Two-dimensional Electronic Spectroscopy UsingRotating Optical Flats

Patrick C. Tapping,† Yin Song,‡ Yoichi Kobayashi,¶ Gregory D. Scholes,§ andTak W. Kee∗,†

†Department of Chemistry, The University of Adelaide, North Terrace, Adelaide, SouthAustralia 5005, Australia

‡Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan48109, United States of America

¶Department of Applied Chemistry, College of Life Sciences, Ritsumeikan University, 1-1-1Nojihigashi, Kusatsu, Shiga 525-8577, Japan

§Department of Chemistry, Princeton University, Washington Road, Princeton, NewJersey 08540, United States of America

E-mail: tak.kee@adelaide.edu.auPhone: +61-8-8313-5314

Abstract

In two-dimensional electronic spectroscopy(2DES), precise control of the arrival time ofultrashort laser pulses is critical to correlat-ing the molecular states that are accessed inthe experiment. In this work, we demonstratea 2D electronic spectrometer design with aninterferometric phase stability of ∼λ/250 at600 nm. First, we present a new method forcontrolling pulse delay times based on trans-mission through pairs of optical flats rotatedperpendicular to the beam propagation direc-tion. Second, the calibration methods requiredto achieve adequate timing precision are alsoreported. Compared to existing designs usingtranslating wedges, the rotating optical flatscan achieve equivalent optical delay with ashorter path length in glass, reducing errors dueto spectral dispersion of the broadband laserpulses used in 2DES. Our approach presents asimple, low-cost technique for multidimensionaloptical spectroscopy that is capable of resolvingcomplex light-induced dynamics.

Introduction

The use of two-dimensional (2D) spectroscopyin the visible region is a relatively recent devel-opment,1,2 owing to the difficulty of maintain-ing high phase stability of the multiple laserpulses required in this spectral region. As anextension of pump-probe or transient absorp-tion spectroscopy, 2D visible spectroscopy, or2D electronic spectroscopy (2DES), can resolveelectronic interactions and energy pathways inphotoactive materials, thus has proven usefulin a variety of fields such as organic or inor-ganic semiconductors and light-harvesting ma-terials.3–12 The mechanisms of photosynthesishave received particular attention,13–17 where2DES has revealed the presence of quantum co-herences in biological systems and sparked de-bate over their role in the light-harvesting pro-cess.18–23 A wide variety of spectrometer de-signs have been demonstrated, with several re-views in the literature describing the theory ofoperation and common layouts, including theirstrengths and weaknesses.2,24–31 Spectral cov-erage across the visible range and into the ul-traviolet has been demonstrated,32–34 and the

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technique extended to higher-order, multidi-mensional spectrometers.35–37

Fundamental to all designs is the generationof a Fourier transformed excitation axis, whichis produced by the varied delay of a pair of laserexcitation pulses with interferometric precision.A widely used delay scheme in 2DES involvestransmission of laser beams through a pair ofantiparallel glass wedges,25,38–42 where translat-ing one wedge varies the path length throughglass. Another scheme that has been employedinvolves the use of a pulse shaper,33,34,39,43–46

which offers convenience and rapid data acqui-sition through a programmable pulse sequence.Compared to pulse shapers, glass wedges offera wider transmission bandwidth and a signifi-cantly lower cost of implementation. However,the transmitted beam exhibits a displacementafter passing through a pair of glass wedges. Asa result, the generated signal is misaligned rela-tive to the reference beam, potentially decreas-ing the sensitivity of 2DES. This issue, however,is absent in spectrometers employing a pulseshaper. With drawbacks from the use of glasswedges and pulse shapers in 2DES, the develop-ment of an alternative approach that addressesthese issues is desirable.

