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Journal of the Physical Society of Japan

Nonlinear Optical Phenomena with Finite Memory Effects

Hirokazu Tsunetsugu, Eiichi Hanamura

Published Oct 15, 1986• 18 citations
Publisher

Abstract

Several nonlinear optical phenomena are described exactly for two-level electronic systems with a Gaussian frequency modulation under a pump field of arbitrary strength. We discuss the emission spectrum and the absorption spectrum of weak probe field under pumping in the frequency region, and the free induction decay (FID) and the optical nutation (ON) as examples of the coherent optical transients in the time region. It is shown that the relaxation behavior depends upon the pumping field intensity, i.e., the effect of the frequency modulations is reduced when the Rabi frequency increases beyond the amplitude or the inverse correlation time of the frequency modulation. We further show that the relaxation behavior depends upon the particular nonlinear optical phenomena, i.e., the vertex correction due to the frequency modulation works in the FID but does not in the ON.

DOI
10.1143/jpsj.55.3636

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Physical Review A•Sep 1, 1985•18 citations
Several nonlinear optical phenomena are described exactly for two-level electronic systems with a Gaussian frequency modulation under a pump field of arbitrary strength. We discuss the emission spectrum and the absorption spectrum of weak probe field under pumping in the frequency region, and the free induction decay (FID) and the optical nutation (ON) as examples of the coherent optical transients in the time region. It is shown that the relaxation behavior depends upon the pumping field intensity, i.e., the effect of the frequency modulations is reduced when the Rabi frequency increases beyond the amplitude or the inverse correlation time of the frequency modulation. We further show that the relaxation behavior depends upon the particular nonlinear optical phenomena, i.e., the vertex correction due to the frequency modulation works in the FID but does not in the ON.
Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.
The effect of frequency modulation on optical phenomena is reduced critically when the Rabi frequency increases beyond the inverse correlation time or the amplitude of the frequency modulation. This is observed in the time region as the change of the free induction decay rate from the Bloch type into the Redfield one. That is shown in this paper to be observable also in the frequency region as the narrowing of the central line and the side bands split-off by the Rabi frequency above and below it in the emission spectrum beyond the Rabi frequency equal to the inverse correlation time.
A consistent explanation of recent studies by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989); 38, 5928 (1988)] on the experimental test of modified optical Bloch equations is presented. It is shown that the observed peculiarities of optical transients in solids are connected with the mechanism of relaxation in systems with slow stochastic modulation. A theory of laser-modified relaxation and analysis of free induction decay (FID), hole burning, and rotary echo (RE) in such systems are presented. The universal character of the FID time dependence and field-independent RE decay is predicted.
We report theoretical and experimental studies of the propagation of a square-modulated laser pulse through a laser-cooled atomic ensemble of two-level absorbers, as well as through a three-level system with electromagnetically induced transparency. We find that the transmission characteristics over a wide range of optical depth can be fully accounted for as optical coherent transients excited by the wide spectral content of the square-modulated optical pulse. We show that both time-domain atom-field coupled equations and frequency-domain linear dispersion theory give precisely the same description of the optical transients at a weak power limit. At low optical depth with moderate absorption, resonant excitation dominates and free-induction decay (FID) contributes mostly to the transient field. At high optical depth when absorption and propagation effects become significant, lossless optical precursors start to dominate the transient response. By varying the optical depth from 0 to 45, we observe that optical transients evolve gradually from FID to optical precursors. We thus show that FID and optical precursors, which have been considered as two different optical transients for many decades, can be unified within a single theoretical frame and they are the manifestations of the same physical process in two different regimes.
We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.