Australasian Physical & Engineering Sciences in Medicine Volume 27 Number 4, 2004
SCIENTIFIC NOTE
Spectrally resolved femtosecond 2-colour 3-pulsephoton echoes: a new spectroscopic tool to studymolecular dynamics*
L. V. Dao, C. Lincoln, M. T. T. Do, P. Eckle, M. Lowe and P. Hannaford
Centre for Atom Optics and Ultrafast Spectroscopy, School of Biophysical Sciences and Electrical Engineering,Swinburne University of Technology, Melbourne, Australia
AbstractWe present a new multidimensional femtosecond spectroscopy technique based on spectrally resolved 2-colour 3-pulsephoton echoes for investigating molecular dynamics in a variety of systems including proteins. In this technique thesample is illuminated by two femtosecond ‘pump’ pulses with wave vectors k1, k2 and wavelength λpump and afemtosecond ‘probe’ pulse with wave vector k3 and wavelength λprobe. Nonlinear signals are generated in the phase-matching directions k4 = – k1 + k2 + k3 and k6 = – k3 + k1 + k2. These signals are analysed in spectrometers equippedwith CCD detectors and the spectra of the signals are recorded for various values of (i) the delay t12 between pulses 1and 2, (ii) the delay t23 between pulses 2 and 3, and (iii) the wavelengths λpump, λprobe. The technique has been used forstudying vibrational and electronic dynamics of dye molecules, such as cresyl violet in methanol, and ultra-fasttransient processes that occur during the photo-dissociation of carbonmonoxy myoglobin (MbCO) into myoglobin (Mb)and CO.
Following the pioneering of ‘femtochemistry’1 in the1980s, there has been much interest in developingmultidimensional femtosecond laser techniques, similar tothose successfully used in NMR, to study ultra-fastdynamical processes in complex molecular systems2-4.These techniques include nonlinear coherent spectroscopiessuch as stimulated photon echoes based on sequences offemtosecond laser pulses and Raman echoes involving twoor more pairs of femtosecond pulses followed by a probepulse. Multiple-pulse nonlinear coherent techniques probecorrelations between the electric fields generated in the
phase-matching directions by the different pulses and allowdetailed spectroscopic information to be obtained in thepresence of inhomogeneous broadening. Spreading theinformation over more than one dimension, for example, byusing several pulses with independently controllable timedelays, helps to unravel and extract the complex dynamicaland spectroscopic information, such as relaxation rates ofthe level populations, dephasing rates or inhomogeneousbroadening of the optical transition, vibrational structureand couplings.
The detection of DNA at very low concentration ismade possible by labelling the DNA with a dye. Theoxazine dye cresyl violet binds strongly to DNA and RNA-rich cell compounds, e.g., in nerve tissues. This highaffinity implies the use of cresyl violet for labelling andvisualization of these tissue types. Dye molecules are oftendistinguished by a relatively complex structure and in manycases this makes the assignment of vibrational modes, evenby isotope substitution, or comparison with relatedstructures quite difficult5. For studying the dynamics ofproteins it is necessary to know the details of the vibrationalstructures and the structural dynamics of the labellingmolecules.
We present a multidimensional spectroscopy techniquebased on spectrally resolved 2-colour 3-pulse photonechoes in the visible wavelength range for investigatingvibrational and electronic dynamics of the dye moleculecresyl violet in methanol and ultra-fast transient processes
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that occur during the photo-dissociation of carbonmonoxymyoglobin (MbCO) into myoglobin (Mb) and CO.
Theoretical background
The polarization induced in an isotropic medium bypulsed optical radiation may be expanded as a sum of termsinvolving odd powers of the optical electric field E:
where χ(1), χ(3),….. are the first-order, third-order …..susceptibilities. The induced nonlinear polarizationgenerates a signal electric field ES(t), which for low opticaldensity and perfect phase matching is directly proportionalto the nonlinear polarization. For low light intensities thenonlinear polarization is given by the third-order term P(3).
For excitation with three temporally separated opticalpulses, having electric fields E1, E2, E3 and (angular)frequencies ω1, ω2, ω3, the third-order nonlinearpolarization may be expressed in terms of nonlinearresponse theory as2
where t1, t2, t3 are time variables between pulses 1 and 2, 2and 3, and 3 and the signal, respectively; and N is thesample concentration. RA and RB are optical responsefunctions given by
where t12, t23 are the time delays between pulses 1 and 2, 2and 3, respectively. RI to RIV and their complex conjugatesare third-order nonlinear response functions.
