Femtosecond laser spectroscopy peter hannaford

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Femtosecond Laser

Spectroscopy

Edited by

Peter Hannaford

Femtosecond Laser

Spectroscopy

Springer

Print ISBN: 0-387-23293-1

Print ©2005 Springer Science + Business Media, Inc.

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1 Phase Controlled Femtosecond Lasers for Sensitive,

Precise and Wide Bandwidth Nonlinear Spectroscopy 1

Introduction to femtosecond optical frequency comb

Precision atomic spectroscopy – structure and dynamics

Molecular Spectroscopy aided by femtosecond optical

frequency comb

1812

hyperfine interactions, optical frequency standards and

2 Supercontinuum and High-Order Harmonics: “Extreme”

Coherent Sources for Atomic Spectroscopy and Attophysics 29

Phase coherence in harmonic generation

Some insight into the microscopic generation process

Collinear, phase-coherent, harmonic pulses

Ramsey spectroscopy with high-order harmonics

Collinear, phase-coherent, supercontinuum pulses

Multiple-beam interference from an array of

super-continuum sources: a spatial comb

Phase preservation in chirped-pulse amplification

Frequency combs, absolute phase control, and attosecond pulsesConclusions

3 The Measurement of Ultrashort Light – Simple Devices,

FROG and cross-correlation FROG

Dithered-crystal XFROG for measuring ultracomplex

supercontinuum pulses

OPA XFROG for measuring ultraweak fluorescence

Extremely simple FROG device

Conclusions

References

4 Femtosecond Combs for Precision Metrology

S.N Bagayev, V.I Denisov, V.M Klementyev, I.I Korel,

S.A Kuznetsov, V.S Pivtsov and V.F Zakharyash

Frequency stability of femtosecond comb by passage of

femtosecond pulses through a tapered fibre

Conclusions

References

61

6163646875858687

878994102106107

Femtosecond Laser Spectroscopy vii

5 Infrared Precision Spectroscopy using

Femtosecond-Laser-Based Optical Frequency-Comb Synthesizers

P De Natale, P Cancio and D Mazzotti

Evolution of metrological sources in the IR: from

synthesized frequency chains to fs-optical frequency combs

Molecular transitions for IR frequency metrology

IR coherent sources

3.1

3.2

Present coherent sources

Future IR sources and materials

Extending visible/near-IR fs combs to the mid-IR

4.1

4.2

Visible/near-IR combs

Bridging the gap with difference frequency generation

and optical parametric oscillators

Conclusions and perspectives for IR combs

References

6 Real-Time Spectroscopy of Molecular Vibrations with

Sub-5-Fs Visible Pulses

Stationary absorption and Raman spectra

Sub-5-fs real-time pump-probe apparatus

3 Results and discussion

Dynamics of the electronic states

Two-dimensional real-time spectrum

Dynamics of excitonic states

Analysis of coherent molecular vibration

Analysis of phase and amplitude of oscillation

Wave-packet motion on excited-state potentialenergy surface

Dynamic intensity borrowingTheoretical analysis of results

133134137137137139144144146148150150152153153154155156159159

dipole momentEvaluation of magnitude of the oscillatorstrength transfer

4 Conclusions

References

7 Vibrational Echo Correlation Spectroscopy: A New Probe

of Hydrogen Bond Dynamics in Water and Methanol

John B Asbury, Tobias Steinel and M.D Fayer

Hydrogen bond population dynamics in MeOD

Photoproduct band spectral diffusion in MeOD

Structural evolution in water, an overview

Local structure dependent evolution in water

4 Concluding remarks

References

8 Spectrally Resolved Two-Colour Femtosecond Photon Echoes

Lap Van Dao, Craig Lincoln, Martin Lowe and Peter Hannaford

Bloch equation description

Nonlinear optical response theory

Spectrally resolved photon echoes

One-colour two-pulse photon echoes

One-colour three-pulse photon echoes

Two-colour three-pulse photon echoes

4.3.1

4.3.2

Detection ofDetection of

5.3 Biological molecules

6 Summary and future directions

References

161163164164

167168170174174179184190193195197197199199202205207208208209211211216217217219219220221222223

Femtosecond Laser Spectroscopy ix

9 Optimal Control of Atomic, Molecular and Electron

Dynamics with Tailored Femtosecond Laser Pulses

Tobias Brixner, Thomas Pfeifer, Gustav Gerber

Matthias Wollenhaupt and Thomas Baumert

1

2

Introduction

One-parameter control on prototypes: atoms and dimers

in the gas phase

2.1 Control in the perturbative limit

2.1.1

2.1.2

2.1.3

Excitation schemeControl via the Tannor-Kosloff-Rice schemeControl via simple shaped pulses

2.2 Control in strong laser fields

2.2.1

2.2.2

Coherent coupling of molecular electronic statesCoherent coupling of atomic electronic states– control beyond population transfer andspectral interferences

3 Many-parameter control in the gas phase

Closed-loop femtosecond pulse shaping

Control of product ratios

Bond-selective photochemistry

Organic chemical conversion

Multiple optimization goals

4 Many-parameter control in the liquid phase

Coherent transfer to free electrons

Selective optimization of high-order harmonic

Chirped pulses and pulse shapers

Observation and control of coherent transients in one-photontransitions

3.1

3.2

3.3

Introduction

Control of transient dynamics with shaped pulses

Chirped pulses in the weak field regime: observation

225

226228229229232235238238

241243244247248249251252253254255255258262263

267

271271273267269

Control of coherent transients with simple temporal

shapes: temporal Fresnel lenses

Strong field: saturation of coherent transients

Reconstruction of wave function and laser pulse from

11 Ultrafast Processes of Highly Excited Wide-Gap Dielectric

Modelling of processes following fs pulse excitation

2.1 Microscopic model based on the Boltzmann equation

Electron-phonon-photon interactionCarrier-decay into defects

2.2 Phenomenological model of dielectric breakdown

3

4

Dielectric breakdown behaviour of oxide thin films

Time-resolved reflection and transmission studies

4.1

4.2

4.3

Experiments

Retrieval of the dielectric constant

Interpretation of the experiments

Contributing Authors

Number in parentheses indicates first page of author’s contribution.

