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Cambridge University Press eBooks

Complement 3G: Nonlinear spectroscopy

G. Grynberg, Alain Aspect, Claude Fabre, Claude N. Cohen-Tannoudji

Published Sep 2, 2010• 0 citations
Publisher

Abstract

The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.

DOI
10.1017/cbo9780511778261.019

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The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.
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.
Because of inevitable size distribution, shape variations, different concentration of impurities and defects, and fluctuations of local environment and charge distribution, every ensemble of nanocrystals dispersed in some solid or liquid medium possesses inhomogeneously broadened absorption and emission spectra. Therefore, a number of properties inherent in molecular and atomic inhomogeneously broadened spectra can be a priori foreseen for nanocrystals. These include spectral hole-burning, fluorescence line narrowing under selective excitation, and decay time distribution. At the same time, spectrally selective techniques developed for inhomogeneously broadened molecular and atomic structures have been successfully applied to nanocrystals providing evaluation of individual parameters smeared as a result of inhomogeneous broadening. This chapter gives a brief overview of specific phenomena inherent in all spectrally inhomogeneous media and a survey of the relevant experimental techniques including nonlinear pump-and-probe spectroscopy, fluorescence excitation spectroscopy, and single molecule spectroscopy. Population-induced optical nonlinearity and spectral hole-burning Every real system consisting of particles with discrete energy levels exhibits absorption saturation under intense optical excitation. The only example of a nonsaturable system is an ensemble of ideal harmonic oscillators that possess an infinite number of equally spaced energy levels, optical transitions allowed only for a couple of neighboring levels, and the probability of optical transitions being proportional to the level number (Stepanov and Gribkovskii 1963).
1. Introduetion For a long time aresolution of the optical met h ods was worse compared to that of the methods u s ed in the other wave length ranges. The last years saw a c ons i d er able progre s s in optical spectros copy in improving aresolution. This i s du e to tho development of new physical co nc epts und erlying the a t tai n­ ment of nonlinear s uper na r r ow optical r e sonanc es wi t h no Doppler broad ening. At present thre e methods are u sed to obtain narrow optical resonances: the mothod of s a t ur a t ed ab sorption, two-photon resonances in a standing-wavo field, and r esonances in s epar­ ated optical fields. The three methods involve the elimination of the influence of Doppl er broadening , so the narrowness of resonances is mostly determined by the time of coherent part­ icles-field interaction. The first t wo methods are weI l knovm and developed (see /1/). Just these methods h ave permitted receiving the principal results on obtaining and using super­ narrow resonances. The saturation resonances with a relative width of < 10- 11 have been obtained by using telescopic beam expanders to increase the time of particles-field interaction. The development of the third method has been started in 1976 (see / 2/). This method has showed interesting potentialities. The use of forbidden transitions and tunable lasers will permit to obtain resonanceswith a relative width of < 10- 13• Narrow resonances enabled one to observe in optics some phenomena that could not be earlier studied. Some results in this field received in the Institut e of Thermophysics of the Siberian Branch of the USSR Academy of Sciences are discussed in this r epor t .
The study of optical relaxation processes in solids at low temperature has progressed tremendously in the last 20 years due to the development of coherent optical techniques. The latter would not have been possible without the advent of narrow-band tunable lasers, on the one hand, and lasers with very short pulses (picoseconds, femtosecoods) on the other hand. Such coherent techniques are necessary because spectral line shapes of solids doped with guest molecules are seldom determined by dynamical interactions but principally by strain or structural disorder. This gives rise to inhomogeneous broadening, rlOh, which in crystalline hosts at low temperature varies between ' 0.1 and 10 cm -I, whereas in glasses it may amount to � 100-500 em-I. One of the techniques to achieve narrowing of spectral lines is site­ selection spectroscopy (1-3). A sub-ensemble of molecules within thc inhomogeneously broadened absorption band is selectively excited by mcans of a narrow-band laser, and the fluorescence or phosphoresccnce signal is detected with a high-resolution monochromator and/or a Fabry­ Perot interferometer. Fluorescence line-narrowing ( I) is a special case of this technique (for a review see 3). The intrinsic or homogeneous spectral linewidth, r hom, which yields information on the relaxation processes of the excited state, is given by the effective optical dephasing time, T2:
Abstract The book so far is almost entirely concerned with linear optical processes, where the response of a material to incident light is described by its linear susceptibility and the rates of optical processes are proportional to the incident intensity. However, examples of nonlinear behaviour occur in the saturation of atomic transitions, discussed in §1.7, and in the power-broadened susceptibility, derived in eqn (2.8.6). Atomic saturation is also an important component in the laser theory of§§t.10 and 7.3. The expressions derived in these examples contain the electromagnetic energy density or photon number in denominators whose expansions include terms proportional to all positive powers of the optical energy. The higherorder, or nonlinear, terms are normally much smaller than the linear term for conventional light sources but their influence is often significant in experiments that use laser sources. The present chapter treats the effects of the nonlinear terms in modifying the properties of incident light beams.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.