Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence...

JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 7 15 FEBRUARY 2003

Multiphoton intrapulse interference. II. Control of two- and three-photonlaser induced fluorescence with shaped pulses

Vadim V. Lozovoy, Igor Pastirk, Katherine A. Walowicz, and Marcos Dantusa)

Department of Chemistry and Department of Physics and Astronomy, Michigan State University,East Lansing, Michigan 48824

~Received 26 August 2002; accepted 30 October 2002!

Nonlinear optical processes are controlled by modulating the phase of ultrafast laser pulses takingadvantage of multiphoton intrapulse interference. Experimental results show orders of magnitudecontrol over two- and three-photon excitation of large organic molecules in solution using specificphase functions. We show simulations on the effect of phase modulation on the second- andthird-order amplitude of the electric field spectrum, and demonstrate that the observed control is notcaused by simple changes in peak intensity. ©2003 American Institute of Physics.@DOI: 10.1063/1.1531620#

ina

ulo-

presttth

thho-

ine

ua,dler-tro

n.

eRn

lsa

e

lsenhodtoa-udep-ro-ess,nts

-he, thesultsex-heno

s ofulsernediousin

en-

oweesthe

sy betivethe

ma

I. INTRODUCTION

Multiphoton processes play a fundamental rolestrong-field control of laser–matter interactions and in pticular control of chemical reactivity.1–3 The four-decadelong pursuit of laser control of chemical reactions,4 hasyielded the following valuable observations:~i! Laser inter-actions must be faster or comparable to the intramolecdynamics,~ii ! multiphoton transitions open a number of phtophysical pathways simultaneously, and~iii ! quantum inter-ference can be exploited to enhance the desired and supthe undesired pathway. In principle, the combination of ththree concepts should allow general control of laser–mainteractions. Here, we explore a pulse shaping methodcan control~enhance or suppress! multiphoton transitions.The method is based on intrapulse interference, whichtakes place within the ultrashort laser pulse during multipton excitation. This work is a continuation of our work towards predictive laser control with shaped pulses determby a reduced number of control parameters.5

The search for appropriate pulse shapes to control mtiphoton processes can be divided into three generalproaches. The first involves a smooth phase modulationprovided by linear chirp. Results from this search inclutwo-photon excitation,6–9 and the yield of chemicareactions.10–12 The second involves modulation of the laspulses, using a pulse shaper,13 to achieve specific timefrequency profiles. Results from this search include conof second harmonic generation~SHG! ~Ref. 14! and two-photon excitation15–18 using a sine or step phase functioThe third involves closed-loop learning algorithms,19,20

which converge towards the ‘‘optimal’’ pulse shape as dfined by a series of phases and amplitudes in the mask.sults from this search include adaptive pulse compressio21

one- and two-photon transitions in atoms,22 and methodsbased on parameterized phase functions to compress puoptimize the SHG and two-photon transitions in isolated

a!Author to whom correspondence should be addressed. [email protected]

3180021-9606/2003/118(7)/3187/10/$20.00

Downloaded 31 Jan 2003 to 35.8.27.44. Redistribution subject to AIP

r-

ar

esseerat

at-

d

l-p-ase

l

-e-

,

es,t-

oms and diatomics.23 With adaptive control has come thoptimization of electronic population transfer,24,25 Ramantransitions,26,27 and control of chemical reactions.28,29

Here we describe the technique multiphoton intrapuinterference~MII ! and its application to control multiphotoprocesses in large organic molecules in solution. The metis based on rationally designing an electric field requiredachieve a particular target with a minimum number of prameters. The method is based on calculating the amplitof thenth-order electric field and comparing it to the absortion spectrum of the molecules being controlled. This pvides a strong physical understanding of the control procwhich can be very useful in the interpretation of experimewhere the field is optimized by a learning algorithm.

We begin with a brief review of the theory of multiphoton transitions and the effect of phase shaping on MII. Texperimental section gives details about the laser systempulse shaper, and the different samples studied. The resection presents data obtained for two- and three-photoncitation for several different pulse shaping parameters. Tdata are also compared to simulations calculated withadjustable parameters. The Discussion explores detailMII and explores the issue of phase interference versus plengthening. The Conclusion summarizes the lessons leahere and gives a perspective for interpreting some prevexperiments from other groups involving phase controlcondensed phases.

II. THEORY

Multiphoton processes are maximized when the totalergy ( i 51

n \v i is resonant with a particularnth-order transi-tion. As realized by Broerset al.,15,16 two-photon transitionscan focus the energy from an ultrafast pulse into a narrfrequency distribution; just like Fresnel diffraction can bused to construct a focusing lens. Conceptually, MII takadvantage of the interference term that is associated withphase of each frequencyv i within the pulse that contributeto the multiphoton process and can enhance or what maas valuable, suppress a multiphoton transition. The effecelectric field that drives the two-photon process throughil:

7 © 2003 American Institute of Physics

license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

o

th

de

bte

thiose

ithd

toaM

seden, tonanh

ganttic

th

mthex-

ally

-

ske

euseom-

isTLthatnd-

r ofr-

enter

and-ctraby

rderr tori-hey in

seion

ate

es

ly.nd

ncy.