S AKTURK (61), School of Physics, Georgia Institute of Technology,Atlanta, Georgia 30332-0430, USA

J B ASBURY (167), Department of Chemistry, Stanford University,Stanford, CA 94305, USA

S.N BAGAYEV (87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, Russia

T BAUMERT (225), Institute of Physics, University of Kassel, Plett-Str 40, 34132 Kassel, Germany

Heinrich-M BELLINI (29), Istituto Nazionale di Ottica Applicata (INOA), LargoFermi 6, 50125, Florence, Italy

T BRIXNER (225), Physics Department, University of Würzburg, AmHubland, 97074 Würzburg, Germany

P CANCIO (109), Istituto Nazionale di Ottica Applicata (INOA), LargoFermi 6, 50125 Florence, Italy, and European Laboratory for NonlinearSpectroscopy (LENS), Via Carrara 1, 50019 Sesto Fiorentino FI, Italy

Q CAO (61), School of Physics, Georgia Institute of Technology, Atlanta,Georgia 30332-0430, USA

B CHATEL (267), Laboratoire de Collisions, Agrégats et Réactivité (CNRSUMR 5589), IRSAMC, Université Paul Sabatier, 31062 Toulouse CEDEX,France

L.V DAO (197), Centre for Atom Optics and Ultrafast Spectroscopy,Swinburne University of Technology, PO Box 218, Hawthorn, Victoria

3122, Australia

P DE NATALE (109), Istituto Nazionale di Ottica Applicata (INOA), LargoFermi 6, 50125 Florence, Italy, and European Laboratory for NonlinearSpectroscopy (LENS), Via Carrara 1, 50019 Sesto Fiorentino FI, ItalyV.I DENISOV (87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, RussiaM.D FAYER (167), Department of Chemistry, Stanford University, Stanford,

X GU (61), School of Physics, Georgia Institute of Technology, Atlanta,Georgia 30332-0430, USA

P HANNAFORD (197), Centre for Atom Optics and Ultrafast Spectroscopy,Swinburne University of Technology, PO Box 218, Hawthorn, Victoria

3122, Australia

V.M KLEMENTYEV (87), Institute of Laser Physics, Siberian Branch,Russian Academy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk,Russia

T KOBAYASHI (133), Department of Physics, University of Tokyo, Hongo7-3-1, Bunkyo, Tokyo 113-0033, Japan

Femtosecond Laser Spectroscopy xiiiI.I KOREL (87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, RussiaS.A KUZNETSOV (87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, Russia

C LINCOLN (197), Centre for Atom Optics and Ultrafast Spectroscopy,Swinburne University of Technology, PO Box 218, Hawthorn, Victoria

M MERO (305), Department of Physics and Astronomy, University of NewMexico, Albuquerque NM 87131, USA

T PFEIFER (225), Physics Department, University of Würzburg, AmHubland, 97074 Würzburg, Germany

V.S PIVTSOV (87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, Russia

W RUDOLPH (305), Department of Physics and Astronomy, University ofNew Mexico, Albuquerque NM 87131, USA

A SHREENATH (61), School of Physics, Georgia Institute of Technology,Atlanta, Georgia 30332-0430, USA

T STEINEL (167), Department of Chemistry, Stanford University, Stanford,

J YE (1), JILA, National Institute of Standards and Technology andUniversity of Colorado, Boulder, Colorado 80309-0440, USA

V.F ZAKHARYASH(87), Institute of Laser Physics, Siberian Branch, RussianAcademy of Sciences, Pr Lavrentieva, 13/3, 630090 Novosibirsk, Russia

J ZELLER (305), Department of Physics and Astronomy, University of NewMexico, Albuquerque NM 87131, USA

The embryonic development of femtoscience stems from advances made

in the generation of ultrashort laser pulses Beginning with mode-locking ofglass lasers in the 1960s, the development of dye lasers brought the pulsewidth down from picoseconds to femtoseconds The breakthrough in solidstate laser pulse generation provided the current reliable table-top lasersystems capable of average power of about 1 watt, and peak power density

of easily watts per square centimeter, with pulse widths in therange of four to eight femtoseconds Pulses with peak power densityreaching watts per square centimeter have been achieved in laboratorysettings and, more recently, pulses of sub-femtosecond duration have beensuccessfully generated

As concepts and methodologies have evolved over the past two decades,the realm of ultrafast science has become vast and exciting and has impactedmany areas of chemistry, biology and physics, and other fields such asmaterials science, electrical engineering, and optical communication Inmolecular science the explosive growth of this research is for fundamentalreasons In femtochemistry and femtobiology chemical bonds form andbreak on the femtosecond time scale, and on this scale of time we can freezethe transition states at configurations never before seen Even for non-reactive physical changes one is observing the most elementary of molecularprocesses On a time scale shorter than the vibrational and rotational periodsthe ensemble behaves coherently as a single-molecule trajectory

But these developments would not have been possible without thecrystallization of some key underlying concepts that were in the beginningshrouded in fog First was the issue of the “uncertainty principle”, whichhad to be decisively clarified Second was the question of whether one could

sustain wave-packet motion at the atomic scale of distance In other words,would the de Broglie wavelength of the atom become sufficiently short todefine classical motion – “classical atoms” – and without significantquantum spreading? This too had to be clearly demonstrated and monitored

in the course of change, not only for elementary processes in molecularsystems, but also during complex biological transformations And, finally,some questions about the uniqueness and generality of the approach had to

be addressed For example, why not deduce the information from resolution frequency-domain methods and then Fourier transform to obtainthe dynamics? It is surely now clear that transient species cannot be isolatedthis way, and that there is no substitute for direct “real time” observationsthat fully exploit the intrinsic coherence of atomic and molecular motions

