Advances in CHEMICAL PHYSICS

EDITED BY

I. PRIGOGINE University of Brussels

Brussels, Belgium and

University of Texas Austin. Texas

AND

STUART A. RICE Department of Chemistry

and The James Franck InstitL te The University of Chicq,o

Chicago, Illinois

VOLUME XLM

AN INTERSCIENCE@ PUBLI4:ATION

JOHN WILEY & SONS

NEW YORK * CHICHESTER * BRISBANE * ‘TORONTO * SINGAPORE

ADVANCES IN CHEMICAL PHYSICS

VOLUME XLIX

EDITORIAL BOARD

C. J. BALLHAUSEN, Kobenhaven Universitets Fysisk-Kemiske Institut, Kemisk

J. J. M. BEENAKKER, Rijksuniversiteit te Leiden, Kamerlingh Onnes Laboratory,

RICHARD B. BERNSTEIN, Department of Chemistry, Columbia University, New

H. HAKEN, Institut fur Theoretische und Angewandte Physik der Technischen

Yu L. KLIMONTOVITCH, Moscow State University, Moscow, USSR RYOGO KUBO, Department of Physics, University of Tokyo, Tokyo, Japan M. MANDEL, Chemie-Complex der Rijks-Universiteit, Wassenaarseweg, Leiden,

PETER MAZUR, Institute Lorentz voor Theoretische Natuurkunde, Nieuwsteeg,

GREGOIRE NICOLIS, Pool de Physique, Faculte de Sciences, Universite Libre de

S. ONO, Institute of Physics, University of Tokyo (College of General Education),

MICHAEL PHILPOTT, IBM Research Center, San Jose, California, U. S. A. J. C. POLANYI, Department of Chemistry, University of Toronto, Toronto, Ontario,

YVES POMEAU, Commissariat a l'Energie Atomique, Centre &Etudes nucleares de

B. PULLMAN, Institut de Biologie, Physico-Chimique, Universite de Paris, Paris,

C. C. J. ROOTHAAN, Departments of Physics and Chemistry, The University of

IAN ROSS, Department of Chemistry, Australian National University, Canberra,

JOHN ROSS, Department of Chemistry, Massachusetts Institute of Technology,

R. SCHECTER, Department of Chemical Engineering, University of Texas at Austin,

I. SHAVITT, Battelle Memorial Institute, Columbus, Ohio, U. S. A. JAN STECKI, Institute of Physical Chemistry of the Polish Academy of Sciences,

GEORGE SZASZ, General Electric Corporate R & D, Zurich, Switzerland KAZUHISA TOMITA, Department of Physics, Faculty of Science, Kyoto University,

M. V. VOLKENSTEIN, Institute of Molecular Biology, Academy of Science, Moscow,

E. BRIGHT WILSON, Department of Chemistry, Harvard University, Cambridge,

Laboratorium IV, Kobenhaven, Denmark

Leiden, Netherlands

York, New York, U. S. A.

Hochschule, Stuttgart, Germany

Netherlands

Leiden, Netherlands

Bruxelles, Bruxelles, Belgium

Tokyo, Japan

Canada

Saclay, Division de la Physique, Gif-sur-Yvette, France

France

Chicago, Chicago, Illinois, U. S. A.

Australia A. C. T.

Cambridge, Massachusetts, U. S. A.

Austin, Texas, U. S. A.

Warsaw, Poland

Kyoto, Japan

USSR

Massachusetts, U. S. A.

Advances in CHEMICAL PHYSICS

EDITED BY

I. PRIGOGINE University of Brussels

Brussels, Belgium and

University of Texas Austin. Texas

AND

STUART A. RICE Department of Chemistry

and The James Franck InstitL te The University of Chicq,o

Chicago, Illinois

VOLUME XLM

AN INTERSCIENCE@ PUBLI4:ATION

JOHN WILEY & SONS

NEW YORK * CHICHESTER * BRISBANE * ‘TORONTO * SINGAPORE

Copyright 0 1982 by John Wiley & Sons, Inc.

All rights reserved. Published simultaneously in Canada.

Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc.

