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The Journal of Chemical Physics

Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation

Allison Albrecht Ferro, John D. Hybl, David M. Jonas

Published Mar 8, 2001• 24 citations
Publisher

Abstract

A complete (both amplitude and phase) measurement of the femtosecond linear free induction decay on a Raman active dye in solution (IR144 in methanol) is demonstrated. For weak femtosecond pulses passing through a homogeneous material, Beer’s Law can be used to predict the spectral amplitude changes, and dispersion relations can be used to calculate the spectral phase change. A modified fast Fourier transform algorithm calculates the phase change by applying dispersion relations to a symmetrical absorption spectrum spanning positive and negative frequencies. A reformulation of the rotating wave approximation in the frequency domain shows that related limits on the accuracy of the rotating wave approximation in nonlinear optics arise from the width of the linear spectrum relative to the center frequency, and not from the excitation pulses.

DOI
10.1063/1.1346638

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Physical Review A•Dec 1, 1974•44 citations
A complete (both amplitude and phase) measurement of the femtosecond linear free induction decay on a Raman active dye in solution (IR144 in methanol) is demonstrated. For weak femtosecond pulses passing through a homogeneous material, Beer’s Law can be used to predict the spectral amplitude changes, and dispersion relations can be used to calculate the spectral phase change. A modified fast Fourier transform algorithm calculates the phase change by applying dispersion relations to a symmetrical absorption spectrum spanning positive and negative frequencies. A reformulation of the rotating wave approximation in the frequency domain shows that related limits on the accuracy of the rotating wave approximation in nonlinear optics arise from the width of the linear spectrum relative to the center frequency, and not from the excitation pulses.
Propagation of femtosecond light pulses in a resonant absorption medium is studied. The propagation time of the light pulses was measured in a dye solution by the optical-Kerr-gate method. Nonadherence to the conventional group velocity domega/dk , which is defined in weak absorption region, was found. The observed wavelength dependences of the group delay and the spectral change in the anomalous dispersion region are qualitatively in good agreement with the theoretical prediction obtained from the new definitions of group velocity, which can be clearly defined even in strong absorption region.
Summary form only given. Coherent optical transients such as photon echo are a versatile method far measurement of the homogeneous absorption spectrum of molecular systems in the presence of strong inhomogeneous broadening. Such experiments require measurement of the decay of the optical coherence, typically accomplished by gradually varying the time delay between the excitation pulses. Time-domain information is then Fourier transformed to frequency domain by a computer. In this paper we demonstrate a new method that yields the homogeneous spectrum in a single shot of femtosecond laser pulse illumination by performing Fourier transformation of coherent optical transient signal with a lens. We apply this method to measure the homogeneous spectrum of dye molecules in a polymer film in a broad range of temperatures.
Time-domain spectroscopy using dual, coherent frequency combs is used to measure free-induction decay from a molecular gas sample in the near-IR with a time-domain signal-to-noise ratio of approximately 10(6) over a approximately 6 ns window at 55 fs time resolution (corresponding to the 9 THz source bandwidth) and a frequency/timing accuracy set by the frequency combs. The free-induction decay exhibits the expected periodic pulses from the rephasing of the multiply excited rovibrational levels. This demonstration represents the first high-resolution, high-accuracy, broadband measurement of optical free-induction decay, to our knowledge.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
A new feature of optical free induction decay (FID) is observed in a coherently prepared sample of 13CH^{13}\mathrm{CH}13CH3F_{3}\mathrm{F}3​F by the method of Stark switching. The preparative phase is due to the resonant steady-state excitation by a cw laser beam, and is followed by FID upon sudden application of a dc Stark field that switches the molecular sample out of resonance. The emission is not observed as a simple decay but instead appears as a train of sharp pulses regularly spaced in time as a result of a repetitive interference. This situation arises because an entire set of infrared transitions within the Stark split manifold are initially prepared, in contrast to our previous study of a nondegenerate transition. The emission, which beats with the laser, produces a heterodyne beat spectrum, consisting of a set of regularly spaced frequencies, that is the Fourier transform of the slowly decaying pulse progression observed. We thus demonstrate what is the optical analog of the well-known NMR method of high-resolution pulse Fourier spectroscopy. The detailed behavior of the pulse train agrees well with an FID theory that assumes the transitions to be uncoupled. The subtle behavior of FID near the time origin is explored also by approximate analytic expressions that reveal either a near zero amplitude or sizable amplitude depending on the degree of saturation in the preparative stage. The experimental technique discussed offers an attractive way for obtaining high-resolution optical spectra without Doppler broadening, and for generating an optical pulse train whose time scale can be compressed by simply increasing the Stark field.