When the signal is recorded with a slow detector, i.e.,in a time-integrated measurement, the photon echo signal isgiven by
∞S(t12, t23) ∝ ∫ |P(3)(t, t12, t23)|2 dt (4)
0
where P(3) is given by Eqs. (2), (3). In such a time-integrated measurement information about the temporalshape of the nonlinear polarization is lost and to retain suchinformation additional measurements such as time-gated orheterodyne-detected measurements may be used6.
An alternative way to obtain detailed information aboutthe temporal evolution of the nonlinear polarization isto record the spectrum of the photon echo signal usinga spectrometer4. The frequency-domain nonlinearpolarization is determined by Fourier transformation of thetime–domain nonlinear polarization [Eq. (2)] with respectto t:
When the first and second pulses temporally overlap(or partially overlap) in the sample, the pulses interfere tocreate a periodic standing wave pattern, which can induce apopulation grating by absorption in the sample. In thepresent 2-colour 3-pulse experiments in which ω1 = ω2
≠ ω3, the probe pulse can be diffracted by the populationgrating in the phase-matching direction k4 = – k1 + k2 + k3
with frequency ω4 = ω3. In this case the spectrum of thepopulation grating signal is determined by the spectralprofile of the probe pulse Iprobe(λD). The total nonlinearsignal spectrum, including the contribution of thepopulation grating, can then be written as
where η(λD, t12, t23) is the efficiency of the (transient)population grating, which is proportional to [exp(–t23/τlife) –exp(–t23/τrise)], and τlife and τrise are the lifetime and build-up time of the population grating, respectively.
For two-colour experiments with ω1 = ω2 ≠ ω3,conservation of momentum and energy leads to thefollowing phase-matching directions and signalfrequencies: k4 = – k1 + k2 + k3; k5 = – k2 + k3 + k1; k6 = –k3 + k1 + k2; ω4 = ω3 + δω4; ω5 = ω3 + δω5; ω6 = – ω3 +2ω1 + δω6, where the δω represent frequency shiftsassociated with the transfer of optical coherence betweentransitions of different frequency. Thus, in 2-colourexperiments in which ω1 = ω2 ≠ ω3, the signal for k5 is thesame as for k4 but with the sign of the coherence time t12reversed, while the signal for k6 can yield additionalinformation to that of k4 or k5.
Experiments
Our femtosecond laser system consists of a mode-locked Ti: sapphire oscillator and a regenerative amplifierwhich delivers 80 fs, 1 mJ pulses at a wavelength of 800nm and repetition rate 1 kHz. The laser pulses from theregenerative amplifier are split into two beams which pumptwo independently tunable optical parametric amplifiers(OPAs), thus providing a two-colour source of femtosecondlaser pulses. Frequency resolved optical gating (FROG)measurements show that the pulses from the OPAs, whenoptimised, have very little linear chirp. The OPAs haveseveral options for frequency generation – second harmonic
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Figure 1. Time evolution of nonlinear signal spectra for 10-4M cresyl violet in methanol versus delay timet23 at fixed delay time t12 = - 30 fs detected in the k4 direction for different probe wavelengths a) λ3 = 575nm, b) λ3 = 585 nm, c) λ3 = 615 nm and d) λ3 = 620 nm.
generation (SHG), fourth harmonic generation (FHG) orsum frequency generation (SFG) – allowing coverage of abroad range of wavelengths (250 – 2000 nm) with pulseduration of about 100 fs. The FWHM of the spectralprofile of the pulses from the OPAs is 250 – 350 cm-1 (7 – 12 nm in the visible wavelength range). The output of thefirst OPA is split into two beams, which act as the pumppulses k1 and k2, and the output of the second OPA acts asthe probe pulse k3. The three pulsed beams with time delayst12 and t23 are aligned in a triangular configuration andfocussed by a 15 cm focal length lens into the sample. Thesignal is measured in the phase-matching directions k4 andk6 and detected by spectrometers equipped with CCD arraysand having a spectral resolution of about 1 nm.