high-Theory has enjoyed a similar explosion in areas dealing with ab initio

electronic structures, molecular dynamics, and nonlinear spectroscopies.There has been progress in calculating potential energy surfaces of reactivesystems, especially in their ground state On excited-state surfaces it is nowfeasible to map out regions of the surface where transition states and conicalintersections are important for the outcome of change For dynamics, newmethods have been devised for direct viewing of the motion by formulatingthe time-dependent picture, rather than solving the time-independentSchrödinger equation and subsequently constructing a temporal picture.Analytical theory has been advanced, using time-ordered density matrices, toenable the design of multidimensional spectroscopy, the analogue of 2-D(and higher) NMR spectroscopy That the coupling between theory andexperiment is profound is evident in many of the chapters in this volume.Other areas of studies are highlighted in this volume The making offemtosecond combs for precision metrology and spectroscopy, and theadvances in nonlinear and multidimensional optical techniques are twoexamples of such frontiers The ability to count optical oscillations of morethan cycles per second can potentially provide all-optical atomic clockswith a new limit of precision Similarly, the ability to generate sub-femtosecond pulses pushes the limit and resolution toward new studies ofelectron dynamics Besides these advances in precision (optical cycles) andpulse duration (pulse width) there are those concerned with the phase.Beginning in 1980, the phase of an optical pulse has been experimentallyunder control and pulses of well-defined phases etc) have beengenerated and utilized in, among other applications, the control of emissionfrom molecules But only recently could composite phases be prescribedwith a feedback algorithm to control the outcome of a reactive channel, asshown in this volume Coherent control is a frontier field stimulatingresearch in both theory and experiment

Femtosecond Laser Spectroscopy xviiEdited by Peter Hannaford this volume is a welcomed edition to thefield as it brings together the latest in some areas of developments with animpressive mix of new methodologies and applications The use offemtosecond combs for precision measurements is well covered andcoherent control is presented with demonstrations for atomic, molecular andelectronic processes Nonlinear optical methods, including novel geometries

of photon and vibrational echoes, are described for the investigation ofmolecular systems, in particular dye molecules, hydrogen-bonded networks,semiconductor quantum dots, and biomolecules Measurements of ultrashortpulses, time-resolved reflection and transmission methods, and real-timespectroscopy with sub-5-femtosecond visible pulses provide the means forexploring new regimes and resolutions

This book in the series on Progress in Lasers gives an exposé of some

current and exciting research areas in the technology of pulse generation and

in the applications of femtoscience

Ahmed ZewailCalifornia Institute of TechnologyPasadena, California

May 2004

When I was first approached to edit a volume on Femtosecond Laser

Spectroscopy in 2000, I did not anticipate that the field was about to explode,

with the announcement of a series of remarkable new developments andadvances This volume describes these recent developments in elevenchapters written by leading international researchers in the field It includessections on:

Femtosecond optical frequency combs, which are currentlyrevolutionising ultrahigh precision spectroscopy and optical frequencymetrology;

Soft X-ray femtosecond laser sources, which promise to have importantapplications in biomedical imaging;

Attosecond laser sources, which will provide the next generation ofsources to study ultrafast phenomena such as electron dynamics;

Novel methods for measuring and characterizing ultrashort laser pulsesand ultrashort pulses of light;

Coherent control of atomic, molecular and electron dynamics withtailored femtosecond laser pulses;

Real-time Spectroscopy of molecular vibrations with sub-5-fs pulses; andMultidimensional femtosecond coherent spectroscopies for studyingmolecular and electron dynamics

Indeed, it is gratifying to see that with the recent advent of attosecond lasersources the title of this volume may soon be rendered obsolete

I would like to thank each of the contributors for their cooperation inpreparing this volume, and Ahmed Zewail for writing the Foreword Iappreciate the amount of work that goes into writing chapters of this typewhen the authors are heavily burdened with other demands on their time I

feel honoured and privileged to have been associated with such an eminentgroup of researchers I also thank my co-workers in the UltrafastSpectroscopy group at Swinburne University of Technology – Lap Van Dao,Martin Lowe, Craig Lincoln, Shannon Whitlock, Xiaoming Wen, Tra My

Do, Petrissa Eckle and David McDonald – for their help and encouragementduring the preparation of this volume and for critical reading of some of thechapters I thank Tien Kieu, Grainne Duffy and David Lau for theirassistance with the preparation of the camera-ready chapters, and GustavGerber for kindly allowing the use of Figure 9-12 on the front cover of thisvolume Finally, I thank the publishers of the following journals and booksfor permission to reproduce material in this volume: Applied Physics B,Applied Physics Letters, Journal of Chemical Physics, Journal of Physics B,Laser Spectroscopy Proceedings, Nature, Optics Express, Optics Letters,Optical Review, Review of Scientific Instruments, Physical Review Letters,Physical Review A, and SPIE Proceedings

Peter HannafordSwinburne University of TechnologyMelbourne, June 2004

Chapter 1

PHASE CONTROLLED FEMTOSECOND

LASERS FOR SENSITIVE, PRECISE, AND WIDE BANDWIDTH NONLINEAR SPECTROSCOPY

Jun Ye

JILA, National Institute of Standards and Technology and University of Colorado

Boulder, Colorado 80309-0440, USA

Ye@jila.colorado.edu

Abstract: Recent progress in precision control of pulse repetition rate and

carrier-envelope phase of ultrafast lasers has established a strong connection between optical frequency metrology and ultrafast science A wide range of applications has ensued, including measurement of absolute optical frequencies, precision laser spectroscopy, optical atomic clocks, and optical frequency synthesis in the frequency-domain, along with pulse timing stabilization, coherent synthesis of optical pulses, and phase-sensitive extreme nonlinear optics in the time-domain In this chapter we discuss the impact of the femtosecond optical frequency comb to atomic and molecular spectroscopy Measurements performed in the frequency-domain provide a global picture of atomic and molecular structure at high precision while providing radio-frequency clock signals derived from optical standards Time- domain analysis and experiments give us new possibilities for nonlinear optical spectroscopy and sensitive detections with real-time information.

Key words: Phase control, femtosecond lasers, optical comb, precision frequency

metrology, nonlinear spectroscopy.