gth

f-at isird

aredis

3188 J. Chem. Phys., Vol. 118, No. 7, 15 February 2003 Lozovoy et al.

induced ~nonlinear! polarization is proportional toE2(t)~in the absence of intermediate resonance at the one-phlevel!. Its Fourier transformE(2)(v) determines the fre-quency response at the two-photon level. To determineamplitude of the two-photon effective field at 2v0 wecalculate15,16

E(2)~2v0!}E2`

`

E~v02V!E~v01V!dV, ~1!

where spectral detuning isV5v2v0 andv0 is carrier fre-quency of the pulse. The formula integrates over all thetuning combinations that add up to 2v0 .16 Each spectralcomponentE(V) can be expressed as real amplitudeuE(V)uand phase w~V! in complex form E(V)5uE(V)u3exp@iw(V)#. For a two-photon transition

E~V!E~2V!5uE~V!uuE~2V!uexp@ i $f~V!1f~2V!%#,~2!

where the exponential component carries the interferencetween different frequency components. A phase-modulapulse can maximize or minimize the interference term inexponential to suppress or enhance multiphoton excitatrespectively. We call this effect multiphoton intrapulinterference.5

In the early investigations on two photon excitation wshaped pulses it was clear that phase interference coulused to control atomic transitions,17 but it was not clear ifthis method could be used to control two- and three-phoabsorption of large molecules in solution because they hno sharp absorption band. We have recently shown thatcan be used to control nonlinear optical excitation~two-and three-photon laser induced fluorescence! in such systemsincluding proteins.5 Those experiments involved a phamask defined by a cosine function with controlled amplituperiod, and phase. Here we demonstrate that the additiolinear chirp, a quadratic phase delay function of frequencythe cosine function yields order of magnitude greater ctrast and permits the selective control between two-three-photon processes. We concentrate on the effect of cbecause it occurs naturally when optical pulses propathrough condensed phase media. Therefore, it is importadetermine if chirp enhances or diminishes the desired opcontrol.

The phase of each frequency in the pulsew~V! is definedfor all our experiments by

w~V!5a cos~gV2d!1 12f9V21 1

6f-V3, ~3!

where a is the maximum phase retardation,g52pN/(Vmax2Vmin) determines the periodN of the phase function~over the entire spectrum 770–830 nm!, d determines theposition of the mask with respect to the spectrum ofpulse,f9 is the amount of quadratic phase modulation~linearchirp in the time domain!, and f- is the amount of cubicphase modulation~quadratic chirp in the time domain!. Themain advantage of defining the pulse with a minimum nuber of control parameters is that the amplitude ofnth-order electric field can be easily calculated using antension of Eq.~2!.5 For three-photon excitation, in the absence of intermediate resonances we obtain


ton

e

-

e-d

en,

be

nveII

,ofo-dirptetoal

e

-e-

E(3)~D!}E2`

` E2`

`

dV1dV2uE~V1!uuE~V2!u

3uE~D2V12V2!uexp$ i @w~V1!1w~V2!

1w~D2V12V2!#%, ~4!

where each photon in the three-photon transition is spectrdetuned by an amountV1 , V2 or (2V12V2), D is thedetuning from the third-order multiple of the carrier frequency of the pulse (v23v0), uE(V i)u andw(V i) are theamplitude and phase of the intermediate frequenciesi thatadd up to the third-order transition.5

In Fig. 1, we illustrate how changes in the phase magiven by Eq.~3!, change the temporal profile of the pulsuE(t)u2 and the spectrum of thenth-order electric fielduE(n)(D)u2. First, note that the first order spectrum of thelectric field is not affected by the phase function becathere is no interference term at this order. All cases are cpared to transform limited~TL! pulses~thin line!. For case~a!, a sine function, we see that the second order fieldfocused to a much narrower bandwidth compared topulses, the amplitude at the center wavelength matchesfor TL pulses. The third order spectrum is narrower aweaker. For case~b!, a cosine function, we see that the amplitude of the second order field is reduced by one ordemagnitude while the third order field is reduced by two oders of magnitude. For case~c! a displaced sine function, thsecond order spectrum is narrow and detuned from the cefrequency, the third order spectrum is also detunedweaker than TL pulses. Case~d! corresponds to positive quadratic phase modulation. The second and third order speare not affected, only their amplitude is, which decreasesa factor of 4 or 10, respectively. Case~e! corresponds tonegative cubic phase modulation. The second and third ospectra are narrower. This is caused by an effect similathat observed for the sine function. A quantitative compason between the different time profiles obtained for tshaped pulses is given in the discussion section. Clearlall cases, the shaped pulse~darker line! is longer than the TLpulse.