Librury of Congress Cutu/og Curd Number: 58-9935

ISBN 0-471-09361-0 Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

CONTRIBUTORS TO VOLUME XLIX

MICHAEL BAER, Soreq Nuclear Research Center, Yame, Israel

P. BORCKMANS, Service de Chimie-Physique 11, IJniversite Libre de Bruxelles,

JEREMY K. BURDETT, Department of Chemistry, The 'Jniversity of Chicago, Chicago,

H. T. DAVIS, Department of Chemical EngineeIllig and Materials Science and

G. DEWEL, Service de Chimie-Physique 11, Universite Libre de Bruxelles, Brussels,

W. DERHARDT, Department of Physics, University of Pennsylvania, Philadelphia,

GRAHAM R. FLEMING, Department of Chemistry and James Franck Institute,

L. LATHOUWERS, Dienst Teoretische en Wiskundi ;e Natuurkunde, University of

E. W. PLUMMER, Department of Physics, University of Pennsylvania, Philadelphia,

L. E. SCRIVEN, Department of Chemical Engineering and Materials Science, Univer-

S. A. SOLIN, Department of Physics, Michigan State University, East Lansing,

P. VAN LEWEN, Dienst Teoretische en Wiskund ge Natuurkunde, University of

D. WALGRAEF, Service de Chimie-Physique 11, Universite Libre de Bruxelles,

Brussels, Belgium

Illinois

Department of Chemistry, University of Minne.iota, Minneapolis, Minnesota

Belgium

Pennsylvania

University of Chicago, Chicago, Illinois

Antwerp, Antwerp, Belgium

Pennsylvania

sity of Minnesota, Minneapolis, Minnesota

Michigan

Antwerp, Antwerp, Belgium

Brussels, Belgium

INTRODUCTION

Few of us can any longer keep up with the flood of scientific literature, even in specialized subfields. Any attempt tcl do more, and be broadly educated with respect to a large domain of science, has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists. This series, Advances in Chemical Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, which field we interpret very broadly. Our intent is to have experts presen i comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and sewe as a personalized learning text for beginners in a field.

ILYA PRIGOGINE

STUART A. FWE

CONTENTS

APPLICATIONS OF CONTINUOUSLY OPERATING, SYNC HRONOUSLY

MODE-LOCKED LASERS By Graham R . Fleming

PREDICTIONS OF THE STRUCTURE OF COMPLEX SOLIDS By Jeremy K . Burdett

By L. Lathouwers and P . Van h v e n GENERATOR COORDINATE THEORY OF NUCLEAR M O T O N IN MOLECULES

A REVIEW OF QUANTUM-MECHANICAL APPROXIMATE TREATMENTS OF

THREE-BODY REACTIVE SYSTEMS By Michael Baer

NONEQUILIBRIUM PHASE TRANSITIONS AND CHEM1CP.L INSTABILITIES

By D. Walgraef, G . Dewel, and P . Borckmans

STRESS AND STRUCTURE IN FLUID INTERFACES

THE NATURE AND STRUCTURAL PROPERTIES OF GRAPHITE INTERCALATION COMPOUNDS

By H. T. Davis and L. E . Scriven

By S . A . Solin

ANGLE-RESOLVED ~ O T O E M I S S I O N AS A TOOL FOR TllE STUDY OF SURFACES

By E . W. Plummer and W . Eberhardt

1

47

115

191

31 1

357

455

533

AUTHOR INDEX

SUBJECT INDEX

657

679

ADVANCES IN CHEMICAL PHYSICS

VOLUME XLIX

APPLICATIONS OF CONIINUOUSLY OPERATING, SYNCHRONOUSLY

MODE-LOCKED LASERS

GRAHAM R. FLEMIYG

Department of Chemistry and James Franck Institute The University of Chicligo

Chicago, Illinois

CONTENTS

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 11. Synchronously Pumped Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

A. Pulse-Shortening Mechanism . . . . . . . . . . . . . . . . . . . . . . . 4

111. Detection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

B. Pulse Duration and Structure Measurements . . . . . . . . . . .

A. Ground-Stat . . . . . . . . . . . . . . . . . . . . . . . . . .

inuum Generation . . . . . . . . . . . . . D. Read-In-Rea E. The Coherent Coupling Phenomenon. . . . . . . . . . . . . . . .

G. Fluorescence Up-Conversion Technique . . . . . . . . . H. I.

F. Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I7

Synchronously Scanning Streak Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 9 Time-Correlated Single-Photon Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

IV. Applications to Time-Resolved Spectroscopy . . . . . . . . . . . . . . . . . . . . . .21 A. Vibrational Studies in Solids and Liquids . . . . . . . . . . . . . . . . . . . . .21

1. Mixed Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 2. Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 3. Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

B. Orientational Relaxation in Liquids . . . . . . . . . . . . . . . . .28

Photochemistly and Photophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 1. Gas-Phase Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2. Solution Studies . . . . . . .