1 INTRODUCTION TO FEMTOSECOND OPTICAL

FREQUENCY COMB

Precise phase control of femtosecond lasers has become increasinglyimportant as novel applications utilizing the femtosecond laser-based optical

comb are developed that require greater levels of precision and higherdegrees of coherence and control [1] Improved stability is beneficial forboth frequency-domain applications, where the relative phase or “chirp”between comb components is unimportant (e.g., optical frequencymetrology), and, perhaps more importantly, time-domain applications wherethe pulse shape and/or duration are vital, such as in nonlinear opticalinteractions [2] For both types of applications, minimizing jitter in the pulsetrain and noise in the carrier-envelope phase is often critical to achieve thedesired level of precision and coherence Phase-stabilized mode-lockedfemtosecond lasers have played a key role in recent advances in opticalfrequency measurement [3-5], carrier-envelope phase stabilization [2, 6, 7],all-optical atomic clocks [8, 9], optical frequency synthesizers [10], coherentpulse synthesis [11], and broadband, phase-coherent spectral generation [12].Mode-locked lasers generate short optical pulses by establishing a fixedphase relationship between all of the lasing longitudinal modes Tounderstand the connection between the time-domain and frequency-domaindescriptions of a mode-locked laser and the pulse train that it emits, a keyconcept is the carrier-envelope phase This is based on the decomposition of

the pulses into an envelope function, Ê(t), that is superimposed on a

pulse is written as The carrier-envelope phase, is thephase shift between the peak of the envelope and the closest peak of thecarrier wave In any dispersive material, the difference between group andphase velocities will cause to evolve This group-phase velocitymismatch inside a laser cavity produces a pulse-to-pulse phase shiftaccumulated over one round-trip as

When is constant, the spectrum of a femtosecond optical combcorresponds to identical pulses emitted by the mode-locked laser For asingle pulse, the spectrum is the Fourier transform of its envelope functionand is centered at the optical frequency of its carrier Generally, for anypulse shape, the frequency width of the spectrum will be inverselyproportional to the temporal width of the envelope For a train of identicalpulses, separated by a fixed interval, the spectrum can easily be obtained by

a Fourier series expansion, yielding a comb of regularly spaced frequencies,where the comb spacing is inversely proportional to time interval betweensuccessive pulses, i.e., the inverse of the repetition rate of the laser TheFourier relationship between time and frequency resolution guarantees thatany spectrometer with sufficient spectral resolution to distinguish theindividual comb lines cannot have enough temporal resolution to separatesuccessive pulses Therefore, the successive pulses interfere with each otherinside the spectrometer and the comb spectrum occurs because there arecertain discrete frequencies at which the interference is constructive Usingcontinuous carrier wave with frequency so that the electric field of the

1 Phase Controlled Femtosecond Lasers for Sensitive 3

the result from Fourier analysis that a shift in time corresponds to a linearphase change with frequency, we can readily see that the constructiveinterference occurs at where n is an integer.

When is evolving with time, such that from pulse to pulse (with atime separation of there is a phase shift of then in thespectral domain a rigid shift will occur for the frequencies at which thepulses add constructively This shift is easily determined as

Thus the optical frequencies, of the comb lines can be written as

where n is a large integer of order that indexes the comb line, and

is the comb offset due to pulse-to-pulse phase shift,

The relationship between time- and frequency-domain pictures issummarized in Fig 1-1 The pulse-to-pulse change in the phase for the train

of pulses emitted by a mode-locked laser can be expressed in terms of theaverage phase and group velocities inside the cavity Specifically,

where is the round-trip length of the laser cavityand is the “carrier” frequency

Figure 1-1 Summary of the time-frequency correspondence for a pulse train with evolving

carrier-envelope phase.

Armed with the understanding of the frequency spectrum of a locked laser, we now turn to the question of measuring the absolutefrequencies of comb lines For a frequency measurement to be absolute, itmust be referenced to the hyperfine transition of that defines thesecond From the relations listed above we see that determining the absoluteoptical frequencies of the femtosecond comb requires two radio frequency(RF) measurements, that of and Measurement of is straightforward;

mode-we simply detect the pulse train’s repetition rate (from tens of MHz toseveral GHz) with a fast photodiode On the other hand, measurement of

is more involved as the pulse-to-pulse carrier envelope phase shift requiresinterferometric measurement, whether it is carried out in the time-domain[13] or frequency-domain [14] When the optical spectrum spans an octave

in frequency, i.e., the highest frequencies are a factor of two larger than thelowest frequencies in the spectrum, measurement of is greatly simplified

If we use a second harmonic crystal to frequency double a comb line, with

index n, from the low frequency portion of the spectrum, it will have

approximately the same frequency as the comb line on the high frequency

side of the spectrum with index 2n Measuring the heterodyne beat between

these two families of optical comb lines yields a difference frequency by

which is just the offset frequency.Thus, an octave-spanning spectrum enables a direct measurement of [6].Note that an octave-spanning spectrum is not required; it just represents thesimplest approach We designate this scheme, shown in Fig 1-2(a), as “self-referencing” since it uses only the output of the mode-locked laser Self-referencing is not the only means of determining the absolute opticalfrequencies given an octave-spanning spectrum For example, the absoluteoptical frequency of a CW laser can be determined if its frequency lies close

to comb line n in the low frequency portion of the femtosecond comb

spectrum Then the second harmonic of the CW laser will be positioned

close to the comb line 2n Measurement of the heterodyne beat between the

CW laser frequency, and the comb line n gives

and between the second harmonic of the CW laser and comb line 2n gives

Mixing the beats with appropriate weightingfactors gives

which represents the second detection scheme shown in Fig 1-2(b) [9]

An octave-bandwidth optical comb is not straight-forward to produce AFourier-transform limited pulse with a full width at half maximum (FWHM)bandwidth of an octave centered at 800 nm would only be a single opticalcycle in duration Such short pulses have not been achieved Fortunately,neither a transform-limited pulse nor a FWHM of an octave is actuallyneeded The pulse width is unimportant as the measurement and controltechniques are purely frequency domain approaches Experimentally, it hasbeen found that even if the power at the octave spanning points is 40 dBbelow the peak, it is still possible to observe strong f-to-2f heterodyne beats.Still, the necessary comb bandwidth is larger than that from a typical sub-10-fs mode-locked Ti:sapphire laser One approach to produce this sufficientspectral bandwidth is based on self-phase modulation directly inside theTi:Sapphire crystal itself [15] or inside an additional glass plate locatedinside the laser cavity with secondary coincident time and space foci [16]

1 Phase Controlled Femtosecond Lasers for Sensitive 5

These techniques require carefully designed mirrors and laser cavities.Additional spectral bandwidth can also be obtained by minor changes in thecavity configuration of a high repetition rate laser, although it has not yetyielded sufficient intensity at the octave points for the observation of f-to-2fbeats [17] Another widely adopted approach is to generate the extra combbandwidth using microstructure fibers that have zero group velocitydispersion (GVD) within the emission spectrum of a Ti:sapphire laser [18].The large index contrast for waveguiding inside microstructure fibers hastwo consequences: first, the ability to generate a zero in the GVD at visible

or near-infrared wavelengths and, secondly, the possibility of using a muchsmaller core size This allows broadband continuum generation with onlypulse energies

Figure 1-2 Two equivalent schemes for measurement of using an octave-spanning optical

frequency comb In the self-referencing approach, shown in (a), frequency doubling and comparison are accomplished with the comb itself In the second approach, shown in (b), the fundamental frequency and its second harmonic of a CW optical standard are used

to determine These two basic schemes are employed for absolute optical frequency measurement and implementation of optical atomic clocks.

