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Nonlinear Optics

Extra Resonances in Time-Domain Nonlinear Spectroscopies

John T. Fourkas, Rick P. Trebino, M. D. Fayer, Mark A. Dugan

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Extra resonances between initially unpopulated excited states (IUES) or equally populated ground states (EPGS) have been studied extensively in the context of frequency-domain nonlinear spectroscopies such as Nearly-Degenerate Four-Wave Mixing (NDFWM)1. In the absence of strong laser fields2 or effects such as pure dephasing3, stochastic fluctuations in laser fields4, and laser transients5, the NDFWM extra resonances are either very weak (in the case of EPGS) or nonexistent (in the case of IUES). It is perhaps under-appreciated that "Fourier-transform" time- and frequency-domain FWM techniques do not necessarily provide the same information. For instance, under certain circumstances6, the NDFWM and transient grating (TG) techniques form such a pair, which would imply that TG extra resonances might disappear under the same experimental conditions in which they disappear in NDFWM. This assumption is belied by the TG data shown in Fig. 1. These data were taken by exciting and probing the D1 line of Na atoms in a cell in which there was no buffer gas and the Na pressure was low enough to preclude any significant number Na-Na collisions on the experimental time scale. Even in the absence of pressure-induced dephasing, these data exhibit strong extra resonances at both the 1.77-GHz ground-state hyperfine-splitting frequency and the 189-MHz excited-state hyperfine-splitting frequency. These data have prompted us to undertake a theoretical study of the nature of extra resonances in time-domain nonlinear spectroscopies, the preliminary results of which are discussed here. We show that time-domain extra resonances increase in strength with decreasing dephasing, and that IUES resonances exist even in the complete absence of pure dephasing. Finally, we show that IUES and EPGS extra resonances have a common origin in the time domain.