In Fig. 2, we explore the combination of certain phafunctions with quadratic phase modulation. This exploratis of interest because quadratic phase modulation~linearchirp! occurs naturally when ultrashort pulses propagthrough optical media. For example, if a laser~centered at800 nm! propagates through 100 mm of water it acquir2480 fs2 of positive chirp.30,31 Cases~a! and ~b! combine asine function with positive or negative chirp, respectiveThe temporal profile is identical in both cases. The secoand third order spectra are shifted from the central frequeInterestingly, a change in sign in the sign off9 leads to ashift from redder to bluer frequencies in the peak wavelenof the second and third order spectra. Cases~c! and~d! com-bine a cosine function with positive or negativef9, respec-tively. For positive chirp, the two functions cancel their efects near the center of the pulse. This leads to a pulse thclose to TL except for some wings. The second and thorder spectra are slightly narrower and attenuated compto TL pulses. For negative chirp, the phase modulation


e

d

m

ed

re

3189J. Chem. Phys., Vol. 118, No. 7, 15 February 2003 Multiphoton intrapulse interference: Control

FIG. 1. Multiphoton intrapulse inter-ference effects for different phasfunctions: The first column shows thefirst order spectrum of the pulse anthe phase function~dark line!. Thesecond column shows the transformlimited pulse and the temporal profileof the shaped pulse~dark line!. Thethird column shows the amplitudesquare of the second order spectrufor TL pulses and for the shapedpulses~dark line!. The fourth columnshows the amplitude square of ththird order spectrum for TL pulses anfor the shaped pulses~dark line!. Thefollowing different phase functions areshown:~a! sine,~b! cosine,~c! shiftedsine,~d! linear chirp, and~e! quadraticchirp. The relevant parameters foeach phase function are given in thfigure.

ve,

dt

w

sito

nuatethatitiesro-iving

u-ionion

a-

thelated

accentuated. This leads to very broad temporal pulses,weak second, and third order spectra. For these caseschange in sign off9 makes a very large difference. Case~e!combines negative cubic modulationf- with positive qua-dratic phase modulation. The effect is similar to case~a!,where the second and third order signal is slightly detunelonger wavelengths. In this case, the third order outpuhighly attenuated. Changing the sign off9, not shown,changes the sign of the detuning as observed in case~b!.

From the calculations presented in Figs. 1 and 2,learn that the phase function described by Eq.~3!, achievesmuch more than the simple attenuation of the peak intenof the laser pulse. Thenth order spectrum can be tuned


rythe

tois

e

ty

specific resonances and the phase can be used to attethird order processes by two orders of magnitude. Givenhigher nonlinear processes require higher peak intensthis results seems trivial, however, when third order pcesses cause irreparable damage of optical elements or ltissue it is useful to know how to suppress them. The simlation in Fig. 1 show that simple attenuation or attenuatusing only quadratic chirp is not as efficient as the additof a cosine function. The cosine function~d50! achievesmaximum spreading of the pulse, well beyond what qudratic chirp alone achieves.

The spectra calculated for Fig. 1 are the spectra thatmolecules experience in the presence of a phase modu


eicte

e

fL

r

-n


FIG. 2. Multiphoton intrapulse inter-ference effects for different phasfunctions in the presence of quadratchirp: The first column shows the firsorder spectrum of the pulse and thphase function~dark line!. The secondcolumn shows the transform limitedpulse and the temporal profile of thshaped pulse~dark line!. The third col-umn shows the amplitude square othe second order spectrum for Tpulses and for the shaped pulses~darkline!. The fourth column shows theamplitude square of the third ordespectrum for TL pulses and for theshaped pulses~dark line!. The follow-ing different phase functions areshown:~a! sine and positive chirp,~b!sine and negative chirp,~c! cosine andpositive chirp,~d! cosine and negativechirp, and~e! quadratic chirp and posi-tive linear chirp. The relevant parameters for each phase function are givein the figure.

dc

ie

tns

ioonpt

ur

the.ur

of

laser pulse. The molecular response to the electric fieldetermined by calculating the amplitude of the frequendependent nonlinear susceptibility of the molecule multiplwith the nth order electric field.32 In the case of very sharpmultiphoton absorption lines~as in isolated atoms! action ofthenth field depends primarily onuE(n)(D)u2 at the resonanfrequencyD5v2nv0 . In the case of large molecules isolution the action of thenth order electric field dependonly from the amplitude of this fielduE(n)(D)u2 integratedover the broad nonlinear excitation spectrumg(n)(D) be-cause of the extremely fast intramolecular phase relaxatHere our concern focuses control of large molecules in cdensed phase. Therefore, we assume a broad absor


isyd

n.-ion

spectrum ignoring intramolecular dynamics to simulate oexperimental results according to

S(n)}E2`

`

g(n)~D!uE(n)~D!u2dD. ~5!

In the two limits~isolated atom or large molecule in solution!the outcome is independent of the interaction betweenindividual phasesw (n)(D) and the intramolecular dynamicsWe have found this to be a very good approximation in ostudies of large molecules in condensed phase.5 The role ofintramolecular dynamics becomes important in the studylaser control of gas phase molecular dynamics.33–37


o

rwthtoanswsutreheney

owiothe

reto

obaho

a.2

toeanaa

n-

ns

re

n-

a

horn

en-ionpti-as

a,

et-

-

ics

500as-

n

e


III. EXPERIMENT

The experiments were performed using an ultrash;50 fs pulse regeneratively~1 kHz! amplified Ti:sapphirelaser with;1 mJ/pulse. The beam was sent through the zedispersion pulse shaper consisting of two gratings, tlenses, and two 128-pixel liquid crystal-based arrays atFourier plane. The programmable spatial light modula~CRI, Inc.! was calibrated so that phase retardation atgiven frequency could be accomplished without changethe output polarization and amplitude. Phase retardationcalibrated by determination of accurate retardation vervoltage curves for each phase mask. We operated withinlower voltages with a measured accuracy of one deg~;0.0074 fs!. When no phase modulation was applied, tpulses after the pulse shaper arrangement weretransform-limited with FWHM 50 fs and a maximum energof 5 mJ. For most experiments the laser was attenuated dto 0.5mJ. The magnitude of the quadratic phase modulatwas controlled by translation of a compressor grating inlaser amplifier. Reproducibility was ensured using a mchanical indicator with 2.5mm resolution. The quadraticphase modulation was calibrated using SHG frequencysolved optical gating.38 The experiments presented here dpend critically on the input pulses. We were very carefuluse transform limited pulses to avoid these types of prlems. We found that the presence of a small cubic phmodulation, for example, can distort the observed multipton response.