For the purpose of using a femtosecond optical comb for absolute opticalfrequency measurements, it is straight-forward to establish the frequencyvalues of all of the comb components The comb’s frequency spacingcan be phase locked with high precision via detection of higher harmonics ofrelative to an RF standard The value of is determined and controlled

using schemes shown in Fig 1-2 Control of requires a servo transduceracting differentially on the intracavity group and phase delays One commonmethod for adjusting is to swivel the end mirror in the arm of the lasercavity that contains the prism sequence [19] An alternative method ofcontrolling is via modulation of the pump power, with likely contributionsfrom the nonlinear phase, spectral shifts, and the intensity dependence in thegroup velocity [20] It is worth noting that a scheme implemented by Telle

et al [21] allows the frequency comb to be free running (without any activestabilization) while making highly precise measurement or connection for anoptical frequency interval located within the comb bandwidth

The dramatic simplification of a complex optical frequency chain to that

of a single mode-locked laser has greatly facilitated optical frequencymeasurement Another important aspect of this new technology is its highdegree of reliability and precision and lack of systematic errors Forexample, recent tests have shown that the repetition rate of a mode lockedlaser equals the mode spacing of the corresponding comb to within themeasurement uncertainty of The uniformity of the comb mode spacinghas also been verified to a level below even after spectral broadening

in a fiber [3, 4] Comparison between two separate fs comb systems, bothlinked to a common reference source (microwave or optical), allows one toexamine the intrinsic accuracy of a femtosecond-comb-based frequencymeasurement system, currently at a level of a few parts in with nomeasurable systematic effects [22] Direct comparisons of absolute opticalfrequency measurements between the femtosecond comb technique and thetraditional harmonic frequency chain approach have also produced assuringmutual confirmations at the to level [5, 23]

As the measurement precision for optical frequencies continues toadvance, the stability limitation imposed by available RF standards used for

fs comb stabilization becomes an important issue [23, 24] Instead ofoperating a fs comb using RF references, it appears to be advantageous tooperate the comb by stabilizing it to an optical frequency standard The fscomb in turn produces optically derived stable clock signals in the RFdomain, leading to a so-called “optical atomic clock” [8, 9, 25] Recentexperimental demonstrations support the concept that, in the future, the moststable and accurate frequency standards will be based on optical transitions[26, 27] Stepping down the stability level by one or two orders ofmagnitude, portable optical frequency standards that offer compact, simple,and less expensive system configurations have also shown competitiveperformance with (in)stability near at 1 to 10 s averaging time [28]

To realize an optical atomic clock, an optical comb needs to be stabilized

to a pre-selected optical frequency source at a precision level that exceedsthe optical standard itself can be extracted in a straight-forward manner

1 Phase Controlled Femtosecond Lasers for Sensitive 7

using either schemes shown in Fig 1-2 is then stabilized with respect toeither or an auxiliary stable RF source It is worth noting thatstabilization of at a few mHz is more than adequate, as it yields fractionalfrequency noise of for an optical carrier A heterodyne beat betweenone of the comb components and the optical standard yields informationabout fluctuations in For the particular case shown in Fig 1-2(b),

producing adirect link between the frequencies and After appropriate processing,this error signal is used to stabilize the phase of coherently to therebyproducing an output clock signal in the RF domain derived from

Besides the capability of deriving RF signals from an optical frequencystandard, a fs comb can, of course, also be used to transfer the stability ofoptical standards across vast frequency gaps to other optical spectral regions.Easy access to the resolution and stability offered by optical standards willgreatly facilitate the application of frequency metrology to precisespectroscopic investigations For spectroscopy applications, we indeed oftendesire a single-frequency and reasonably powered optical carrier wave thatcan be tuned to any desired optical spectral feature of interest Realization ofsuch an optical frequency synthesizer (analogous to its RF counterpart) willadd a tremendously useful tool for modern spectroscopy experiments.Ideally, one would realize a high precision optical frequency synthesizerbased on a stable fs comb linked to an optical frequency standard One couldforesee an array of diode lasers, each covering a successive tuning range of

~ 10 to 20 nanometers that would collectively cover most of the visiblespectrum Each diode laser frequency would be controlled by the stabilizedoptical comb, and therefore be directly related to the absolute time/frequencystandard in a phase coherent fashion, while the setting of the opticalfrequency would be accomplished via computer control

In our preliminary implementation of such an optical frequencysynthesizer [10], the fs comb system is referenced by an opticalfrequency standard at 532 nm A CW diode laser, as well as a CWTi:sapphire laser, is used to tune through targeted spectral regions (forexample, Rb D1 and D2 lines at 795 and 780 nm for the diode laser andhyperfine transitions in the region of 490 - 520 nm) with desired frequencystep sizes, while maintaining absolute reference to the stabilized opticalcomb A self-adaptive search algorithm first tunes the CW laser to aspecified wavelength region with the aid of a wavelength measurementdevice (100 MHz resolution) A heterodyne beat signal between the laser’sfrequency and that of a corresponding comb line is then detected andprocessed For fine-tuning, an RF source provides a tunable frequency offsetfor the optical beat Once the laser frequency tuning exceeds we reset the

RF offset frequency back to the original value to start the process over again

The laser frequency can thus be tuned smoothly in an “inch-worm” manneralong the comb structure We have demonstrated two fundamental aspects of

an optical frequency synthesizer; namely continuous, precise tuning of theoptical frequency as well as arbitrary frequency setting on demand Theentire search process takes about a minute

