modes can be used in photon echo processors to process signals in the light range.
The excitation of the primary and stimulated photon echoes by pulses modulated in phase with Barker codes is modeled. The shape of the complex envelopes of the primary and stimulated echoes is found by solving the optical Bloch equations. Linear and nonlinear excitation modes are considered. In linear modes, it is possible to realize a time delay and form the correlation function of modulated pulses. The results obtained can be used in modeling and analyzing the corresponding algorithms of the photon echo excitation and in calculating the characteristics of signal processors based on the phenomena of photon and spin echoes.