A 200 mm focal length lens focused the laser ontoquartz cell containing the dye solution. Fluorescence wdetected at right angles with f/1 optics and directed to a 0m spectrometer with a liquid nitrogen cooled CCD detecIn most cases we integrated the fluorescence signal forphase function. Typical data acquisition required the sigdetection for 128 different phase functions, twice. Data wcollected for approximately 100 laser pulses for each phfunctions and the entire scan was repeated four times.

Experiments were carried out on Coumarin 500~Exci-ton!, andtrans-stilbene~Eastman!, both 0.01 M solutions inmethanol. The fluorescence was detected as a functiochirp ~f9! and phase shift of the mask~d! across the spectrum, centered near 800 nm, with a bandwidth~FWHM! of24 nm. For all cases the valuesa51.5p andN51, from Eq.~3!, were kept constant. For the experiments on two- athree-photon excitation in the same solution we made alution of Coumarin 500 and para-terphenyl 1026 and1024 M, respectively, in cyclohexane. For these measumentsa52.5p, N51, andf952000 fs2.

IV. RESULTS

Figure 3~a! displays the signal obtained for two-photolaser induced fluorescence~LIF! for Coumarin 500 as a function of f9 and d ~darker shades indicate higher intensity!.Notice that maximum and minimum values for the signal cbe easily found for certain combinations ofd and f9, withcontrast ratios or two and more orders of magnitude. Tdata is normalized such that the signal induced by transflimited pulses equals unity. The maximum observed sig


rt

o-oeryinass

hee

ar

nne-

e--

-se-

as7

r.ch

alsse

of

do-

-

n

emal

matches that obtained with transform limited pulses. In geral, for low intensity excitation, in the absence of saturator an intermediate resonance, transform limited pulses omize multiphoton transitions. The data in this article wobtained under these conditions.

In Figs. 3~b!–3~d! we present simulations of the datcalculated with Eqs.~1! and ~2!. Notice that the overalltrends are perfectly matched by the theory. To provide a bter quantitative perspective cuts forf950 and 4400 fs2 areshown in Figs. 3~c! and 3~d!, respectively. Differences between the simulations~no adjustable parameters! and thedata are small and may indicate that intramolecular dynam

FIG. 3. Control of two-photon laser induced fluorescence in Coumarinwith multiphoton intrapulse interference. The contour-plots indicate increing yield ~darker color! of 500 nm fluorescence as a function of chirpf9 andphase shiftd. ~a! Experimental measurement of the yield of two-photolaser induced fluorescence from Coumarin 500.~b! Theoretical simulation ofthe data.~c! A cut through the experimental data forf950 fs2, togetherwith a theoretical simulation of the signal.~d! A cut through the experimen-tal data for f954000 fs2, together with a theoretical simulation of thsignal.


.on

-ai

thitya,

th

nsest-

ve a

canorer ofee-

o-ee-

the

elf-ble

iontwod atnd

al,tonn ass aumis

heiseit.es-

n-d ho-only

ie

in

a

lowers in-three


play a minor but detectable role in multiphoton excitationFigure 4~a! displays the signal obtained for three-phot

LIF for t-stilbene as a function off9 and d ~darker shadesindicate higher intensity!. Notice that maximum and minimum values for the signal can be easily found for certcombinations ofd and f9, with contrast ratios or two andmore orders of magnitude. The data is normalized suchthe signal induced by transform limited pulses equals un

In Figs. 4~b!–4~d! we present simulations of the datcalculated with Eqs.~1! and ~3! ~no adjustable parameters!.Notice that the overall trends are perfectly matched bytheory. Cuts are shown forf950 and 3400 fs2 in Figs. 4~c!

FIG. 4. Control of three-photon absorption intrans-stilbene with multipho-ton intrapulse interference. The contour-plots indicate increasing y~darker color! of 350 nm fluorescence as a function of chirpf9 and phaseshift d. ~a! Experimental measurement of the yield of two-photon laserduced fluorescence from Coumarin 500.~b! Theoretical simulation of thedata.~c! A cut through the experimental data forf950 fs2, together with atheoretical simulation of the signal.~d! A cut through the experimental datfor f953400 fs2, together with a theoretical simulation of the signal.


n

at.

e

and 4~d!, respectively. Differences between the simulatioand the data are greater for three-photon excitation. Interingly, the signal obtained ford5p and 3p in Fig. 4~d! isgreater than that observed for transform limited pulses.