In this Article, we demonstrate a 2D elec-tronic spectrometer that employs a delay tech-nique using a pair of rotating optical flats(ROFs). The methods required to achieve thenecessary interferometric precision and theirimplementation for 2DES are also reported.The ROFs provide comparable accuracy anddelay range as wedges with the benefits of ashorter glass path length, reducing effects ofspectral dispersion which can be severe withthe broad bandwidth laser pulses used in 2DES.Additionally, the use of a pair of ROFs allowsthe laser pulse to be delayed precisely withoutany beam displacement. In contrast to the lim-itations of pulse shapers, ROFs offer transmis-sion of a broad bandwidth and a low cost ofimplementation.

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Methods

The pulse sequence for 2DES is depicted in Fig-ure 1a. The delay between the first two pulses,k1 and k2, defines the coherence time, τ , whilethe delay between the second and third pulse,k3, is the population time, T .25 The detectedsignal, ks, is emitted following the third pulseand is detected interferometrically with an at-tenuated local oscillator (LO) pulse separatedby some time, t. The two phase matchingconditions to produce a third-order signal areks = −k1 + k2 + k3 and ks = +k1 − k2 + k3,which are termed the rephasing and nonrephas-ing components, respectively.24,25,47 In the box-

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cars geometry (Figure 1b), the nonrephasingcomponent is collected separately by swappingthe roles of the k1 and k2 pulses (Figure 1a), inthat k2 arrives before k1.

Driving the spectrometer requires a suitablelaser source with a spectrum that covers theregion of interest for the target sample. Ide-ally, the source should be compressed to thetransform limit to yield the highest time res-olution for the experiment. In this work, theoutput of a regenerative amplifier (Spitfire ProXP 100F, Spectra-Physics) provided 100 fs laserpulses centered at 800 nm with 1 kHz repe-tition rate. This output was directed to ahome-built, 400 nm-pumped non-collinear opti-cal parametric amplifier (NOPA) to produce abroadband output centered around 600 nm.48,49

A single-grating and single-prism compressorcompressed the pulses down to ∼13 fs,50–53 asmeasured by frequency-resolved optical gating(FROG).54 The NOPA spectrum and FROGtraces are shown in the Supporting Information.

The spectrometer was based on a diffractiveoptic (DO) and boxcars layout, which is de-picted in Figure 1b. The compressed laserpulse was focused on the DO (MS-203-Q-Y-A,Holo/Or) using a f = 500 mm concave mirror(CM1). The four first-order beams generatedby the DO were directed with a small steer-ing mirror onto a f = 500 mm concave mirror(CM2) which collimated the beams to form thebox geometry. The locations of the excitationbeams k1, k2, k3, and the local oscillator (LO)are shown in Figure 1b. k1 and k2 each passedthrough separate ROFs, which comprised a pairof fused-silica windows (226-1211M, Eksma Op-tics) with a thickness of ∼0.8 mm. Each pairwas formed from a single window, cut in halfto ensure the closest possible match in thick-ness and optical properties. Each window wasmounted on a piezo rotation stage (CONEX-AG-PR100P, Newport), capable of 0.001◦ angleincrements. Back reflections from the opticalflat (OF) were used to align the windows androtation stages so the rotational axis was per-pendicular to the beam propagation. The rota-tional axis was also parallel to the direction ofthe beam spatial dispersion caused by the DO,as shown in Figure 1b, in order to optimize the

usable area of the OF once rotated. By rotatingthe OF pair in equal but opposite directions,delay was produced by changing the effectiveglass thickness and path length. However, over-all the beam remained undeviated through thedelay stage, as shown in Figure 1c. k3 passedthrough a fixed delay glass (DG), chosen to ap-proximately match the maximum possible delayavailable for k1 and k2. The LO passed througha ∼1 mm thick neutral density (ND) filter toattenuate it by 4 orders of magnitude and anadditional ∼0.8 mm OF to place it ∼250 fs af-ter k3. The four beams were focused using af = 300 mm concave mirror (CM3) and steeredonto the sample. A beam block (BB) maskedall beams except the LO and the third-ordersignal emitted collinearly with the LO, whichwere collimated with a f = 300 mm concavemirror (CM4) and directed to an imaging spec-trograph and camera (Shamrock SR303-i andNewton 970, Andor). The camera acquiredspectra at 500 Hz, synchronized to a mechani-cal chopper wheel (MC2000B, ThorLabs) posi-tioned to modulate one of the excitation beamsat 250 Hz. In this way, each spectrum from thecamera consisted of light from two laser shots.True shot-to-shot acquisition would provide anincremental improvement in data quality,55 butin this case the acquisition rate was limited bythe speed of the camera. Consecutive pairsof spectra alternating between Iλ,on (signal +LO) and Iλ,off (LO only) were collected to giveIλ = (Iλ,on − Iλ,off) /Iλ,off . An acquisition for agiven time (τ, T ) contained 100 pairs of spectra,which were averaged to give the ∆I/I signal inthe 2DES spectrum.

The output from the compressor was horizon-tally polarized, which was maintained for allbeams in the spectrometer, however insertionof λ/2 plates in to the lines for polarization-sensitive experiments is possible provided thecorrect relative timings are preserved.56 Thepulse energy at the sample position was 15 nJper excitation pulse with a full-width-at-half-maximum spot size of 25 µm.

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Results and Discussion

The relationship between the OF rotation an-gle and optical delay can be modeled to a firstapproximation by considering the changes inbeam path through the OF and air, as shownin Figure 2a and detailed in the Supporting In-formation. The model was used to fit the databy varying the OF thickness and refractive in-dex. An accuracy of ∼1 fs was achieved acrossthe full OF rotation range. However, the ac-curacy of this model is insufficient for 2DES,which requires control of pulse arrival times toa sub-cycle precision, hence a more accuratemethod of delay calibration is required. To ad-dress this issue, we used a spectral interferom-

etry method inspired by techniques describedpreviously,25,57,58 and the results are shown inFigure 2. Using this method, the sample wasreplaced with a 50-µm pinhole, the k2 and LObeams were blocked, and scattered light in thesignal direction from the k1 and k3 beams wascaptured by the spectrograph. The OF rota-tion angle, θ, for the k1 delay was stepped from0◦ to 45◦ and the resulting interference pat-tern recorded, a segment of which is shown inFigure 2b. Because of the nonlinear relation-ship between θ and delay time, a variable an-gle step was used, equivalent to approximately0.1 fs intervals. The spectra were processed bya Fourier transform, Heaviside-like filter, andinverse Fourier transform, followed by unwrap-ping of the complex phase angle along the OFrotation angle axis.58 The result is a measureddelay time as a function of θ, as shown in Fig-ures 2a and c (solid red); the equivalent model-only curve is also shown for comparison (dottedblue). The calibration process was repeated forthe second delay stage by stepping the k2 delaywith the k1 beam blocked. Deviations from themodel are clearly visible in Figure 2c as wavycurves. The obtained calibration curves wereinterpolated and used as delay-to-angle lookuptables by the spectrometer control software. Wenote that a calibration curve can be obtainedfor every pixel in the detection frequency axis,which may be used to study the extent of spec-tral dispersion caused by the changing OF pathlength as a function of delay time. This effectis discussed further below, with analysis foundin the Supporting Information.

The importance of the delay calibration pro-cedure is demonstrated in Figure 3. The datasegments show spectral slices where τ = 0 fs,which require movement of the k1 and k2 rela-tive to the k3 pulse (Figure 1a) to yield T valuesranging from 0 to 50 fs. This transient-gratingexperiment is highly sensitive to any spectrom-eter phase issues attributed to pulse timing er-rors. With given τ and t values, a steady in-terference pattern should be produced, mani-festing as straight horizontal lines (the intensityvariations are due to the sample response fromvarying T ). The data collected using the modelonly (Figure 3a) exhibits severe deviations from

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straight lines, which are attributable to the mis-match of the k1 and k2 delays over this range,thus any 2D data collected under these con-ditions would be unreliable. In contrast, Fig-ure 3b shows an identical segment of data, butusing the delay-to-angle lookup tables. Thesedata appear as a series of straight lines, indicat-ing that the k1 and k2 delays are well matched.Re-calibration of the delays should only be re-quired if the rotational stages or OFs are movedor realigned. The calibration of the delays isinsensitive to changes to the NOPA spectrumor compressor, provided that the input align-ment to the spectrometer is maintained. Sta-bility and repeatability of the rotational stagesand calibrations can be checked by performinga transient grating experiment such as thoseshown in Figure 3. Because this experimentdepends on the precise, synchronous movementof both the k1 and k2 delay times (thus all fourrotational stages), any errors in the calibrationcurves or drift in the rotational stage position-ing can be observed clearly. We note that thetransient grating data shown in Figure 3b werecollected several weeks after the lookup tables

were generated, showing the stability of the cal-ibration over this period. Futhermore, each setof collected 2D data contains a transient gratingslice (τ = 0) which may be inspected to ensurevalidity of the calibration lookup tables.

The k1, k2 and k3 were overlapped in timeby performing a procedure analogous to a 2DFROG measurement conducted in the transientgrating geometry.54 Using a methanol samplewith the LO blocked, the k1 and k2 delays wereindependently varied by approximately ±20 fsaround the arrival time of the k3 pulse. Theintensity of the signal as a function of the k1 andk2 delay times was fitted to a bivariate normaldistribution to find the origin, where τ = T =0 fs.

The passive phase stability afforded by theboxcars layout is demonstrated in Figure 4,where phase analysis as a function of acquisitiontime is shown. In this experiment, the interfer-ogram from a cresyl violet (dye) sample wascollected while τ and T were fixed (Figure 4a).Variations in the measured interferogram are

Figure 4: (a) Interference pattern and (b) com-puted phase stability of the spectrometer over ashort time scale, approximating the duration ofa single 2D scan (for a given population time,T ). Sample was a cresyl violet solution withdelays fixed so that τ = 0 fs, T = 195 fs andspectra acquired at 2 s intervals. The stabilityover a longer time scale is shown in the Sup-porting Information.

reflected as phase offsets, attributed to mis-

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match of the ks and LO arrival times due to fac-tors such as vibration, air turbulence and tem-perature changes, or through scattering fromthe sample. The measured phase stability at597 nm was λ/247 over 10 minutes (Figure 4b),which approximates the data acquisition timerequired for a single 2D spectrum for a givenT . Over a longer period of 6 hours the phasestability was measured at λ/217 (SupportingInformation), comparable to or exceeding thespecifications of some previously reported de-signs.33,38,42,58–62

In the experiment, data were collected by ac-quiring spectra while stepping the k1 or k2

delay over τ to create the rephasing or non-rephasing components, respectively, for a givenT (Figure 1a). The k1 and k2 delays werethen moved by equal delay times to producea new value of T and the process repeated.The raw data set is thus intensity as a functionof detection wavelength at each τ and T time,I(λ, τ, T ). Typical values for τ is 45 fs at 0.2 fssteps for both the rephasing and nonrephasingcomponents of the 2D electronic spectrum. Theupper limit of T is constrained by the achievableoptical delay produced by the ROFs, which isapproximately 600 fs at θ = 45◦ in this appara-tus (Figure 2a). Beyond θ = 45◦, the resolutionof the rotation stages starts to decrease, wherea 0.001◦ increment yields an optical delay of∼30 as for a 0.85 mm thick glass. At θ = 5◦,the accuracy of the delay is an order of magni-tude higher than that.

Processing of the raw data to produce a 2Dspectrum follows a similar procedure describedby Anna et al. 63,64 The raw intensity data,I(λ, τ, T ), is converted to separate rephasingand nonrephasing components in the frequencydomain, IR(f3, f1, T ) and INR(f3, f1, T ), first byinterpolating the detection wavelength, λ, todetection frequency, f3, using significant over-sampling (212 or 213 points) to avoid peak shapedistortions due to the nonlinear relationship.65

An inverse Fourier transform along f3 revealsthe detected signal appearing around time t.The LO and background noise components areremoved while retaining the signal, which isFourier transformed back to the frequency do-main to give the signal spectrum. These spectra

are complex-valued, but the real and imaginaryparts are identical apart from a π/2 phase shift.A Fourier transform with respect to τ gives theexcitation frequency axis, f1. During this step,edge-padding to the same dimensions as f3 maybe used to smooth the peak shapes. Finally, thedata are phased,2,24,64 removing the linear spec-tral phase due to the signal–LO delay t, plus ac-counting for contributions from k1 and k2 tim-ing errors. The final complex-valued spectrahave the real or imaginary parts representingthe absorptive or dispersive components of thesample, respectively. The complete procedurefor phasing using the projection-slice theoremis detailed in the Supporting Information.