Results and discussion
We illustrate the spectrally resolved two-colour threepulse photon echo technique for cresyl violet in methanol(10-4 M). The maximum of the linear absorption band ofcresyl violet occurs at 600 nm.
i) Detection of k4 = – k1 + k2 + k3: Figure 1 shows thespectrum of the signal in the k4 direction versus thepopulation time t23 with a fixed coherence time t12 = -30 fs (where enhancement of the echo signals can beexpected) and λ1 = λ2 = 600 nm (maximum ofabsorption). The wavelength of the probe pulse isvaried from the blue side (λ3 = 575 nm, λ3 = 585 nm) tothe red side (λ3 = 615 nm, λ3 = 620 nm) of theabsorption maximum. The detected signal has awavelength λ4 = λ3 + δλ4, where δλ4 represents thewavelength shift that reflects the molecular dynamics
associated with coherence transfer between vibrationaltransitions of different frequencies. When λ3 < 600 nmδλ4 is small and increases slightly with an increasingprobe wavelength. When λ3 > 600 nm δλ4 is large (~ 20nm at 615 nm) and strong oscillations and spectralsplitting are observed. The signal at long detectionwavelengths is delayed along t23 due to the finiterelaxation times in the vibrational manifold4.
ii) Detection of k6 = – k3 + k1 + k2: Figures 2 and 3 showspectra of the signals in the k6 direction. The photonecho signal has a wavelength λ6 ≈ – λ3 + 2λ1 + δλ6. Atthe time delay t23 = - 30 fs and for detection in the k6direction, the pulse k3 precedes k2 and k1 and the‘coherence time’ is now given by t23 and the‘population time’ by t12. When scanning the delay timet12 and for short wavelengths λ3 signal in the spectralregion at – λ3 + 2λ1 is not observed. A signal appears inthis region for the case of a probe wavelength at 615nm and contributes to the blue shift observed in Fig. 2d.The oscillations and spectral splitting observed in thedetected spectra can be used to determine the splittingof vibrational energy in the ground and excited states.The clear spectral splitting is observed for the probewavelengths at 615 and 620 nm, ~ 340 cm-1 (~12 nm),is in close agreement with the lowest vibrational wavenumber of the cresyl violet spectrum, 335-343 cm-1.5
By scanning t23 the spectrum around – λ3 + 2λ1 can beobserved at either a short delay time (for λ3 < 600 nm)or a long delay (for λ3 > 600 nm). The evolution of thespectrum versus delay t23 can be considered as tworegions corresponding to δλ6 < 0 and δλ6 > 0 whichcan be related to the dynamics of coherence transfer inthe ground and excited states, respectively.
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Figure 2. Time evolution of nonlinear signal spectra versus delay time t12 at fixeddelay time t23 = - 30 fs detected in the k6 direction for different probe wavelengthsa) λ3 = 575 nm, b) λ3 = 585 nm, c) λ3 = 615 nm and d) λ3 = 620 nm.
Figure 3. Time evolution of nonlinear signal spectra versus delay time t23 at fixeddelay time t12 = 0 detected in the k6 direction for different probe wavelengthsa) λ3 = 575 nm, b) λ3 = 585 nm, c) λ3 = 615 nm and d) λ3 = 620 nm.
For a qualitative interpretation of the observations inthe k6 direction we consider a two electronic state systemS0 - S1 consisting of two excited vibrational levels |e⟩ and|e′⟩ and two ground vibrational levels |g⟩ and |g′⟩, as
illustrated in the molecular energy level diagram in Fig.1Aand Fig.1B). When λ3 > λ1 = λ2 (energy level diagram A ofFig. 1), the first pulse k3 with wavelength λ3 can generateoptical coherence ρg′e between the higher ground level |g′⟩
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and the lower excited level |e⟩. The second pulse k2 withwavelength λ2 < λ3 takes the system down to level |g⟩ tocreate optical coherence ρeg. The third pulse k1 withwavelength λ1 = λ2 can then create optical coherence ρg′e′
between levels |g′⟩ and |e′⟩, allowing generation of a ‘pure’four-wave mixing (FWM) signal for the transition |e′⟩ → |g⟩at wavelength ~ – λ3 + 2λ1 in the phase-matching directionk6. The four-wave mixing signal is expected to be observedwhen the three pulses are present at the same time and todecay rapidly at the effective optical dephasing time T2. Ifthe effective dephasing time is very short (e.g., for levels|g′⟩ and |e′⟩) the ‘pure’ FWM signal is not observable whichis the case in Fig. 2a and Fig. 2b. A similar set of transitionscan be considered for the case of λ3 < λ1 = λ2 as illustratedin the energy level diagram B of Fig.1. The interaction ofthe first two pulses with the system cannot createpopulations in the ground levels ρg′g′, ρgg or in the excitedlevels ρee, ρe′e′ directly because the two pulses havedifferent frequencies. However, when the opticalcoherence ρg′e can be transferred from the transition |g′⟩ →|e⟩ to |g⟩ → |e⟩ during vibrational relaxation in the groundstate |g′⟩→ |g⟩, population can be generated in the groundand excited states which can then lead to generation of aphoton echo signal at frequency ω6 with a time delaycharacteristic of the ground-state vibrational relaxationtime.