In general, both two- and three-photon processes hasimilar response phase modulation as seen in Figs. 3~a! and4~a!. However, there are certain sets of parameters thatbe chosen where the two-photon LIF signal is much mintense than the three-photon LIF signal. One such paivalues is chosen from Figs. 3 and 4. Cuts of the thrdimensional data with fixedf9, are shown in Fig. 5. Thearrows indicate the positions where the maximum ratio tw:three-photon excitation is observed; coinciding with a thrphoton ‘‘dark’’ pulse. As can be seen in Fig. 5~b!, for certainpulse-shaping conditions, three-photon LIF exceedsvalue obtained for transform limited pulses~normalized tounity!. This observation may indicate some degree of sfocusing or that additional excitation pathways are availathrough real electronic intermediate states.39

In Figure 6 we compare two- and three-photon excitatprocesses in a single sample containing a mixture ofdifferent dyes. One dye has an absorption band centere400 nm~Coumarin 500! and another has an absorption bacentered at 267 nm (p-terphenyl!. The experimental resultsare shown as a function ofd, with a52.5p andf952000 fs2

in Fig. 6~a!. The two photon induced fluorescence signcollected at 500 nm, is shown as a thin line, the three-phoinduced fluorescence signal, collected at 350 nm, is showa heavy line, and the ratio between the two is shown adashed line. The contrast ratio observed between maximand minimum signal for 3-photon induced fluorescencealmost four orders of magnitude. In fact the signal in tregion ofd near zero is comparable to the systematic nolevel, the reported four orders of magnitude is a lower limThe contrast ratio observed for two-photon induced fluorcence, in this case is one order of magnitude.

V. DISCUSSION

Our findings indicate that multiphoton processes in codensed phase molecules, where the inhomogeneous anmogeneous broadening is large, can be controlled using

ld

-

FIG. 5. ~a! A cut along the experimental data shown in Figs. 3~a! and 4~a!showing the variation of two-~dashed line! and three-photon~solid line!induced fluorescence as a function ofd for a fixed amount of chirpf952000 fs2. ~b! A cut along the experimental data shown in Figs. 3~a! and4~a! showing the variation of two-~dashed line! and three-photon~solidline! induced fluorescence as a function off9 for d5p/2. Notice that thesmoother onset of two-photon processes creates regions where theorder process dominates even under strong-field excitation. The arrowdicate the condition when two photon processes are not suppressed butphoton processes are.


tioe

ulithorthdieul

igx

leea

nant

e

reser-thetio

-

-

tndsFig-e-staln-canif-is

It isonictionWeree-

sislse

fsig-

ee-

aseis

d on

-

the

ontbe

-ra-

e

inacee-re

by

to


a few control parameters. We have explored the combinaof a cosinusoidal function with linear chirp to show largcontrast for two- and three-photon transitions. Our resindicate chirp has an important and nontrivial coupling wother phase modulation functions. This is particularly imptant if phase modulated pulses are used in applicationsrequire propagation through dispersive media. Here wecuss to what extent control of multiphoton excitation dpends on intrapulse interference and to what extent to plengthening.

In comparing the two different signals presented in F6~a!, we consider what role pulse lengthening plays in eplaining the observed results. For this analysis we neginterference and intramolecular dynamics leaving only pintensity ~a function of pulse duration!. The signal observedfollowing n-photon excitationS(n) is proportional toI nt,whereI n is the intensity of pulse to thenth power, andt is itsduration. The energy of the pulse is given byW}I t, there-fore the signal isS(n)}Wnt12n. With this simple expressionwe can calculate the ratio between the two nonlinear sigusingS(n)/S(n21)}W/t. If the energy of the pulse is constathen

S(n)/S(n21)}t21 ~6!

FIG. 6. Two- and three-photon excitation of large organic moleculessingle mixture as a function of phase modulation. Solid thin line is normized on the transform limited condition two-photon induced fluorescensolid thick line is normalized on the transform limited condition threphoton induced fluorescence, both emissions was excited in the mixtu1026 M para-terphenyl~detected at 350 nm! and 1024 M Coumarin 500~detected at 500 nm! in cyclohexane with phase modulation determinedEq. ~3! and a52.5p, N51, andf952000 fs2 as function of parameterd.The dashed line is ratio of three-photon excitation to the two-phoexcitation.


n

ts

-ats--se

.-ctk

ls

for any value ofn. If we start withn52, we find that theratio is justS(2) becauseS(1) is independent of changes in thpulse duration~in the absence of saturation!. This analysisdepends only on the change in peak intensity and ignointramolecular dynamics or quantum mechanical interfence. The result, however, is very valuable to ascertaineffect of pulse duration, and indicates that the raS(n)/S(n21) is proportional to the two-photon signalS(2) forall n.

The simulation ofS(2) and S(3) @no adjustable parameters using Eq.~5!# is shown in Fig. 6~b!. Notice thatS(2)

andS(3)/S(2) ~dashed line! are very similar. Under these conditions the pure interference effect of MII is only~10%–40%! from the full contrast ratio. A much stronger MII effecis obtained for shorter laser pulses and multiphoton bathat are detuned from the center frequency of the pulse.ure 6~a! shows the ratio of the experimental two- and threphoton signal~dashed lines!. We can see that the ratio doenot coincide with the 2-photon excitation. The experimenratio of S(3)/S(2) shows one order of magnitude greater cotrasts than are predicted by theory. The main discrepancybe attributed to the three-photon excitation signal, which dfers significantly from the simulation. We cannot explain thdifference based on pure two- and three-photon effects.possible that higher order processes and other electrstates that are detuned from the center of the excitawavelength play an important role in the observed signal.note that the greatest differences occur when the thphoton induced signal is minimized.