E. Photobiology. . . . . . . . . . . .

A. B. High-Resolution Spectroscopy

C. Anisotropic Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.

V. Applications to Time-Independent . . . . . . . . . .34

VI. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42

Surface Raman Spectroscopy with Synchronour

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1

C. Pulse- to-Pulse Reproducibility . . . . . . . . . Detection Systems . . . . . . . . . . . . . . . . . . . . . A. Ground-State Recovery . . . . . . . . . . . . . . B. Double Dye Laser Technique . . . . . . . : . . C. Amplification and Continuum Generation . D. Read-In-Read-Out Technique . . . . . . . . .

2 G . R. FLEMING

I. INTRODUCTION

The ability to produce wavelength-tunable, ultrashort light pulses at very high repetition rates has significantly extended the scope and reliability of picosecond spectroscopy. Important applications of such light sources are also being found in other areas of spectroscopy, for example, in the tour de force of Heritage, Levine, et al['* 2] of measuring stimulated Raman spectra of monolayers without any surface enhancement, and in the two-photon Doppler free measurements of Hansch and co-workers on the sodium 3s-4d transition. L31

This chapter describes the basic physical principles involved in synchro- nously pumped, mode-locked dye lasers and the operating characteristics of the most common type of laser- the actively mode-locked argon or kryp- ton ion- pumped dye laser combination. Methods of application to time- resolved spectroscopic studies are then described. The chapter concludes with discussions of the applications of synchronously pumped lasers to vibra- tional spectroscopy and to high-resolution spectroscopy.

11. SYNCHRONOUSLY PUMPED LASERS

A synchronously pumped laser is one in which the cavity length is set equal to (or as a submultiple of) the interpulse spacing of a pump laser. In this way the cavity gain is modulated at the round-trip frequency and mode locking results. The initial synchronously pumped lasers were dye lasers pumped by high-power, mode-locked ruby L41 or Nd-glass['] lasers, and their output thus consisted of a burst of ultrashort pulses following the pulse train of the pump laser. Synchronous pumping also enables a truly continuous train of ultrashort pulses to be generated, provided the pump laser operates continuously. The most common high-power continuous lasers are the argon and krypton ion lasers, and the finding that these lasers are readily actively mode locked to provide a stable, continuous train of pulses of 100 to 200 psec duration has led to a good deal of interest in the use of these lasers as a synchronous pump source. The synchronously pumped laser has generally been an organic dye laser, although more recently F-center lasers have also been used.l61 The synchronously pumped organic dye laser retains the tuna- bility of the normal continuous-wave (cw) dye laser, and is capable of pro- ducing pulses of < 1 psec.

A typical experimental setup is shown in the lower portion of Fig. 1, with an actively mode-locked argon laser pumping a cw dye laser with its cavity length extended to match the pump laser and thus achieve synchronous pumping. Mode locking of the ion laser is achieved by an acousto-optic modulator placed close to the rear mirror. About one watt of radio frequency (rf) power is applied through a transducer to a quartz prism, and the

CONTINUOUSLY OPERATING, SYNCHRONOUS1,Y MODE-LOCKED LASERS 3

pulse

- TIME- TIME -

'I, Amplified '. PUISI! Ar' pump

- impulse-

I I M t - I IMf - U LT R ASTA B LE RF SOURCE RF AMPLIFIER

output dV4 A r t Laser a Coupler

I WATT RF POWER Dye Jet

I 75 MHz Filter

Fig. 1. Optical system and pulse-shortening mechanism in synchronously pumped dye lasers. (a) Argon laser pumping pulse and dye gain as a functior of time. ( b ) Qualitative representa- tion of the dye gain and pulse shape of input (solid curve) and output (dashed curve) dye laser pulses. The circulating dye laser pulse has arrived late in the gain medium and the amplified pulse envelope has its peak advanced (dye laser cavity slghtly too short). ( c ) The input and output pulses normalized to the same peak height, for two -ound trips: solid curve, initial pulse; dashed curve, first round trip; dotted curve, second rounc trip.

frequency of the rf source is set so that light passing through the prism is diffracted at the cavity round-trip frequency. Ths periodic loss results in locking of the phase of the longitudinal laser modes, and a train of pulses with period w i ' ( - 2 L / c ) , where oM is the modulation frequency, results.t71 All the major argon and krypton lines have been mode locked; and with a stable rf source, pulse widths are typically 100 to 150 psec. Pulses as short as 50 psec have been reported with a mode-loc ced krypton laser.L8] Average powers may be as high as 1.5 W for the stronger lines.

Adoption of a standard cw dye laser for syrchronous pumping simply re- quires extension of the cavity, and provision 01' a sensitive length adjustment on the output mirror. When the dye laser catity length is correctly set, the pulses emerging may be as much as 100 times shorter than the pumping ion laser pulses. The next section gives a brief qualitative description of the pulse-shortening mechanism at work in the dye laser.

