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Optics Letters

Free-induction decay in molecular iodine measured with an extended-cavity diode laser

P. Dubé, M. D. Levenson, J. L. Hall

Published Feb 1, 1997• 13 citations
Publisher

Abstract

The free-induction decay (FID) technique combined with broadly tunable lasers offers a convenient way to survey molecular dephasing times. We measured FID's in molecular iodine by frequency switching an extended-cavity diode laser with a small current modulation. These decay times provide valuable information on the Doppler-free linewidths for frequency-standard applications.

DOI
10.1364/ol.22.000184

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The free-induction decay (FID) technique combined with broadly tunable lasers offers a convenient way to survey molecular dephasing times. We measured FID's in molecular iodine by frequency switching an extended-cavity diode laser with a small current modulation. These decay times provide valuable information on the Doppler-free linewidths for frequency-standard applications.
A novel form of laser frequency switching is devised that extends coherent optical transient studies to a 100-picosecond time scale, the measurements being performed in real time. Free-induction decay (FID) on a subnanosecond time scale reveals new features, such as a first-order FID that dephases with the inhomogeneous dephasing time T2* and interferes with the well-known nonlinear FID. A complete analytical expression for optical FID is derived and supports our FID observations for the sodium D1transition.
A simple method for observing coherent optical-transient phenomena is described. Effects such as photon echoes and free induction decay (FID) should allow studies of the dynamic properties of atoms, molecules, and solids on a time scale ranging from milliseconds to \ensuremath{\sim} 50 ps. The frequency of a cw dye laser is switched with an intracavity electro-optic modulator, producing in an external sample coherent transients which are detected in the forward beam. Measurements of long dephasing times are possible, as in FID, because the laser can oscillate indefinitely at the new frequency following a step-function switching pulse. Measurements of short decay times are also practical because the switching time is not restricted by the laser gain or cavity ringing time. In addition, the dye's dephasing time of a few picoseconds or less is too rapid to interfere with these observations. Since the pulse sequence can be preselected, the entire class of coherent optical transients is accessible. The method thus incorporates all of the advantages inherent in Stark switching, including heterodyne detection and high sensitivity, without being restricted to Stark-tunable systems. Laser frequency switching is discussed also in terms of a theoretical model which exposes the time-dependent properties of a phase-modulated cavity mode. Dephasing studies have been carried out thus far in atomic and molecular gases and low-temperature solids containing inorganic impurity ions or large organic molecules. The utility of the FID effect is emphasized where precise dephasing times are obtained from time-frequency Fourier transformation of FID signals using a digital computer. The first quantitative and detailed test of FID theory is provided by these experimental techniques.
This paper describes a new class of techniques, called time-delayed laser saturation spectroscopy, which combine frequency- and time-domain methods of laser spectroscopy to provide a way of studying a molecular system as it evolves from an initially prepared stationary state to a second, final state. The specific example analyzed here is three-level free induction decay, in which the time-dependent gain of a Doppler-broadened molecular transition is probed after the sudden termination of an intense field resonating with a coupled transition. The theoretical calculation is based on the coupled density-matrix equations of motion in the slowly-varying envelope approximation. The time-delayed line shapes, which may be studied in either transmission or side fluorescence, exhibit linewidth asymmetries, line-shape deformations, Ramsey-type fringes, power broadening and dephasing, and dynamic Stark splittings and oscillatory decays. The technique provides a unique way of distinguishing the influence of Raman-type processes from that of population saturation and a means to separately measure the associated decay rates. The relationship of the present work to other studies is also discussed.
A novel form of laser frequency switching is devised which extends coherent optical transient studies to a 100-psec time scale. The technique incorporates a traveling-wave electro-optic element which imposes with unit efficiency a uniform time-varying phase and thus a frequency shift on a cw laser beam. In contrast to earlier optical traveling-wave modulators which are driven by a microwave oscillator, here the optical phase change is induced rapidly and easily by a dc electric field pulse that propagates in a microwave guide either parallel or antiparallel to the light wave. This advance enables optical free-induction decay (FID) studies on a subnanosecond time scale and reveals such new features as a rapid first-order FID that dephases with the inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​. The well-known nonlinear FID can interfere with the first-order component at short times and decays over the much longer period $\frac{{T}_{2}}{[1+{(1+{\ensuremath{\chi}}^{2}{T}_{1}{T}_{2})}^{\frac{1}{2}}]}$, where $\ensuremath{\chi}$ is the Rabi frequency. A complete analytical expression is derived for optical FID of a transition subject to homogeneous and inhomogeneous broadening and supports detailed observations of the sodium D1{D}_{1}D1​ line.
Coherence phenomena such as photon echoes, free induction, and nutation effects are easily detected in molecular iodine using a frequency-switched tunable cw dye laser. This technique is generally applicable to atoms, molecules, and solids and offers unique ways for probing dynamic interactions in a selective manner. Elastic and inelastic collision mechanisms for I2{\mathrm{I}}_{2}I2​ are examined independently and compared with theory.
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.