2 PRECISION ATOMIC SPECTROSCOPY –

STRUCTURE AND DYNAMICS

The first example of spectroscopic application of a precisely stabilizedfemtosecond comb centers on investigation of a two-photon transition inlaser cooled Rb atoms Phase coherence among the successive pulsesinteracting with a cold atomic sample brings immediately to mind theapproach of Ramsey interference for precision atomic spectroscopy.However, the difference here is that the bandwidth associated with thefemtosecond pulse is so broad that one is enabled to explore the structure of

a large number of atomic states all at once, along with the possibility ofstudying coherent accumulation in a multi-level system [29] It is thuspossible to simultaneously explore the global structure and dynamics of anatomic system The multi-pulse interference in the time domain gives aninteresting variation and generalization of the two-pulse based temporalcoherent control of the excited-state wave-packet

From the frequency domain perspective, it is also straight-forward toappreciate the fact that the spectroscopic resolution and precision will not becompromised by the use of ultrafast pulses since they are associated with aphase-stabilized, wide-bandwidth femtosecond comb Phase coherenceamong various transition pathways through different intermediate statesproduces multi-path quantum interference effects on the resonantly enhancedtwo-photon transition probability in the cold Rb atoms The two-photontransition spectrum can be analyzed in terms of the pulse repetition rateand the carrier-envelope offset frequency [30] Both can be stabilized tohigh precision With a set of measurements taken at a few different, butpredetermined, combinations of and one can essentially derive allrelevant atomic energy level positions in absolute terms

Doppler-free two-photon spectroscopy is carried out usually with twoequal-frequency cw laser beams propagating in opposite directions The two-photon transition rate can be resonantly enhanced via the intermediate stateswith two different laser frequencies [31] or accelerated atomic beams [32],with a small residual Doppler effect High-resolution two-photonspectroscopy using pulsed light has also been demonstrated [33], with therecent extension to cold atoms [34] The unique feature of the present work

1 Phase Controlled Femtosecond Lasers for Sensitive 9

is that the wide bandwidth optical comb allows all relevant intermediatestates to resonantly participate in the two-photon excitation process,permitting the phase coherence among different comb components to induce

a stronger transition rate through quantum interference Following the initialproposal and the subsequent theoretical investigations, we are exploringexperimentally this novel, high-resolution spectroscopy using a femtosecondlaser [35]

Figure 1-3 Top: Schematic of the relevant energy levels of the atom and the domain perspective of the atom-light interaction Bottom: Time-domain picture showing a sequence of mode-locked pulses, with the relevant interaction parameters in and

frequency-Figure 1-3 shows the relevant energy levels involved in the photon transition from the ground state to the excited state Thedipole-allowed intermediate states, and are located ~ 2 nm and

two-17 nm below the virtual level, respectively Also shown is a regularly spacedcomb of optical frequencies around 800 nm The experimental bandwidth ofthe comb is ~ 50 nm, emitted from a 10 fs, 100 MHz repetition-rate mode-locked Ti:sapphire laser Adjustment of and allows the combcomponents to line up with corresponding hyperfine states of and

to resonantly enhance the two-photon transition This dependence of themulti-path quantum interference on and leads to simultaneousstabilization of both quantities, and thereby the entire comb The frequency-

domain analysis is complemented by the time-domain multi-pulse Ramseyinterference picture, as illustrated in Fig 1-3, where the relevant quantitiesfor interaction are and Both the frequency-domain and thetime-domain analyses produce the same result on the two-photon transitionspectra when one assumes a static distribution among the relevant atomicstates However, to follow the time evolution of the system, it is necessary toexplore the interaction dynamics from one pulse to the next, taking intoaccount both the atomic coherence and the optical coherence The generalLiouville equation for the density-matrix components of the atomic states,along with phenomenological decay terms, are used to derive a set of Blochequations describing the evolution of all relevant levels associated with theground, the excited, and the intermediate states.

Figure 1-4 Density-matrix calculation of the excited state population due to the two-photon

transition induced in by the phase-coherent fs pulse train The nominal values of and are indicated The spectrum given by the dashed line corresponds to the case with a static population while the spectrum given by solid line shows dynamic evolution after 4000 pulses.Figure 1-4 illustrates the calculated population of the 5D states due to thetwo-photon transition, showing clear evidence of population transfer whenthe number of interacting pulses increases Not surprisingly, the mostdominant transition pathway when a large number of pulses is involved is

which represents a so-calledclosed transition The horizontal axis represents a scanning of from itsnominal value indicated in the figure The actual optical frequency for thetwo-photon transition is near 385 THz, which represents a harmonic order of

of Therefore, a change in by ~ 26 Hz implies a repeat in

1 Phase Controlled Femtosecond Lasers for Sensitive 11

the optical comb spectrum near the two-photon transition region, and hence

a repeat in the two-photon spectra

Figure 1-5 shows experimental two-photon spectra resonantly enhanced

by the intermediate states We clearly confirm the predicted effect ofpopulation transfer by the pulse sequence when we compare the two spectraobtained under the influence of 1,200 and 250,000 pulses, respectively.Basically, the only transition pathway survived at the limit of a large number

of pulses is It is interesting to notethat we have also observed the pure two-photon transition pathway (energies

of the two photons are degenerate) that is not resonantly enhanced by theintermediate states The signal is indicated in Fig 1-5 by a small peak(around 19 Hz) in the 2.5 ms evolution curve represented by diamonds,which repeats every 13 Hz in the scan of the value This observation isconsistent with the fact that a pure two-photon transition would repeat itssignal every time the pulse spectrum is shifted by half of the repetitionfrequency More recent work has pushed the spectroscopy resolution to thelimit of the natural linewidth of 660 kHz associated with the D-state lifetime,owing to the use of ultracold atoms and careful control of photon momentumtransfer The work on this simple two-photon transition dynamics thusprovides a solid link between the time-domain picture of carrier-envelopephase and the frequency-domain picture of and One practicalconsequence of these results is that we can now control both degrees offreedom for the femtosecond comb directly by a transition in cold atoms

Figure 1-5 Experimental observation of resonantly enhanced two-photon transition in cold

atoms with a clear influence by the pulse sequence on the atomic state dynamics.