Here we make an effort to provide a quantitative analyof pulse lengthening effects. First we determine the pudurationDt, using

Dt5A* uE~ t !u2~ t2tc!2dt/A* uE~ t !u2dt, ~7!

where the center of the pulse is defined bytc

5* uE(t)u2tdt/* uE(t)u2dt. We then calculate the effect ophase modulation on the expected two- and three-photonnal,S(2) andS(3) using Eq.~5! with g(n)(D)51 ~to eliminatespectral tuning effects!. We compare these simulations to thinverse of the pulse durationDt21 and to the squared inverspulse durationDt22 for second- and third-order effects, respectively. The results are shown in Fig. 7. When phmodulation consists of linear chirp only, we find that thereexcellent agreement between the predicted effects basepulse duration and simulated effect based on MII@Eq. ~5!#@see Figs. 7~a! and 7~b!#. Interestingly, when phase modulation includes a cosine function as in Eq.~3!, the agreementbetween the predicted effect based on pulse duration andsimulated effect based on MII@Eq. ~5!# is not good, differingby 60% for two-photon effects and 300% for three photeffects atd50.5 or 1.5p. In Figs. 1 and 2, we showed thathe temporal profile of the pulse can be smooth or it cancomplex ~multiple pulses!. When it is complex pulse duration fails to predict the observed signal. In fact, pulse dution @Eq. ~7!# predicts a maximum ford5p @see Figs. 7~c!and 7~d!# but this turns out to be a local minimum in thsimulated signal based on Eq.~5!. The experimental dataagree with the predicted minimum@see Figs. 7~e! and 7~f!#.

al-,

of

n


n

ial

mthdri

e

te.weaan

t

asethe

con-esng

eardueer,on-

-co-

ag-ndresualionvedu-or

nofmeions.n of

l-th-onatd toatedh-e itiona-i-ra-

avemu-

n-y ad in

el

-

on

re


This observation leads us to the conclusion that Eq.~5! basedon MII is a much better predictor ofnth order processes thasimple pulse duration of the electric field.

The analysis, so far, has ignored thenth order spectrumof the moleculeg(n)(D). MII spectral tuning of the higherorder spectrum of the field can also be used to preferentexcite one type of molecule in a mixture. Walowiczet al.,5

demonstrated this experiment using 50 fs pulses and ature of two different coumarin laser dyes. In essence,second order spectrum of the laser was tuned from oneto the other. In Fig. 8 we show a simulation of the expement obtained for 10 fs pulses.5 Notice that with shorterpulses selective excitation becomes possible purely duMII.

Control of multiphoton processes with phase modulaultrashort laser pulses has been reported in the literature6–8

For example a 40% effect had been measured in the tphoton excitation of green fluorescent protein using linchirp.8 The main difference between those experimentsexperiments from our group5 is laser intensity. We haveavoided saturation while those measurements were in

FIG. 7. Effect of pulse duration and spectral amplitude of the electric fion two- and three-photon excitation. For the~a!–~d! the solid line is thesignal calculated according toS(n)}* uE(D)(n)u2dD, the dashed line is cal-culated signal according toS(n)}Dtn21. ~a,b! Dependence of expected signal from quadratic phase modulationf9, with a50. ~c,d! Dependence ofexpected signal from phased with a51.5p, N51, andf952000 fs2. ~e,f!Experimentally measured dependence of fluorescence yield as a functid with a51.5p, N51, andf952000 fs2 for the solutions of Coumarin 500~two-photon excitation! and trans-stilbene~three-photon excitation!.


ly

ix-eye-

to

d

o-rd

he

saturated regime. In the case of saturation, any form of phmodulation causes pulse lengthening and this alleviatessaturation. One of the most remarkable studies on lasertrol of multiphoton excitation in condensed phase involvthe excitation of two different dye solutions, one containi@Ru~dpb!3#21 and the other DCM.25 In that study the authorswere careful to evaluate the effect of pulse energy, linchirp, and wavelength tuning. They found that changesto those parameters individually were minimal, howevtheir adaptive pulse shaper was able to find a maximum ctrast DCM/@Ru~dpb!3#21 of approximately 50%. They attributed this observation to long-lived molecular phaseherences that persist during the shaped pulse~100 fs–1 ps!.25

In our studies we have concentrated on the order of mnitude differences observed in multiphoton excitation, athese can be accounted for by the MII theory, which ignointramolecular dynamics. In all cases, there is a resid10%–50% difference between experiment and simulatthat is not accounted for. This same difference was obserwhen comparing results from two-photon excitation of comarin 500 and recombinant green-fluorescent protein,three-photon excitation oft-stilbene and the concanavaliA.5 It is possible that this difference arises from the effectelectric field phase and intramolecular dynamics. The tiscale for electronic dephasing in large molecule in soluthas been determined to be in the range of 30 to 70 f40

Perhaps shorter pulses can better harness the contributiointramolecular dynamics in condensed phases.

