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

Processing of noisy signals by four-wave mixing

V. V. Kabanov

Published Mar 2, 2001• 0 citations
Publisher

Abstract

Possibilities are considered of noisy signals processing by four-wave mixing (FWM) of laser radiation in a two-level medium with taking into account of the combined influence of spatial phase matching, nonlinear response inertia, and phase cross-modulation. Regularities of time behavior transformation of randomly modulated signal are collated with particularities of FWM-reflectivity of deterministic pulses. Results are discussed of correlation analysis of FWM with partaking in a random way amplitude (or phase) modulated signals.

DOI
10.1117/12.417749

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Possibilities are considered of noisy signals processing by four-wave mixing (FWM) of laser radiation in a two-level medium with taking into account of the combined influence of spatial phase matching, nonlinear response inertia, and phase cross-modulation. Regularities of time behavior transformation of randomly modulated signal are collated with particularities of FWM-reflectivity of deterministic pulses. Results are discussed of correlation analysis of FWM with partaking in a random way amplitude (or phase) modulated signals.
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An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.
An investigation is reported of the characteristic features of four-wave interaction of a chirped signal with bandwidth-limited pump waves in a resonant medium modelled by a two-level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behaviour of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase-conjugate wave.
An investigation is reported of the influence of self-phase-modulation of high-power pump waves on the degenerate four-wave mixing of bandwidth-limited pulses in a two-level medium. An analysis is made of the characteristic features of spectral broadening of the signal and phase-conjugate waves on the interacting pulses of different durations. The delay of the nonlinear response of the medium is taken into account. The phase modulations of the signal and phase-conjugate waves induced in this four-wave interaction are not mutually conjugate and have the same sign.
An analytic method of decoupling of physical factors is used to investigate the relationship between the temporal and spatial coherence of a randomly modulated light pulse representing a superposition of a signal and noise in a medium with a local nonlinearity. An analysis is made of the factors that influence the transformation of the spatial and temporal characteristics of a diffracted and spreading light pulse in a nonlinear medium. The relationships governing the mutual influence of the signal and noise, resulting in changes in the regular envelopes and statistical characteristics, are determined.
We investigate the influence of the distribution of atom velocities in a hot rubidium sample on the correlation between field-intensity fluctuations of two independently generated four-wave mixing signals and between the transmission signals. The nonlinear process is driven by a single continuous-wave (cw) laser in a pure two-level system due to the forward geometry with circular and parallel polarization of the input fields. The intensity cross correlations of the four-wave mixing signals and the transmission signals present an oscillatory behavior with a clear dependence on the power of the incident fields, which indicates a connection with Rabi oscillations. A two-level theoretical model using stochastic differential equations to account for the mechanism of conversion of phase noise into amplitude noise shows good agreement with our experimental results. Moreover, we show how the response of the system is affected by the different atomic velocity groups.