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Quantum Electronics

Influence of self-modulation on the degenerate four-wave mixing in a resonant medium

V. V. Kabanov

Published Mar 31, 1995• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1995v025n03abeh000341

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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 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 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.
The characteristic features of the conjugate wave's formation under transient four-wave mixing in a two-level medium are investigated. The phase modulations of the signal and conjugate waves induced in the four-wave mixing are not mutually conjugate and have the same sign. The fulfillment of the phase-conjugation for the phase modulated signal has been shown in particular to be connected with the envelope's deformation and the spectrum's change of signal pulses. The transient optical bistability connected with the nonlinear absorption's saturation in the quasi-cw four-wave mixing and with the inertia in the short pulse's regime is observed.
An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.
The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.
We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.