The repetition rate of the dye laser is typi:ally 75 to 80 MHz, and this enables the use of sophisticated signal-averaging detection techniques, giv- ing very precise data, while the low pulse energy (-1 nJ) allows investi- gators to avoid the problems of nonlinear behavior and sample damage,

4 G. R. FLEMING

which plagued much earlier picosecond spectroscopy. The very high repeti- tion rate can lead to problems of its own, however. Sample heating and the building up of steady-state concentrations of transient species are possible problems: these can be overcome by the use of flowing sample cells and pulse repetition rate reduction by electro-optic or acousto-optic techniques. Hesselink and Wiersma['] have exploited the build-up of steady-state tran- sient populations in their observation of photon echoes from an accu- mulated grating in the electronic ground state.

A. Pulse-Shortening Mechanism

Qualitatively the pulse-shortening mechanism at work in the dye pulse laser results from the increasing gain on the rising edge of the dye pulse, fol- lowed by rapid depletion of the gain (gain saturation) at the peak of the dye pulse. These two factors produce greater amplification of the center of the pulse compared with the wings, thus produce pulse shortening. Figure 1 rep- resents a qualitative attempt to depict the pulse-shortening process.

In the absence of a circulating dye pulse, the gain in the dye medium will rise as the convolution of the argon pump pulse with the dye response func- tion (Fig. la). Since the excited-state lifetime of most laser dyes is long com- pared with the pumping pulse, once the gain has reached its maximum value it will decay only very slowly. Figure l b shows the sudden depletion in gain when a circulating dye laser pulse arrives in the jet stream. The pulse short- ening is produced when the increasing gain on the rising edge is followed by rapid depletion of the gain (gain saturation). In the example in Fig. lb the dye pulse has arrived a little late in the gain profile. The result is to advance the peak of the amplified pulse. This effect is clearly seen when the input and output pulses from the amplifying medium are compared normalized to the same height (Fig. lc). If the pulse were to amve too soon in the dye medium, the maximum would be retarded. An extensive discussion of this type of phenomenon has been given by Icsevgi and Lamb." The equi- librium situation then is that the interval between dye pulses emerging from the dye laser is equal to the interval between the argon pulses, even if the dye laser length is not exactly equal to (the inverse) of this frequency. This is an important point because it places specific stability requirements on the rf source driving the argon laser, since, in turn, the argon pulse repetition rate is precisely equal to (twice) the rf source frequency. If there is an optimum dye laser length for minimum dye pulse duration, then any jitter in the rf source frequency will perturb the dye laser operation and produce longer pulses. An rf source stability of at least 1 part per million is required for generation of pulses of less than 5 psec. Amplitude variations in the argon pulses are also equivalent to a timing jitter, and so high pulse-to-pulse am- plitude stability of the argon laser is required.

CONTINUOUSLY OPERATING, SYNCHRONOU!;LY MODE-LOCKED LASERS 5

B. Pulse Duration and Structurc: Measurements

One of the most useful methods for measuling pulse lengths is the zero- background, second-harmonic autocorrelation technique.' ' The technique (Fig. 2) is simple and convenient to operate. Two replica pulses are pro- duced by a beam splitter. One pulse traverses a fixed and the other a varia- ble optical path. The two pulse trains are then brought parallel (but not collinear) and focused to a common spot in s thin crystal of, for example, lithium iodate. The intensity of ultraviolet light generated along a line bi- secting the two input beams is then measured as a function of delay ( 7 ) be- tween the pulses. The signal generated by this method is proportional to the autocorrelation of the pulse intensities:

where the time fluctuations at the spectral frequency are averaged in the in- ner brackets, and the outer brackets indicate an average over a large number of pulses.

The influence of dye laser length is illustrated in Fig. 3, where the laser- tuning element was a three-plate birefringent filter. When the cavity length is optimal, the autocorrelation trace is smoolh and has neghgible intensity between pulses. For cavities too long, the trace becomes broader and devel- ops structure. For cavities that are too short, structure again develops but now, because of the finite duration of the argon pumping pulse, a second pulse appears. Referring again to Fig. 1, if t ie dye pulse arrives early, the gain will increase again after the passage of the dye pulse and it is possible that threshold will be exceeded a second time, allowing a second pulse to circulate. This will not occur for a pulse arriv ng late (cavity too long), since there will be insufficient pump pulse remaining to build up the gain back to threshold.