3 MOLECULAR SPECTROSCOPY AIDED BY

FEMTOSECOND OPTICAL FREQUENCY COMB

Before we study examples of molecular spectroscopy aided by thetechnology of the precision frequency comb, we would like to discuss brieflythe implications of the frequency-domain control of the femtosecond laser tothe time-domain experiments Prior to the development of femtosecondcomb technology, mode-locked lasers were used almost exclusively fortime-domain experiments Although the femtosecond comb technology hasprimarily impacted on the frequency-domain applications described earlier,

it is having an impact on time-domain experiments and promises to bringabout just as dramatic advances in the time-domain as it has in opticalfrequency metrology and optical clocks Indeed, it is fascinating to blur theboundary between traditional CW precision spectroscopy and ultrafastphenomena The time-domain applications put stringent requirements on thecarrier-envelope phase coherence Stabilization of the “absolute” carrier-envelope phase at a level of tens of milliradians has been demonstrated andthis phase coherence is maintained over an experimental period exceedingmany minutes [36], paving the groundwork for synthesizing electric fieldswith known amplitude and phase at optical frequencies Working with twoindependent femtosecond lasers operating at different wavelength regions,

we have synchronized the relative timing between the two pulse trains at thefemtosecond level [37], and also phase locked the two carrier frequencies,thus establishing phase coherence between the two lasers By coherentlystitching optical bandwidths together, a “synthesized” pulse has beengenerated [11] With the same pair of Ti:sapphire mode-locked lasers, wehave demonstrated widely tunable femtosecond pulse generation in the mid-and far-IR using difference-frequency-generation [38] The flexibility of thisnew experimental approach is evidenced by the capability of rapid andprogrammable switching and modulation of the wavelength and amplitude ofthe generated IR pulses A fully developed capability of producing phase-coherent visible and IR pulses over a broad spectral bandwidth, coupled witharbitrary control in amplitude and pulse shape, represents the ultimateinstrumentation for coherent control of molecular systems A pulse train withgood carrier-envelope phase coherence is also very promising forexperiments that are sensitive to i.e., the “absolute” pulse phase [2].This can be manifested in “extreme” nonlinear optics experiments, orcoherent control

The capability to precisely control pulse timing and the pulse-carrierphase allows one to manipulate pulses using novel techniques and achieveunprecedented levels of flexibility and precision, as will be demonstrated inthe work on time resolved spectroscopy of molecules For example, the

1 Phase Controlled Femtosecond Lasers for Sensitive 13

simultaneous control of timing jitter and carrier-envelope phase can be used

to phase coherently superpose a collection of successive pulses from a locked laser By stabilizing the two degrees of freedom of a pulse train to anoptical cavity acting as a coherent delay, constructive interference ofsequential pulses will be built up until a cavity dump is enabled to switch outthe “amplified” pulse [39] Such a passive pulse “amplifier”, along with thesynchronization technique we developed for pulse synthesis, has made astrong impact on the field of nonlinear-optics based spectroscopy andimaging of bio-molecular systems, showing significant improvements inexperimental sensitivity and spatial resolution [40, 41] With the enhanceddetection sensitivity comes the capability of tracking real time biologicaldynamics An ultrafast laser locked to a high stability cavity is also expected

mode-to demonstrate extremely low pulse jitter and carrier-envelope phase noise,which will be particularly attractive for time-domain experiments Inaddition, we are exploring the use of pulse-cavity interactions to obtain ahigh sensitivity in intracavity spectroscopy (linear and non-linear) with awide spectral coverage, as well as to enhance nonlinear interaction strengthsfor high efficiency nonlinear optical experiments

With these new sets of tools in hand, it is appropriate to revisit the topics

of precision molecular spectroscopy It is also interesting to explorespectroscopy in a more broad sense For example, one can now carry outprecision spectroscopy using ultrafast lasers On the other hand, coherentcontrol of molecular motion can be performed in the spirit of precisionmeasurement The capability of absolute optical frequency measurements inthe visible and IR spectral regions adds a new meaning to the term ofprecision molecular spectroscopy Understanding of molecular structure anddynamics often involves detailed spectral analysis over a broad wavelengthrange Such a task can now be accomplished with a desired level of accuracyuniformly across all relevant spectral windows, allowing preciseinvestigations of minute changes in the molecular structure over a largedynamic range For example, absolute frequency measurement of vibrationovertone transitions and other related resonances (such as hyperfinesplitting) reveals precise information about the molecular potential energysurface and relevant perturbation effects We have pursued such a study iniodine molecules, performing high-resolution and high-precision

measurement of hyperfine interactions of the first excited electronic state (B)

of over an extensive range of vibrational and rotational quantum numberstowards the dissociation limit [42] Experimental data demonstratesystematic variations in the hyperfine parameters that confirm calculations

based on ab initio molecular potential energy curves and electronic wave

functions derived from a separated-atomic basis set We have accuratelydetermined the state-dependent quantitative changes of hyperfine

interactions caused by perturbations from other electronic states andidentified the respective perturbing states Our work in near thedissociation limit is also motivated by the desire to improve cell-basedportable optical frequency standards [43] Indeed, lasers havealready demonstrated high stability at 1 s averaging time) andhave served well for optical atomic clocks [9].

4 HYPERFINE INTERACTIONS, OPTICAL

FREQUENCY STANDARDS AND CLOCKS

The hyperfine structure of rovibrational levels includes four

contributions: nuclear electric quadrupole (eqQ), spin-rotation (C), tensorial spin-spin (d), and scalar spin-spin interactions Agreement betweenexperiment and theory using the four-term effective hyperfine Hamiltonian

is at the kilohertz level for a few selected transitions For the first excited

electronic state B with the dissociation limit, our goal is toperform a systematic high-precision investigation of hyperfine interactionsover an extensive range of rovibrational quantum numbers coupled with alarge range of internuclear separations Such a study has allowed us tounderstand the rovibrational dependence of the hyperfine interactions (as

well as the dependence on internuclear distance) based on ab initio

molecular potential energy curves and the associated electronic wavefunctions Careful analysis of various perturbation effects leads to precisedetermination of molecular structure over a large dynamic range