A recent publication about laser control of large moecules in solution compares excitation of two different paways of LH2.41 That study was conducted in the saturatiregime, therefore it is very difficult to determine to whextent phase modulation caused pulse lengthening anwhat extent spectral tuning and phase coherence participin the observed;35% ratio between the two excitation patways. The system is ideal to explore laser control becausprovides two different channels. The preferential observatof ground state dynamics following excitation with negtively chirped pulses,42 as observed in the one-photon exctation of bacteriorhodopsin, can be explained by both satution and intramolecular dynamics that take place as the wpacket being formed in the excited state undergoes stilated emission.

It is becoming clear that for large molecules in the codensed phase multiphoton excitation can be controlled bnumber of mechanisms, and this control can be calculate

d

of

FIG. 8. Multiphoton intrapulse interference with 10 fs pulses.~a! Absorptionspectrum of Coumarin 460~dots! and Coumarin 535~open dots!. The spec-trum of the laser is shown with the thin line.~b! Two-photon induced signalas a function ofd for the two different coumarin dyes. The values anormalized to transform limited pulses.


irpeon

n,

hifop

seef

rosin

ing

threnfrrdfanu

duMteesrein

aeathfi

tiosuin-tesy

a

luasmlso

ns

tion

sedo-

cedinedn-toaricala-tu-nced

pleightns.

es,n-

rgy.

m.

n,

Lett.

m.

,ett.

m.

m

.rey,

ys.

ys.

.

M.


all cases except those involving significant saturation.~i!Changing the pulse duration, for example using linear chis the simplest form of control.~ii ! Changes in the amplitudof the nth order electric field caused by phase modulatiThese effects can be calculated using Eq.~5! ignoring themolecular absorption spectrum (g(n)(D)51). ~iii ! Spectraltuning of thenth order electric field with phase modulatioEq. ~5!. ~iv! Phase modulation of thenth order electric fieldmatching intramolecular dynamics of the system. Tmechanism may result in 30%–50% effects, a formulacalculation has not been provided here. In some cases,ticularly in the gas phase, the laser chirp~a frequency sweep!can coincide with intramolecular dynamics. In these caslow intramolecular dynamics without fast relaxation canfect on the excitation process.43 ~v! High intensity excitation,causes competition among a number of multiphoton pcesses, as well as self-phase modulation and self-focuThe quantitative simulation of these higher order effectschallenging, but it is required to explain the most intriguiresults.

VI. CONCLUSIONS

The results presented here provide information aboutnonlinear excitation of large molecules in solution. Thesults presented in Figs. 1 and 2 indicate that the phase caused to tune the second or third order spectrum in thequency domain as well as suppress third and higher oexcitation. The data in Figs. 3 and 4 show the effect ocosinusoidal function and linear chirp. For certain combintions of parameters three-photon processes can be sigcantly suppressed. The effects presented here are not caby simple attenuation. We have made an analysis basepulse duration alone and showed that in some cases pduration predicts a maximum whereas experiments andsimulations predicts a minimum in the signal. We presenresults that showed competition between two- and thrphoton excitation in a single mixture of two different dyeThe ratio between the two signals followed the trend pdicted by theory but the magnitude of the control foundthe experiment was much greater.

The results and analysis presented here give a clepicture about the effect of phase modulation on nonlinoptical processes. Phase modulation is introduced instudy using a pulse shaper. The analysis presented in thetwo figures shows the drastic effect that phase modulacan have on second and third order processes. Our reimply that pulse characterization is critical in all studiesvolving nonlinear optical processes, given that unwanphase modulation takes place in all femtosecond lasertems.

Third and higher order excitation and nonlinear opticdistortions~self-focusing, for example! are usually detrimen-tal, making strategies for their suppression technically vaable. Our findings indicate that with a simple phase mmaximum suppression can be achieved. The phase maskbe introduced with passive optics rather than a costly pushaper. Suppression of three-photon process will be theject of further investigation, because in medical applicatio


,

.

srar-

s-

-g.s

e-be

e-era-ifi-sedonlseIIde-.-

rerrisrstnlts

ds-

l

-kayeb-,

such as photodynamic therapy, three-photon absorpcauses DNA damage.44

In summary, we present a pulse-shaping method baon intrapulse interference that provides control of multiphton transitions under strong field excitation using a redunumber of parameters. The results shown here were obtawith only four control ‘‘knobs’’ that can be adjusted indepedently or can be incorporated into a learning algorithmprovide control over multiphoton transitions and nonlineoptical interactions. The method is robust and the theoretformulation simple enough to provide predictive informtion. We are pursuing the application of this method to siations where nonlinear optical processes must be enhaor suppressed, or where selective excitation~three- versusfour-photon absorption, for example! is desired. The phasemodulation discussed here can be introduced with simpassive optics without the need for sophisticated spatial lmodulators. This advantage may lead to direct applicatio

ACKNOWLEDGMENTS

This research was funded by the Chemical SciencGeosciences and Biosciences Division, Office of Basic Eergy Sciences, Office of Science, U.S. Department of EneM.D. is a Camille Dreyfus Teacher-Scholar.

1S. R. Rice, Nature~London! 409, 422 ~2001!.2H. Rabitz R. de Vivie-Riedle, M. Motzkus, and K. Kompa, Science288,824 ~2000!.