FIXED

UV TRflNSMlTTlNG FlLT R

VARIABLE PMT G ( T ) PATH

LilO,) CRYSTAL

G ( T ) = I(t) I ( t+r}dt

Fig. 2. Optical arrangement for zero-background autocorrelation measurement.

6 G. R. FLEMING

3- Plate Filter 12.5~ Too Long

- 5.7 psec

3-Plate Filter Optimum Cavity Length

3-Plate Filter 12.5~ Too Short

Wedge Etalon Optimum Cavity Length

l . , . l . , . i , , . l . , , l 1 ,

-20 0 20 40 60 80

T (psec)

Fig. 3. Dye laser output pulses as a func- tion of dye laser cavity length. Top three curves, tuning element: three-plate birefrin- gent filter, 45% Toutput coupler 1.2 W pump, 120 mW output. Bottom curve, interference wedge tuning element 80% T output coupler, 1.2 W pump, 20 mW output. The marked durations are the measured full width half- maxima of G(T) (AT) .

The shortest pulse obtainable depends on several factors: ( a ) the band- width of the intracavity filter, ( b ) the gain in the cavity, and (c) pump pulse duration. Table I summarizes our own and published data. The pulse dura- tions shown were obtained by dividing AT by 1.41 to 2 to obtain “the pulse duration.” This method ignores the influence of coherence, and below we show how to analyze G( 7) to obtain the true envelope autocorrelation.

In the noise burst model of Pike and Hersher,” in which the pulse is treated as a burst of bandwidth limit noise, G( T ) is decomposed into the product of two autocorrelations: one for the pulse envelope and one for the bandwidth- limited substructure. Thus

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8 G. R. FLEMING

where GJT) is the autocorrelation of the pulse envelope and GJT) is a Gaussian function resulting from the noise bandwidth.

By combining detailed fits of (2) with measurements of the laser spectrum (obtained with a 1 m spectrograph/SIT Vidicon combination), the influence of coherence in the measured autocorrelation traces can be reliably deter- mined.I3 The influence of cavity detuning on pulse envelope can then be ob- tained without the distortion imposed by coherence, and without confining observations to the “region of good mode locking.” In fact the influence of coherence is particularly insidious at close to optimum cavity length, since ( I ) the spectral width of the laser changes very rapidly in this region (see Fig. 4) and (2) very smooth autocorrelation traces can be obtained when the pulse envelope- bandwidth product is two to three times the transform limit.14 Once the coherence and envelope widths can be extracted reliably from autocorrelation measurements, it should be possible to deconvolute rise times containing both the coherent coupling c~ntribution,’~-” for which the appropriate time scale is determined by the coherence width, and the contri- bution from the molecular response with the pulse envelope.

Figure 4 shows the spectral full width at half-maximum (FWHM) and the FWHM of G N ( 7 ) ( A-rN) obtained by fitting autocorrelations to

Fig. 4. Spectral width (solid curves) and substructure width AT^ (dashed curves) versus cavity length mismatch for ( a ) 70% output coupler and birefringent filter, ( b ) 55% output coupler and bire fringent filter, and (c) 55% output coupler and wedge etalon. Note the change in the vertical scale in Fig. 4c.

CONTINUOUSLY OPERATING, SYNCHRONOU!;LY MODE-LOCKED LASERS 9

(13). Gaussian fits were excellent to both thc spectrum and the coherence spike and the product At,Av=0.43 k0.06 wit tin experimental error for all cavity lengths. For a Gaussian spectrum this ixoduct should be 0.441. Fig- ure 5 shows the dependence of the pulse envelope autocorrelation width ( AT-) on cavity length. Also shown in Fig. 5a is the FWHM of the full autocorre- lation trace G( 7 ) over the region where G( T ) appears as a smooth function. This function is clearly a shallower function of cavity length than AT^ and also leads to a considerable underestimate of ibe actual pulse duration. The variation in pulse envelope is qualitatively quite similar to the calculations of Kim et al.I8 Generally our envelope width does not increase as rapidly for short cavities as in the calculations of Kim et al.I3 A second difference is that the minimum envelope duration occurs for cavities in exact synchrony with the pump laser,14 rather than for slightly longer cavities.I8

The excellent fit of autocorrelations obtaincd with close-to-optimum cav- ity lengths to functions of the form exp( - a 1 A I) has led several authors 19-21

to hypothesize that their pulses are bandwidth-limited, single-sided expo- nentials (see Fig. 6). This conclusion is not supported by our spectral data;13 we do not observe the required Lorentzian s?ectral profile for a single- or double-sided exponential profile. Also the ti me-bandwidth product for an

Fig. 5. Pulse envelope width A? versus cavity length misnatch for ( a ) 70% output coupler and birefringer t filter, 55% output coupler and bire fringent filter, and (c) 55% output coupler and

-400 -200 0 200 400 wedge etalsn. For comparison, the FWHM of the autocomelition AT is included in (a). Covi ty Mismatch ( p m l

10 G. R. FLEMING

Fig. 6 . Autocorrelation trace for near- optimal cavity, birefringent filter, and 70% output coupler. ( a ) Semilogarithrnic plot of

-15 -10 -5 0 5 10 15 data (dotted curve) and fit to (2) (solid curve). ( b ) Linear plot of the data.

