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

Multiple photon echo signals when the dielectric crystals are excited by laser pulses of different amplitude

V. S. Kuz’min, V. M. Kolesenko

Published Nov 15, 2001• 0 citations
Publisher

Abstract

Multiple photon echo signals were found to be the reflection of the oscillation structure of the primary echo signals formed by excitation of two-level active centers. Amplitude pulses are of the same length, but their amplitude is different. The length of the pulse is comparable with the delay between them. The primary photon echo of the oscillation structure is shown to exist in the intervals (-t1,t1) and (-2t1,2t1). It was established that under certain correlation between the amplitudes of exciting pulses the oscillation signal structure becomes asymmetric. That is why in the regime of square-law detection of the primary photon echo signal its asymmetry oscillation structure is observed in the form of frequent of isolated signals (multiple photon echo), the distance between them being equal to the pulse length.

DOI
10.1117/12.447944

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Multiple photon echo signals were found to be the reflection of the oscillation structure of the primary echo signals formed by excitation of two-level active centers. Amplitude pulses are of the same length, but their amplitude is different. The length of the pulse is comparable with the delay between them. The primary photon echo of the oscillation structure is shown to exist in the intervals (-t1,t1) and (-2t1,2t1). It was established that under certain correlation between the amplitudes of exciting pulses the oscillation signal structure becomes asymmetric. That is why in the regime of square-law detection of the primary photon echo signal its asymmetry oscillation structure is observed in the form of frequent of isolated signals (multiple photon echo), the distance between them being equal to the pulse length.
It is theoretically established that multiple photon-echo signals reflect the oscillatory structure of the primary echo signal, which arises under the conditions of collinear excitation of two-level active centers by laser pulses having the same width but different amplitudes. It is shown that the oscillatory structure of the primary photon echo exists within the intervals (−t 1, t 1) and (−2t 1, 2t 1), where t 1 is the pulse width. It is found that, when the pulse width is of the same order of magnitude as the delay between the pulses and the amplitudes of the excitation pulses obey certain relations, the oscillatory structure of the primary photon-echo signal becomes asymmetric. In the mode of quadratic detection of the primary photon-echo signal, the asymmetric oscillatory structure of the primary echo manifests itself as a manifold of isolated signals (multiple photon echoes), with the time intervals between these signals being equal to the pulse width.
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.
It is shown theoretically that, when two-level atoms are nonresonantly excited by a double light pulse that is a superposition of two rectangular pulses of identical frequency but different amplitude, it is possible to form multiple nutational echo signals whose amplitude is determined by the relationships between the Rabi frequencies of the double pulse, the inhomogeneous line width, and the detuning from resonance. It is established that these signals result from null beats between polarization vibrations at variable frequencies and at the generalized Rabi frequency. The optimum conditions for observing multiple echo signals in different experimental situations are considered.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Two-frequency correlation between the profiles of signals of the primary and long-lived (stimulated) photon echos in a three-level medium excited by combined sequences of resonance quasimonochromatic (encoding) signals and femtosecond pulses consisting of a few optical oscillations (down to one) is predicted. It is shown that the profiles of echo responses of both frequencies correlate with each other and with the profiles of encoding pulses, copy them, and induce mirror rotations, as well as scaling transformations in time in dependence on the methods of forming exciting sequences.