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Optics Letters

Spectroscopic decay-rate measurements below the laser linewidth

William E. Cooke, S A Bhatti, Christopher L. Cromer

Published Feb 1, 1982• 48 citations
Publisher

Abstract

When two levels can be strongly coupled by a pulsed laser, it is possible to measure the decay rate from the upper state by applying sufficient laser power to depletion broaden the transition. The depletion broadening is proportional to the square root of the decay rate times the total energy density of the laser pulse. With sufficient laser power, this technique can be used even if the decay rate is smaller than inhomogeneous broadenings or the laser linewidth. The technique is used here to measure autoionizing rates of some 6P((1/2))ns states.

DOI
10.1364/ol.7.000069

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When two levels can be strongly coupled by a pulsed laser, it is possible to measure the decay rate from the upper state by applying sufficient laser power to depletion broaden the transition. The depletion broadening is proportional to the square root of the decay rate times the total energy density of the laser pulse. With sufficient laser power, this technique can be used even if the decay rate is smaller than inhomogeneous broadenings or the laser linewidth. The technique is used here to measure autoionizing rates of some 6P((1/2))ns states.
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.
Until the advent of laser, optical spectroscopy was limited to absorption and emission. These linear techniques often provided incomplete information because of the presence of inhomogeneous broadening, which arises in gases from Doppler shifts and in solids from random crystal elds or structural disorder (Figure 10.1). Lasers provided the high intensity needed to implement nonlinear spectroscopic techniques, which can make measurements “below” the CONTENTS 10.1 Introduction 371 10.1.1 Physical Description of TFWM for a Two-Level System 373 10.1.2 Overview of Variants and Extensions of TFWM 375 10.1.3 Use of TFWM Spectroscopy in Solids, Semiconductors, and Complex Systems 376 10.2 Theory 377 10.2.1 TFWM Signal from an Inhomogeneously Broadened Ensemble of Two-Level Systems 378 10.2.2 Phenomenological Inclusion of Many-Body Effects 381 10.3 Experimental Details of TFWM 382 10.3.1 Basics of Excitation Pulse Generation, Alignment, and Signal Detection 382 10.3.2 Time-Integrated Two-Pulse TFWM 385 10.3.3 Time and Spectrally Resolved Two-Pulse TFWM 386 10.3.4 Three-Pulse TFWM 386 10.3.5 Co-Linear TFWM 387 10.4 Case Study: TFWM from Excitons in GaAs Quantum Wells 387 10.4.1 Dephasing 388 10.4.2 Many-Body Effects 389 10.4.3 Disorder 391 10.4.4 Quantum Beats 391 10.4.5 Polarization Dependence 392 10.5 Multidimensional Fourier Transform Spectroscopy 392 10.6 Summary 393 References 393 inhomogeneous line width and determine the underlying homogeneous line widths. Often the homogeneous width is more interesting because it reects dynamics such as scattering and/ or radiative decay.
We present a variation of the isolated-core excitation (ICE) method that measures the linewidths of autoionizing resonances regardless of the limitations imposed by an instrumental linewidth. By exciting an autoionizing state via different ICE satellite transitions, we determine the linewidth of the state from Fano q values of asymmetric spectral profiles. Since the Fano q is insensitive to instrumental broadening, we can measure autoionizing resonance linewidths below the bandwidth of our laser.
The use of the optogalvanic technique to obtain the line profile of the Cu 5s' 4^{4}4D5/2{\mathit{D}}_{5/2}D5/2​ autoionization level with different degrees of saturation broadening is demonstrated. The experimental results point out that the growth of the autoionization-level breadth follows the square root of the increase in the laser intensity. The measured value of the natural breadth of the Cu5s' 4^{4}4D5/2{\mathit{D}}_{5/2}D5/2​ autoionization level is 7.2\ifmmode\pm\else\textpm\fi{}0.6 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The laser saturation intensity was measured by two different methods, and its value is about 0.39\ifmmode\pm\else\textpm\fi{}0.09 MW/cm2{\mathrm{cm}}^{2}cm2.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy.In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels.It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid.Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180" pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes.The role of pulse phase is extensively analyzed.Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters.The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem.Phys.Lett.48, 256 (1977); Orlowski et al., ibid.54, 197 (1978)).The relative merits offluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences.Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions.In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.