L5 l0,000

0

Delay , T ( p s e c l

exponential pulse is almost one order of magnitude smaller than that ob- served for our pulse if we assume exponential shape. Synchronously pumped dye lasers do not give bandwidth-limited, single-sided exponentials, and by assuming that they do, many authors have underestimated the pulse widths by about a factor of 3. For example, a symmetric exponential G ( 7 ) with FWHM of 2 psec would correspond to a Atp of about 2.7 rather than 1 psec.

How then does the exponential shape of G ( T ) for a perfectly matched cavity arise? Autocorrelations very closely resembling the experimental ex- ponential shape are given by (2) with G I and G, both Gaussian and AtP in the range two to three times AtN.14 The envelope shapes obtained through (2) for closely matched cavities, although much shorter than for mismatched cavities, are essentially the same shape at all cavity lengths and are roughly Gaussian. Van Stryland,, has pointed out the importance of remembering that (1) contains an ensemble average over more than lo7 pulses for each data point. Some pulses are likely to be longer than others, for example, those occurring shortly after lasing has been interrupted by a bubble in the dye jet. It is possible to generate almost any shape of autocorrelation by sum- ming the appropriate distribution of Gaussian functions of differing widths. Van Stryland22 obtains a symmetric exponential by using a rather large dis- tribution. He ignores, however, the presence of the coherence spike, the in- clusion of which obviates the necessity for such a large distribution. As pointed out above, the sum of two Gaussian functions comes very close to the mark, and a large distribution of pulse widths is not required to explain our results. A distribution of exponential or Lorentzian pulses does not re- produce our data. We conclude, then, that the pulses are Gaussian or skewed Gaussian.

CONTINUOUSLY OPERATING, SYNCHRONOUSLY MODE-LOCKED LASERS 1 1

We have also looked at the autocorrelation function obtained from the optical Kerr effect in CS,.23 This is a third-order autocorrelation

convoluted with the rotational correlation function of CS,. The G 3 ( 7 ) is sensitive to pulse asymmetry, but our measured traces are symmetric, indi- cating that the pulses are skewed only slightly if at all.

C. Pulse-to-Pulse Reproducibility

The technique shown in Fig. 2 measures the ensemble average of the auto- correlation function, since different pulses give rise to different parts of G( T )

and very many (lo9 to 10") pulses contribute to a single measurement. The pulse-to-pulse reproducibility is of consideIable significance for studies of molecular population risetimes and coherence phenomena. We have stud- ied this reproducibility by measuring cross-coi relations of the form ]In( t ) X Zn-J t + ~ ) d t , where n labels an individual puhe and m the number of round trips separating the pair, as a function of m."' Our results are illustrated in Fig. 7. When the dye laser cavity is set for optimum pulse length with no discernible structure or satellite pulses in the autocorrelation trace, the cross- correlation of a pulse with its near neighbors (n, n - m ) is indistinguishable from the autocorrelation (n, n) function. We studied m=O to 6 and found identical results. The results for m=O and 6 (Figs. 7d and 7 e ) are very reas- suring and strongly imply that there are no Iapid pulse-to-pulse variations in shape or duration.

Perhaps more revealing are the results presented in Figs. 7a to 7c, where the dye laser cavity length is incorrectly set and partial mode locking results. Autocorrelation traces such as the curve in Fig. 7c, consisting of a broad base with a sharp central spike, are characteristic of a noise burst.', In other words, Z ( t ) is not a single smooth pulse but has considerable random amplitude structure. In this case the duration of the burst of noise is related to the FWHM of the broad base. The G( T ) functio I has this shape because since the noise is random, only when the pulses arc exactly superimposed ( T = O ) do the noise spikes exactly overlap; at all other delay times there is consider- able cancellation. If the noise is nearly randoin and closely approaches zero amplitude between maxima, the spike and base will have heights in the ratio 2 : 1. The contributions from G , and Gp (equation 2) can be easily observed in Figs. 7a to 7c, where there is large (500 pni) cavity mismatch.

