Two-dimensional Fourier transform spectroscopyin the pump–probe geometry
Lauren P. DeFlores, Rebecca A. Nicodemus, and Andrei Tokmakoff*Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Two-dimensional optical and infrared spectroscopyhave emerged as important tools for describing mo-lecular dynamics, electronic and vibrational cou-plings, and structure in applications ranging from bi-ology to materials [1–3]. Two-dimensional (2D)Fourier transform (FT) methods transform a third-order nonlinear signal field acquired as a function ofan initial excitation and a final detection period to es-tablish the axes of the 2D spectrum that correlatesthe frequency evolution. In their different implemen-tations, obtaining maximum frequency resolutionand retaining relative phase information across thespectrum require the ability to separate real andimaginary contributions to the 2D signal and theability to selectively separate rephasing (R) and non-rephasing (NR) coherence pathways through phasematching or pulse ordering [4]. Present 2D FT meth-ods face the time-consuming problem of phasing inconstructing absorptive spectra. Phasing is used tocorrect subwavelength errors in relative and absolutepulse timings that in the Fourier transforms mix theabsorptive and dispersive components. Using theprojection-slice theorem, experiments are commonlyconstrained by fitting the projection of the 2D absorp-tive surface to a dispersed pump–probe spectrum [4].In time domain techniques, this applies one con-straint to a problem with three unknowns: the rela-tive timing of R and NR and the absolute �1 and �3timings. Alternatively, methods such as double-resonance experiments eliminate the need for phas-ing by using a spectral narrowed pump and broad-band probe at the cost of losing the distinctadvantages intrinsic to FT techniques [5]. Additionalcontrol over pulse phases and timing has beenachieved by use of acousto-optic pulse shaping inboth the visible and infrared [6,7]. With these meth-ods one balances the advantage of a high level of con-trol over pulse timing and phase with the disadvan-tage of low efficiencies and cost.
In this Letter, we demonstrate a method for per-forming 2D FT spectroscopy in the time domain us-ing a pulse-pair pump and probe geometry thatgreatly simplifies phasing and readily provides ab-sorptive 2D spectra. This implementation has been
discussed previously in the theoretical literature [4],
and the experiment advantages demonstrated usingan alternate pulse sequence for acquisition of elec-tronic photon echo signals [8]. However, despite itssimplicity, demonstration as a viable 2D FT tech-nique has not been shown with conventional optics.
In traditional 2D FT experiments, 2D surfaces areacquired by stepping the delay between the first andthe second pulse, the excitation period �1, as a func-tion of delay between the third pulse and a local os-cillator, which define the detection period �3. Numeri-cal transformation of the signal as a function of �1and �3 leads to a 2D spectrum in the conjugate vari-ables �1 and �3 as a function of �2. In the boxcar ge-ometry, R and NR coherence pathways are separatedthrough pulse time orderings and phase matchingconditions [4,9]. Time reversal of the independentlyFourier transformed R and NR spectra allows thedispersive lobes to cancel, yielding absorptive lineshapes.
Our 2D FT method uses a crossed-beam geometrybetween a collinear pulse-pair pump and a probebeam. The pulse pair induced change to the probe in-tensity that is measured by spectral interferometryas a function of the pulse-pair delay �1. Fourier trans-formation along �1 provides information identical tothe real part of the 2D correlation experiment pre-formed in the boxcar geometry [4,8]. Since the pulsepair is collinear and indistinguishable with respect totime ordering, both R and NR coherence pathwayscontribute to the signal, thus removing the need forrelative phasing of these two signals. The probe fieldnot only acts as an interaction field but also intrinsi-cally heterodynes the signal, thus eliminating theneed for absolute �3 phasing. This leaves absolute �1timing as the only unknown to be constrained by thepump–probe fit. With the �3 timing fixed and both co-herence orders contributing, spectrally dispersed de-tection of the probe can be used to directly obtain theabsorptive 2D FT spectrum. The single technical dis-advantage of this geometry is the inability to inde-pendently control the local oscillator intensity for op-timizing the heterodyne signal. However, our resultsshow that there is a sufficient signal-to-noise ratio for
Figure 1 shows the design and layout of the 2D FTIR spectrometer. The home-built laser system used togenerate the infrared pulses consists of an amplifiedTi:sapphire (650 �J, 40 fs, 800 nm, 1 kHz) laserpumping an optical parametric amplifier. The outputinfrared laser is centered at 2050 cm−1 with a 90 fspulse duration and 8 �J of energy. The IR source issplit into three beams by 50/50 KBr beam splitters(BSs), and the pulse-pair pump is created by combin-ing beams 1 and 2 onto a third beam splitter. Pulsetimings are controlled through translation of ZnSewedges (Ws) giving a time step accuracy of0.01 fs/�m [10], and a wave-plate–polarizer (WP, P)pair for controlling polarization and pulse intensity.After the sample, the probe beam is spectrally dis-persed by using a monochromator equipped with a100 groove/mm grating and imaged onto a 64 chan-nel mercury–cadmium–telluride �MCT� array. Inten-sity changes are collected as a function of delay be-tween the pulse pair. To remove the contribution ofone pump–probe signal, beam 2 is chopped (C) at500 Hz, and consecutive shots are subtracted. Thepulse-pair time delay is generated by stepping orscanning stage 1 relative to the other pulses. Thescanning method allows rapid acquisition of 2D spec-tra at a rate of �1 ps delay per 15 s. The other pump–probe signal generated between beams 1 and 3 is re-moved by the final FT along �1.
In conjunction with acquisition of the 2D spectrum,the field autocorrelation and interference fringes forstage calibration are simultaneously collected toachieve subfringe timings in �1. An out-of-phase rep-lica of the pulse pair is generated off the back side ofthe third beam splitter. A small reflection of the pulsepair is directly monitored by using a single-channelMCT detector to collect the field autocorrelation. Thesignal measured here defines an absolute time zerofor the experiment, which is required for accuratephasing of the 2D FT spectrum. In addition, interfer-ence fringes generated by imaging the remaining IRpulse pair through a monochromator centered at2050 cm−1 with a resolution of 1 cm−1 are collected by
Fig. 1. (Color online) Experimental setup of the 2D IRspectrometer, including (A) acquisition of 2D spectra, (B)interferometric autocorrelation, and (C) stage calibration.
a single-channel MCT detector. With this method, the
stage positions can be determined with better than� /100 precision. These additional elements allowreal-time data acquisition and calibration of pulsetiming, which to this point have been a major ob-stacle in 2D FT spectroscopy.
In Fig. 2, we present polarization 2D IR spectra ofrhodium dicarbonylacetylacetonato �RDC� in hexaneand deuterated chloroform �CDCl3�. Time-frequency2D surfaces are collected in approximately 1 min byscanning stage 1 from �1 of −250 to 4250 fs, and sur-faces are numerically Fourier transformed to acquirethe real part of the 2D correlation spectrum. Due tothe wedge design, the longest relative stage delayachieved was 4500 fs; thus truncation of the timescans relative to the inverse line width of the sym-metric and asymmetric modes causes small aliasingpeaks to appear in �1 in the case of RDC in hexane.Absolute zero is determined from the field autocorre-lation to better than a fringe, and the projection ofthe 2D surface onto the �3 axis is then fitted to thedispersed pump–probe to achieve subfemtosecondtiming. This reduces the phasing problem to one vari-able, the absolute �1 timing, to fit one constraint, thedata projected onto �3. Alternatively, symmetric
Fig. 2. (Color online) (a),(b) ZZYY 2D FT spectrum of RDCin CDCl3 and RDC in Hexane. (c)–(f) ZZZZ 2D FT waiting
scanning of the pulse pair can be performed to defineabsolute zero. This, however, requires the use of twochoppers to properly remove the pump–probe re-sponse.
By comparing the line shapes in 2D spectra of RDCin hexane and CDCl3, the degree of inhomogeneity inthese systems can be seen. In agreement with previ-ous studies [1], the peak structure of RDC in hexaneis narrow and symmetric [Fig. 2(b)], while RDC inCDCl3 is diagonally elongated, indicative of inhomo-geneous broadening [Fig. 2(a)]. In addition, the ap-pearance of cross peaks, arising from vibrational cou-pling, is seen in all these spectra.
Spectra reflecting vibrational dynamics and relax-ation are acquired by controlling the waiting time de-lay between the pulse pair and the probe beam. Figs.2(c)–2(f) waiting spectra �2 of 0, 240, 480, and 3000 fsin the ZZZZ polarization are shown. In this system,energy coherently transfers between the modes inRDC with an oscillation period of 480 fs [11]. The in-tensities and tilts of the cross peaks, reflecting corre-lated broadening, are modulated at this period, asseen in the �2=240 fs and �2=480 fs spectra. At awaiting time of 3000 fs, the off-diagonal peaks growin and the diagonal resonances become symmetric.Both are salient features of vibrational relaxation ina 2D spectrum [11].
We have also demonstrated the capabilities of ac-quiring polarization-sensitive 2D spectra, which pro-vide information about dipole orientation and mo-lecular structure. This is seen by comparison of theoff-diagonal resonance intensities in the ZZYY andZZZZ �2=0 surfaces [Figs. 2(a) and 2(c)]. The relativeincrease in intensity of the ZZYY cross peaks arisesfrom the �90° angle between the transition dipolemoments of the symmetric and asymmetric modes ofthe RDC molecule. All tensor elements of the third-order polarization can be obtained by implementingschemes used in transient dichroism and birefrin-gence techniques. The ZYZY element is obtained byplacing the pump pulse pair at 45° and 135° and theanalyzer at approximately 90° with respect to theprobe. This allows for the analyzer to act as the het-erodyning field with a small misalignment of the po-larization. In principle, introduction of a quarter-wave plate in the path of beam 3, using the abovepolarization scheme, allows for the dispersive compo-nent of the third-order polarization to be acquired,making this technique highly versatile with few ex-perimental drawbacks.
As a further test of the simplicity and reliability ofthe technique and the ability to measure weaker sig-nals, we show a 2D spectrum of the �-sheet proteinConcanavalin A in D2O in Fig. 3. The amide I 2Dspectrum shows the characteristic features of an an-tiparallel �-sheet with strong cross peaks betweenthe �� and �� modes as well as a high degree of inho-mogeneous broadening along the diagonal [12]. Theappearance of inhomogeneous broadening in all thesespectra implies the proper balance of R and NR sig-
nals.
Here we have demonstrated a simplified imple-mentation of 2D IR spectroscopy in the pump–probegeometry. Due to the indistinguishablility of thepulse pair with respect to time ordering and phasematching, and because of the third field acting as aprobe and reference field, the underdetermined phas-ing problem is eliminated. This method also providesopportunities for a simple extension of 2D FT spec-troscopy to multicolor and broadband continuum ex-periments without the need to account for phasematching conditions.
We thank Ziad Ganim, Sean Roberts, and Poul Pe-tersen for intriguing conversations and Kevin Jonesfor the protein sample. This work was supported bythe U.S. Department of Energy (DE-FG02-99ER14988). R. A. Nicodemus thanks the Depart-ment of Defense for a National Defense Science andEngineering Graduate fellowship.
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Fig. 3. (Color online) ZZYY 2D FT spectrum of Con-canavalin A.