DOI
10.1364/nlo.1992.tud2

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Extra resonances between initially unpopulated excited states (IUES) or equally populated ground states (EPGS) have been studied extensively in the context of frequency-domain nonlinear spectroscopies such as Nearly-Degenerate Four-Wave Mixing (NDFWM)1. In the absence of strong laser fields2 or effects such as pure dephasing3, stochastic fluctuations in laser fields4, and laser transients5, the NDFWM extra resonances are either very weak (in the case of EPGS) or nonexistent (in the case of IUES). It is perhaps under-appreciated that "Fourier-transform" time- and frequency-domain FWM techniques do not necessarily provide the same information. For instance, under certain circumstances6, the NDFWM and transient grating (TG) techniques form such a pair, which would imply that TG extra resonances might disappear under the same experimental conditions in which they disappear in NDFWM. This assumption is belied by the TG data shown in Fig. 1. These data were taken by exciting and probing the D1 line of Na atoms in a cell in which there was no buffer gas and the Na pressure was low enough to preclude any significant number Na-Na collisions on the experimental time scale. Even in the absence of pressure-induced dephasing, these data exhibit strong extra resonances at both the 1.77-GHz ground-state hyperfine-splitting frequency and the 189-MHz excited-state hyperfine-splitting frequency. These data have prompted us to undertake a theoretical study of the nature of extra resonances in time-domain nonlinear spectroscopies, the preliminary results of which are discussed here. We show that time-domain extra resonances increase in strength with decreasing dephasing, and that IUES resonances exist even in the complete absence of pure dephasing. Finally, we show that IUES and EPGS extra resonances have a common origin in the time domain.
We show that extra resonances, such as those caused in frequency-domain nonlinear wave mixing by pure dephasing or laser fluctuations, can also be induced by operation in the time domain. These pulse-length-induced extra resonances arise in transient-grating experiments when the laser pulses are short enough that a steady state cannot be achieved during the excitation process. We show theoretically that these resonances increase in strength with decreasing excitation pulse length until the pulse length becomes shorter than the dephasing time of the medium and quote an experimental example to support this interpretation.
Nonlinear perturbative susceptibilities have been used successfully to analyze experiments in nonlinear optics for two decades. By its very nature, a perturbative approach is limited to a small value of the expansion parameter, and nonlinear susceptibilities are not useful for strong saturating fields. Presently, a theory is presented for the treatment of FWM which is applicable to arbitrary strength of the input fields, both on and off resonance. The field harmonic time dependences are removed by a transformation to the proper rotating frame, and the resulting eigenvalue problem is solved numerically. Several new effects are predicted. For strong fields resonance frequencies are shifted and lines are split (similar to the ac Stark effect). When such a split line is acted on by another strong field (a phenomenon not studied so far), a new effect of stirring is observed, which results in the broadening and merging of the two separate components. A new extra resonance appears which is induced by the strong field and is present even in the absence of any collisions or other dephasing processes or of laser phase fluctuation. This new extra resonance is a new member in the family of extra resonances which were discussed in various previous publications.
Optical four-wave mixing resonances in sodium vapor induced by collisions with inert buffer gases (He, Ar, Xe, N2{\mathrm{N}}_{2}N2​) are characterized at high resolution ( 5 MHz) using lasers tuned near the DDD lines of Na. These resonances are interpreted in terms of coherent scattering from a population grating established by collisional absorption of the incident radiation. The roles of homogeneous and inhomogeneous contributions to the resonance line shapes are clarified. The line shapes exhibit structure sharper than the predicted linewidth, that characteristic of the 3P3P3P-to-3S3S3S transition rate. We show that this is caused by collision-induced optical pumping which introduces the ground-state lifetime into the grating relaxation physics. These long-lived gratings are exemplified dramatically by experiments in the presence of N2{\mathrm{N}}_{2}N2​ which collisionally quenches the Na 3P3P3P states. Similar results are obtained in Xe where it is argued that excimer formation with the 3P3P3P states plays a role in the population dynamics. Model calculations of the effects of sodium level degeneracy on the grating dynamics are presented to support these conclusions. Finally we present data illustrating interference between the collision-induced population grating resonances detailed here and collision-induced coherent Raman resonances between Zeeman sublevels of the ground state.
The purpose of this research is to study the dynamic behavior of a resonant system using four-wave-mixing spectroscopy (FWM). From this study, we have obtained rich information about the FWM spectral response of systems which have different state-specific reservoir couplings. Atomic sodium (Na) is used as our model system. It is shown that the FWM spectral response depends strongly on how each level couples to the vacuum radiation field (through spontaneous emission). This effect is illustrated in the line shape obtained from a nearly degenerate FWM (NDFWM) experiment for a simple two-level system in Na. A narrow spike on top of a wide resonance is observed at zero pump-probe detuning (δ\deltaδ = 0) when the upper-state decay rate $\gamma\sb2$ to the reservoir is larger than the lower-state decay rate $\gamma\sb1$. The width of the spike is 2$\gamma\sb1$ and the width of the wide resonance is determined by the total upper-level decay rate (2$\gamma\sbsp{2}{\rm t}$). From the NDFWM spectrum, all the decay rates characterizing a two-level system may be measured directly. If magnetic substate degeneracy is included, the NDFWM line shape has contributions arising from orientation and alignment gratings, as well as from population gratings. For a two-level system closed with respect to population, the orientation or alignment gratings may contribute a narrow resonance at δ\deltaδ = 0 in the NDFWM response. These features are demonstrated for the first time by using NDFWM. Reservoir coupling can also occur through collisions with externally added gas. Collisions can cause a closed two-level system to become open, resulting in NDFWM spectra that show a narrow resonance at δ\deltaδ = 0 with a width below the residual Doppler width (Dicke narrowing). This is also the first time that Dicke narrowing has been observed in population terms. Finally, we present a calculation of the NDFWM response for strong degenerate pump fields and a weak probe field. We compare the differences between NDFWM spectra of closed two- and three-level systems in the presence of strong pumps.
The effects of finite-bandwidth excitation are incorporated into the theoretical treatment of degenerate four-wave mixing (DFWM) spectroscopy by employing a general description of applied electromagnetic fields, thereby permitting the transient nature of typical laser sources to be taken explicitly into account. A computationally efficient perturbative (weak-field) formalism is developed by exploiting exponentially-decaying wave forms as a flexible basis for expanding the temporal envelope functions of incident quasimonochromatic pulses. This approach has the distinct advantage of yielding time-domain response integrals that can be evaluated analytically since they are almost as simple in form as their monochromatic counterparts. The resulting frequency-domain expressions for the induced DFWM signal polarization reflect the pronounced influence of finite-bandwidth excitation without needing to cobble such behavior into phenomenological rates for population decay and coherence dissipation. Spectral line shapes are examined for both stationary and nonstationary ensembles of isolated (gas-phase) target molecules, with the latter analyses demonstrating the systematic degradation of spatial discrimination introduced by nonmonochromatic implementations of the sub-Doppler (phase-conjugate) four-wave mixing scheme. In keeping with recent experimental findings, the precipitous drop in signal intensity accompanying the action of collisional dephasing processes is predicted to be tempered greatly by the use of short-duration excitation pulses.
The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.