We are currently using spectrally resolved 2-colour 3-pulse photon echoes to investigate ultra-fast transientprocesses that occur during the photo-dissociation ofcarbonmonoxy myoglobin (MbCO) into myoglobin (Mb)and CO. Myoglobin is the single heme analogue of themore complex haemoglobin and is responsible for thestorage of oxygen in animals and plants. Broad absorptionbands occur near 560 nm (Q-band) and 420 nm (Soret-band).
Figure 4 shows the contour plots of the temporalevolution of the photon echo spectra versus populationtime t23 for Mb and MbCO for λ1 = λ2 = 580 nm,λ3 = 600 nm and t12 = 0 fs. The spectrum for MbCO issignificantly narrower than for Mb and the populationlifetimes are comparable when allowance is made forthe slowly decaying background of photo – productstates. MbCO exhibits a sustained blue shift of ~ 42 cm-1,7
relative to Mb, which is close to the assigned frequencyfor the heme doming mode, involving Fe motion out ofthe mean heme plane and an associated distortion ofthe heme from planarity. This shift, in addition tothe narrower spectral shape of MbCO, may be due tothe partially dissociated photo-product [Mb*….CO],which still contains the carbon monoxide moleculecompared with the fully dissociated Mb. The photonecho spectra also exhibit quantum beat oscillations, whichhave frequencies and decay time in reasonable agreementwith the Raman ground state vibrational data reportedelsewhere for myoglobin7. Fourier spectra of the quantumbeat patterns show significant difference in the intensitiesof given vibrational modes for the MbCO photo-productand Mb.
Figure 4. Contour plots of three-pulse photon echo spectradetected in the direction k4 versus population time t23 for (a)myoglobin and (b) carbonmonoxy myoglobin and λ1 = λ2 = 580nm, λ3 = 600 nm and t12 = 0.
Conclusions and future directions
Spectrally resolved 2-colour 3-pulse photon echospectroscopy in the visible provides a potentially powerfulmultidimensional technique for studying vibrational andelectronic dynamics of molecules on a femtosecond timescale. The detection of the spectra of the photon echosignals in a spectrometer equipped with a CCD detectorprovides a convenient way of obtaining an additionaldimension without the requirement of an additional scan(and hence additional data collection times). In particular,the multidimensional spectra can be used to probe the timeevolution of the amplitude of the third-order nonlinearpolarization induced in the sample by the three laser pulses.The large number of available degrees of freedom allowsone to separate and extract certain specific types ofspectroscopic information in complex molecular systems.The use of different colours for the pump and probe pulsestogether with spectral analysis of the photon echo signalsallows separation of the dynamics of the ground and excitedstates. The use of spectrally resolved photon echoes alsoallows the resolution of different quantum beat frequenciescorresponding to different selected energy levels.
We plan to apply the technique of spectrally resolved2-colour 3-pulse photon echoes to study molecular andelectronic dynamics in a range of complex molecularsystems including biological protein molecules and light-harvesting molecules.
Acknowledgments
We thank Mark Aizengendler and Alex Stanco fromLastek Laboratories, Thebarton, Australia for theircontributions to the multi-channel detection system with the
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Garry CCD array. This project is supported by a SwinburneUniversity Strategic Initiative Grant and an AustralianResearch Council Discovery Grant.
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5. Vogel, E., Gbureck, A., Kiefer, W., Vibrational spectroscopicstudies on the dyes cresyl violet and courmarin 152, J. ofMolecular Structure 550-551, 177-190, 2000.
6. de Boeij, W. P., Pshenichnikov, M.S. and Wiersma, D. A.,Heterodyne-detected stimulated photon echo: applications tooptical dynamics in solution, Chem. Phys. 233, 287-309, andreferences therein, 1998.
7. Rosca, F., Kumar, A. T. N., Ye, X., Sjodin, Th., Demidov, A.A., Champion, P. M., Investigations of coherent vibrationaloscillations in myoglobin, J. Phys. Chem. A104, 4280-4290,2000.