Figures 7a and 7b show the results of c1 oss-correlation measurements (n, n - 6 ) for dye laser cavities either too sho1 t or too long.I4 Here the noise spike marches to one side of the broad bas:, the direction depending on whether the dye cavity is too long or too short, and the distance depending

12 G. R. FLEMING

Coherence Spike

0

d Envelope

L

Fig. 7. Autocorrelation (n, n) and cross-correlation (n, n - m) function measurements. (a)-(c) Cavity length mismatched; ( d ) , ( e ) cavity length optimized. (a) n, n-6, cavity length 500 pm too short; ( b ) n, n-6, cavity length 500 pm too long; (c) n, n, cavity length 500 pm too long; (d) n, n-6, cavity length optimum; (e) n , n, cavity length optimum.

linearly on m. The center of the broad base remains in the same position in all cases.

Figure 8 depicts our explanation. Recalling the discussion of Fig. 1, if the circulating dye pulse arrives late in the gain profile, the rising edge of the pulse receives more amplification than the trailing edge and the pulse peak is advanced. The simulations in Fig. 8 shows that the “new” part of the pulse has “new” noise unrelated to noise on the same part of the pulse on its pre- vious round trip. The “old” noise on the “old” part of the pulse is, however, replicated. But the pulse shape has changed, and the old noise no longer oc- curs on precisely the same part of the pulse profile as on the pulse from the previous round trip. Thus the noise spikes add in phase for a value of 7

different from zero. This argument predicts a linear dependence of spike displacement on both m and cavity mismatch (in micrometers). Both linear dependences are observed experimentally (Fig. 9).

Perhaps the main significance of this experiment is that it allows experi- mental determination of the dye laser cavity length corresponding to exact match with the argon laser. The discussion above indicates that this will

c h

2m

Pulse Ptopagatlon - Maximum Envelope Overlap Maximum Substruclure Overlap

Fig. 8. Origin of the “coherence spike” for auto- and cross-correlations. Each trace repre- sents the same sample of random noise shaped with a Gaussian envelope. The envelopes are of equal width but are progressively displaced in the series n , n - m , n - 2 m . The cases shown cor- respond to maximum envelope overlap and maximum co ierence of the noise (maximum sub- structure overlap).

30.0 I

I jil 10.0

Fig. 9. Plot of displacement of coherence spike (in picoseconds) from the center of the pulse envelope against cavity mismatch (in microme:ers): squares. m = 6; triangles, m= 4;

250 500 750 circles. ni= 1. The solid lines are calculations accordin,; to our model.

-L. ~~ I --I .~

Cavity Displacement i p m )

13

14 G. R. FLEMING

occur when the cross-correlation trace becomes precisely symmetrical. We conclude, in contrast to theoretical predictions of optical pulse duration for dye laser slightly short24 or slightly long,18 that the shortest pulses are formed at exact cavity match.

111. DETECTION SYSTEMS

Results obtained from the application of synchronously pumped lasers to a range of relaxation processes are described in Section IV. This section briefly reviews the basic experimental techniques used in these applications.

and 265-350 nm for the second harmonic26) have been obtained from syn- chronously pumped dye lasers, and this range will certainly be extended in the near future both through new dyes and through frequency-mixing tech- niques (e.g., with ion laser linesz8). Economou et al.29 have reported the gen- eration of tunable vacuum ultraviolet radiation near 1700 A by resonantly enhanced four-wave mixing in strontium vapor. Thus a single ion-dye laser combination can provide almost all the excitation wavelengths one could wish for and is an ideal source for fluorescence spectroscopy. On the other hand, time-resolved absorption spectroscopy in general also requires an in- dependent range of monitoring wavelengths to record the spectra of tran- sient species. There are a number of solutions to this problem of varying complexity and generality. All the techniques described here use the pulses themselves to provide the time resolution- they are all variants of the pump-probe principle where the sample is excited by a strong pump pulse and the response of the sample to a probe pulse measured as a function of time delay between pump and probe. The optical setup is very similar to that in Fig. 2, where the frequency doubling crystal is replaced with sample cell and the intensity of the variable path length beam monitored as a function of delay time ( 7 ) .

A. Ground-State Recovery

The return of excited molecules to the ground state can be followed by the decrease in transmission of a weak probe pulse through the sample as a function of time delay after the arrival of the strong pump pulse. In this spe- cial case the pump and probe pulses may have the same wavelength, that is, they may originate from the same dye laser. A significant advantage of the high repetition rate, synchronously pumped source in any kind of absorp- tion rtieasurement is that lock-in amplifier detection may be used. If the pump beam only is chopped, then very small modulation depths may be de- tected on the probe beam, since the lock-in rejects the large dc component in the probe beam. A variant on the basic technique is to use the second

A very wide range of wavelengths (400- 1000 nm for the

CONTINUOUSLY OPERATING, SYNCHRONOUSLY MODE-LOCKED LASERS 15

harmonic for excitation and the fundamental a j the probe.29 This technique, however, has its dangers because with single-w avelength probing the effects of electronic relaxation between states and spectral relaxation within a single state cannot be disentangled. A straightforward example is the case of inter- system crossing where the initially formed triplet state has a different spec- trum from the relaxed triplet3’, 3 1 and single. wavelength probing will not provide accurate intersystem crossing rates. Moreover, if two replica pulses derived by beam-splitting are used for pump and probe, the coherence between the two pulses distorts the observed signal around zero delay time.16. I7 We discuss this point in more detail in Section IV.

B. Double Dye Laser Ttxhnique

A partial solution to the problem of prcviding complete wavelength coverage for the probing pulses is to synchronwsly pump two different dye lasers with some ion laser.32. 33 Interlaser jitters as low as 5 psec have been reported by Heritage and co-worker~.~~ To obtain minimum jitter, it is nec- essary to match the gain in the two lasers to have high pulse-to-pulse amplitude stability in the ion laser. With current mode locker design, the ion laser is mode locked on a single line; thus the range of wavelengths obtain- able in this technique is limited to the dyes that can be pumped by the same ion laser line. Mixing dyes and using energy transfer will extend this range somewhat. Using a non-dispersive mode-locking element (e.g., a rhomb), it is possible to mode lock ion lasers on “all lines” or a group of lines, and al- though longer pulses are expected (since ion laser cavity length will not be perfectly matched for all wavelengths), this may also provide a means of pumping a wider range of dyes. The double wavelength technique has been used to study the surface Raman effect,2* 34-3t photon echoes,33, 37 and Ra- man line shapes in a pulsed CARS (Coheren. Anti-Stokes Raman Scatter- ing) e~periment.~’

C. Amplification and Continuum Generation

The generation of picosecond white light continua by self-phase modula- tion in a variety of liquids (e.g., D20, CCl,, phosphoric acid) has become a common technique in experiments involving mode-locked solid-state lasers.39 The extension of this technique to cw mode-locked dye lasers has been pioneered by Shank and Ippeqm using a passively mode-locked dye laser. The principle is identical for a synchronously ~umped dye laser and has been applied by Martin et al.,’ An amplified Q -switched Nd-YAG laser is frequency doubled and pumps three stages of dye laser amplification, giving a total gain of lo6. The picosecond continuum is then generated by focusing the intense picosecond pulses into D20. Th: major disadvantage of this technique, aside from its cost and complexitj, is that the repetition rate is

16 G. R. FLEMING

lowered to about 10 Hz. On the other hand, this still represents a high repe- tition rate when compared with a Nd-glass laser system (- 10 -’ Hz)! Copper vapor lasers are capable of much higher (> 1 kHz) repetition rates, but these are not yet standard laboratory lasers.

D. Read-In- Read-Out Technique

Read-in- read-out provides a wide spectral coverage while maintaining the high repetition rates of the cw dye lasers. Again, the technique was devel- oped by Ippen and Shank,40, 42 and it has been applied to synchronously pumped dye lasers by Gillbro and Sund~trom.4~ The essential feature of the technique is that the probing pulse is obtained from an indepeildent dye laser that produces pulses long enough to be essentially flat on a picosecond time scale. This means that a small amount of jitter will not affect the probe in- tensity, and the transient information is read out of the probe pulse by a second picosecond pulse (derived from the first by beam splitting and there- fore with zero jitter) in a sum frequency technique. Again, lock-in amplifier detection is used so that only the desired information is recorded. Any wavelength that can be obtained from an ion laser-pumped dye laser can be used for probing, and this technique should assume considerable impor- tance in the near future. The experimental arrangement is shown in Fig. 10.

E. The Coherent Coupling Phenomenon

Pump-probe experiments with both pulses derived from the same pulse show an unexpected peaking or sharp spike at zero time delay.” This spike

n ” Read-in “

-

Chopper

“Read-out” j ;

-.*....... ’ ..‘ l - . - . - I I I Probe -

wz - L I I Sample I I

I I Li103 Filter

w1- + 7 b - Delay ( 7 ) Multichannel

averager -

Fig. 10. Read-in-read-out technique. From Ref. 40.