Prior studies have concentrated on a few isolated rovibrational levels for

the high vibrational levels v' = 40 to 82 in the B state [44-46] For vibrational levels below v' = 43, only functional forms on the state-

dependent variations of the hyperfine interactions have been investigatedfrom empirical data [47] Combining absolute optical frequency metrologywith high-resolution and broad wavelength-coverage laser spectroscopy, wehave measured ~ 80 rovibrational transitions with the upper vibrational

levels (from v' = 42 up to v' = 70) stretching from a closely bonded

molecular basis to a separated-atomic basis appropriate for the

dissociation limit, providing kHz-level line accuracies for most hyperfinecomponents The study is performed in the wavelength region of 530 to

498 nm Measurements performed on a large set of rovibrational quantumnumbers provide systematic information on state-dependent variations in thehyperfine interactions caused by perturbation from other nearby states.Figure 1-6 shows a simple schematic of the ground and the first excitedelectronic states of and their relevant dissociation limits The lower panel

in Fig 1-6 shows a clear trend of linewidth narrowing with decreasing

1 Phase Controlled Femtosecond Lasers for Sensitive 15

transition wavelength However, this tendency is complicated by variations

in linewidths among different rotational or hyperfine components when thetransitions approach the pre-dissociation region The initial linewidthnarrowing at shorter wavelength may indicate among other interestingeffects that the Franck-Condon factor in the transition probability is reducedwhen the excited state reaches a higher vibration level As the excited stateapproaches the dissociation threshold, the limit on lifetime imposed bypredissociation and other effects will need to be taken into consideration

Figure 1-6 The ground state and the first excited state of with their associated dissociation

limit The lower panel shows a narrowing trend of the transition linewidth when the excited state approaches the dissociation limit.

Figure 1-7 illustrates the systematic rovibrational dependences for allfour hyperfine parameters Each solid line is a fit of the experimental data

for rotational dependence belonging to a single vibrational level (v') In

general, all hyperfine parameters have a monotonic dependence on bothrotational and vibrational quantum numbers except for the levels in the

vicinity of v' = 57 to 59 However, the v-dependence of reverses its

trend after v' = 60 For the sake of figure clarity, the data for v' > 60 are not shown Another important observation is that for levels of v' = 57 – 59

all hyperfine parameters except for bear abnormal J-dependences due to

perturbations from a state through accidental rotational resonances

Combining data from this work and the literature [47], investigations ofthe hyperfine spectra now cover the majority of the vibrational levels

in the B state Therefore, it is now possible and useful to explore the global trend of these hyperfine parameters in the B state Suppressing the

rotational dependence, hyperfine parameters as functions of pure vibrational

energy E(v') are found to increase rapidly when molecules approach the

dissociation limit, which is a result of the increasingly strong perturbationsfrom other high-lying electronic states sharing the same dissociation limit

with the B state While the variation of is smooth over the whole range,

and all have local irregularities at three positions: v' = 5 where

the state crosses nearby, around v' = 57 to 59 (see discussions above), and from v' = 76 to 78, due to the same state [44, 46]

To examine these hyperfine parameters in terms of internuclear

separation R, the vibrational average of the hyperfine parameters is removed

by inverting the expression where O(v',J') denotes

one of the four hyperfine parameters Figure 1-7 plots and

against R-centroid evaluated from (with properlynormalized), along with the corresponding residual errors of theinterpolation In Fig 1-8(a), (b), (c), and (d), the solid lines are calculatedfrom and the symbols are the experimental data Consistentwith smooth variation, the interpolation function has small

residual errors (within ±0.03, relative) for the entire range from v' = 3 to 70.

On the contrary, the large residual errors in the interpolation of

and for reflect their abnormal variations observed around v' = 57 and 59, restricting a reliable interpolation only to levels of v' < 56 In the region of R < 5 Å, valuable information can be readily extracted from

to assist the investigation of electronic structure Unlike the other threehyperfine parameters whose major parts originate from perturbations at

nearly all possible values of R, a significant part of is due to the

interaction between the nuclear quadrupole moment Q and the local electric field gradient q(R) generated by the surrounding charge distribution of a largely B state character Thus, for R < 5 Å,where perturbations from other

electronic states are negligible, the vibration-removed interpolation function

coupled with a priori information on q(R), can be used to

determine the nuclear quadrupole moment or serve as a benchmark for

molecular ab initio calculations of the electronic structure at various values

of R.

1 Phase Controlled Femtosecond Lasers for Sensitive 17

Figure 1-7 Rovibrational dependence of the B state hyperfine parameters (a) (b) (c) and (d) Note (b), (c), and (d) are semilog plots and the vertical scale of (c) has

been inverted Each solid line is a fit for J-dependence for each vibrational level (v' indicated

in the figure) Experimental data in squares and open circles show abnormal variations of

and around v' = 57 and 59.

Precision measurements on B-X hyperfine spectra provide an alternative and yet effective way to investigate the potential energy curves (PECs) sharing the same dissociation limit with the B state as well as the associated

electronic wave functions To demonstrate this, we perform calculations of

and based on the available PECs and electronic wave

functions derived from a separated-atomic basis set For both vibrational and

rotational dependences, the ab initio calculation results agree very well with

the experimental data for (R-centroid In short, we haveextended the range of separated-atomic basis calculations from levels near

the dissociation limit to low vibrational levels (v' = 5) and have found very

good agreement with the experimental data on both vibrational androtational dependences.

Figure 1-8 (a) (b) (c) and (d) versus R-centroid Solid lines are calculated

from Symbols are experimental data (dots: this work, squares: literature) (e)

- (h) show residual errors of the interpolation.

Besides these interesting studies in hyperfine structure, the linewidth transitions in this wavelength range also provide excellent cell-based optical frequency references for laser stabilization Frequency-doubled

narrow-at 532 nm has proved to be one of the best portable opticalfrequency standards with compact size, reliability, and high stability

at 1 s) To reach a better frequency stability, it is useful toexplore transitions at wavelengths below 532 nm, where the naturallinewidths decrease at a faster rate than the line strengths We have measuredthe systematic variation of the transition linewidths within the range of

532 - 498 nm, with the linewidth decreasing by nearly 6 times when thewavelength is changed from 532 nm to near the dissociation limit [43] The