3R. N. Zare, Science279, 1875~1998!.4J. C. Polanyi and A. H. Zewail, Acc. Chem. Res.28, 119 ~1995!.5K. A. Walowicz, I. Pastirk, V. V. Lozovoy, and M. Dantus, J. Phys. CheA 106, 9369~2002!.

6B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. WilsoN. Schwentner, R. M. Whitnell, and Y. Yan, Phys. Rev. Lett.74, 3360~1995!.

7G. Gerullo, C. J. Bardeen, Q. Wang, and C. V. Shank, Chem. Phys.262, 362 ~1996!.

8C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, J. AChem. Soc.120, 13023~1998!.

9V. V. Lozovoy, S. A. Antipin, F. E. Gostev, A. A. Titov, D. G. TovbinO. M. Sarkisov, A. S. Vetchinkin, and S. Ya. Umanskii, Chem. Phys. L284, 221 ~1998!.

10A. Assion, T. Baumert, J. Helbing, V. Seyfried, and G. Gerber, ChePhys. Lett.259, 488 ~1996!.

11I. Pastirk, E. J. Brown, Q. Zhang, and M. Dantus, J. Chem. Phys.108,4375 ~1998!.

12O. M. Sarkisov, A. N. Petruchin, F. E. Gostev, and A. A. Titov, QuantuElectron.31, 483 ~2001!.

13A. M. Weiner, Rev. Sci. Instrum.71, 1929~2000!, and references therein14M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerb

Appl. Phys. B: Lasers Opt.73, 273 ~2001!.15B. Broers, L. D. Noordam, and H. B. van Linden van den Heuvell, Ph

Rev. A46, 2749~1992!.16B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Ph

Rev. Lett.69, 2062~1992!.17D. Meshulach and Y. Silberberg, Nature~London! 396, 239 ~1998!.18D. Meshulach and Y. Silberberg, Phys. Rev. A60, 1287~1999!.19R. S. Judson and H. Rabitz, Phys. Rev. Lett.68, 1500~1992!.20H. Rabitz and A. W. Zhu, Acc. Chem. Res.33, 572 ~2000!.21D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett.22, 1793~1997!.22T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M

Motzkus, Appl. Phys. B: Lasers Opt.71, 227 ~2000!.23D. Zeidler, S. Frey, K.-L. Kompa, and M. Motzkus, Phys. Rev. A64,

023420~2001!.24C. J. Baredeen, V. V. Jakovlev, K. R. Wilson, S. D. Carpenter, P.

Weber, and W. S. Warren, Chem. Phys. Lett.280, 151 ~1997!.


, H

.

S

B

n,

hys.

ys.

ys.

J.

ys.

s,

N.


25T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, Nature~London!414, 57 ~2001!.

26T. C. Weinacht, J. L. White, and P. H. Bucksbaum, J. Phys. Chem. A103,10166~1999!.

27T. C. Weinacht, R. Bartels, S. Bakus, P. H. Pearson, J. M. GeremiaRabitz, H. C. Kapteyn, and M. M. Murnane, Chem. Phys. Lett.344, 333~2001!.

28A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, MStrehle, and G. Gerber, Science282, 919 ~1998!.

29R. J. Levis, G. M. Menkir, and H. Rabitz, Science292, 709 ~2001!.30We calculated the dispersion parameterk2524 fs2/mm for 800 nm light

using the index of refraction data for water from A. H. Harvey, J.Gallager, and J. M. H. L. Sengers, J. Phys. Chem. Ref. Data27, 761~1998!.

31A. G. Van Enger, S. A. Diddams, and T. S. Clement, Appl. Opt.37, 5679~1998!.

32S. Mukamel,Principles of Nonlinear Optical Spectroscopy~Oxford Uni-versity Press, New York, 1995!.

33C. J. Bardeen, J. W. Che, K. R. Wilson, V. V. Yakovlev, P. J. Cong,Kohler, J. L. Krause, and M. Messina, J. Phys. Chem. A101, 3815~1997!.

34C. J. Bardeen, J. W. Che, K. R. Wilson, V. V. Yakovlev, V. A. Apkaria


.

.

.

C. C. Martens, R. Zadoyan, B. Kohler, and M. Messina, J. Chem. P106, 8486~1997!.

35H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, J. Chem. Ph116, 946 ~2002!.

36J. B. Ballard, H. U. Stauffer, Z. Amitay, and S. R. Leone, J. Chem. Ph116, 1350~2002!.

37E. J. Brown, I. Pastirk, B. I. Grimberg, V. V. Lozovoy, and M. Dantus,Chem. Phys.111, 3779~1999!.

38K. W. DeLong, R. Trebino, and W. E. White, J. Opt. Soc. Am. B12, 2463~1995!.

39N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, PhRev. Lett.86, 47 ~2001!.

40C. J. Bardeen and C. V. Shank, Chem. Phys. Lett.203, 535 ~1993!.41J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzku

Nature~London! 417, 533 ~2002!.42C. J. Bardeen, Q. Wang, and C. V. Shank, J. Phys. Chem. A102, 2759

~1998!.43J. Cao, J. Che, and K. R. Wilson, J. Phys. Chem. A102, 4284~1998!.44V. Shafirovich, A. Dourandin, N. P. Luneva, C. Singh, F. Kirigin, and

E. Geacintov, Photochem. Photobiol.69, 265 ~1999!.


Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence...

Documents

Transcript of Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence...