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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Random noise processing using photon echo

Баруздин Сергей Анатольевич

Published Nov 15, 2001• 0 citations
Publisher

Abstract

The excitation of stimulated echo by two pulses of Gaussian white noise, which are originated from a single source and short coherent pulse is considered. The present work studies the nonlinear properties of average amplitude of the echo as function of the spectral power density. The mean value of the complex envelope of the echo is obtained by solving stochastic Bloch equations in Stratonovich sense. The results can be used for analysis of nonlinear excitation characteristics based on saturation effect in photon and spin processors.

DOI
10.1117/12.447949

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The excitation of stimulated echo by two pulses of Gaussian white noise, which are originated from a single source and short coherent pulse is considered. The present work studies the nonlinear properties of average amplitude of the echo as function of the spectral power density. The mean value of the complex envelope of the echo is obtained by solving stochastic Bloch equations in Stratonovich sense. The results can be used for analysis of nonlinear excitation characteristics based on saturation effect in photon and spin processors.
The excitation of a stimulated spin echo by two coherent pulses of Gaussian white noise and a δ -function-like radio pulse is studied. The mean value of the complex envelope of the echo is obtained by solving the Bloch equations. The behavior of the mean value of the envelope of the stimulated echo is investigated for a Lorentzian shape of the inhomogeneously broadened absorption line. It is shown that in an excitation regime which is linear for noise pulses the envelope corresponds to the Fourier transform of the line-shape function. Nonlinear distortions of the mean value of the envelope of a stimulated echo can arise outside the linear excitation regime.
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.
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.
Different regimes of excitation of a stimulated spin echo by pseudorandom pulses and short coherent delta-shaped pulses are considered. Radio pulses phase-shifted by a 127-element M sequence are used as pseudorandom signals. The shape of the complex envelope of the stimulated echo is simulated in linear and nonlinear regimes with respect to the phase-shifted pulses. It is demonstrated that the excitation pulses can be described by correlation functions. Appropriate conditions are determined under which the amplitude of the stimulated echo can be greater than the amplitude corresponding to the classical algorithm used for exciting a stimulated echo by three delta-shaped pulses. The results obtained can be used for analyzing the formation of a stimulated photon echo.