Figure 5 shows 2DES spectra at T = 110 fsof cresyl violet perchlorate in methanol with anabsorbance of ∼0.5 in a 1-mm path length cu-vette. The 3 panels present the real parts ofthe (a) rephasing and (b) nonrephasing com-ponents, as well as their (c) sum total, whichrepresents the absorptive spectrum. The dis-persive spectrum is represented by the imagi-nary parts, which are shown in the SupportingInformation. The elongated peak shape in Fig-ure 5c is attributed to overlapping ground-stateabsorption around 590 nm and stimulated emis-sion contributions at 610 nm and 625 nm. Os-cillations of the peaks occur over T (see Sup-porting Information video) in both the rephas-ing and nonrephasing components, indicative ofvibrational coherences and consistent with pre-vious cresyl violet data in the literature.40,66,67

Note that the laser spectrum used can have aninfluence on peak shapes,68 in this case limit-ing the extent of the ground-state absorptionfeature into the high-energy region (SupportingInformation).

The primary requirement for a multidimen-sional spectrometer design is achieving precisecontrol of the laser pulse arrival times whilemaintaining the overall stability of the sys-tem. Vibration, air turbulence, and tempera-ture fluctuations all have the possibility of per-turbing the relative timings of the pulses, caus-ing undesirable phase shifts. The phase shiftsmanifest as either noise or phantom signals, re-sulting in corrupted data. For example, with600 nm light, data corruption can be caused by

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an error in relative pulse delays of 1 fs, equiva-lent to a full π phase inversion. Such an errormay be caused by either movement of a mirrorby merely 150 nm or by refractive index changesof air due to either temperature or turbulence.It is clear that a high phase stability is criticalin the 2DES experiment.

Various spectrometer designs have beendemonstrated and described in several reviewsin the literature.28–30 The two most commonbeam geometries are the boxcars type de-

scribed in this work, and the pump-probe type,where the first and second excitation pulsesare collinear and the signal is emitted in thesame direction as the third pulse, which alsoserves as the LO. The pump-probe geometryautomatically provides purely absorptive spec-tra without the requirement of manual phasingbut, as the first and second excitation pulsesare indistinguishable, it cannot provide sepa-rated rephasing and nonrephasing componentsunless a phase cycling scheme is used.69,70 In-dividual analysis of the rephasing and non-rephasing spectra can be valuable in some sit-uations,27,40,56,71,72 such as distinguishing elec-tronic from vibrational coherences.40

Control of the pulse timings has been achievedin a number of ways. Translating mirrors wereused in the initial designs,2 which have the ben-efit of an all-reflective spectrometer, exclud-ing spectral dispersion effects that are inher-ent in transmissive designs. This advantageis particularly important when ultrabroadbandlaser pulses are used. This approach is effec-tive in producing the relatively coarse popu-lation time delays.39,46,73 Sufficient, sub-fs pre-cision required for coherence time delays canalso be achieved with careful engineering,61,62

but the total delay range is significantly lim-ited. Alternatively, more complicated meth-ods such as rotating reference frame acquisitionare necessary to produce the required coher-ence time steps.66,74 Transmissive delays usingtranslating glass wedges are another commonmethod,25,38–42 where the optical path lengthis changed by modifying the effective glassthickness, as discussed further below. A sim-ilar design based on a Babinet-Soleil compen-sator uses birefringent wedges to produce a pairof collinear, variably delayed pulses suitablefor excitation pulses in a pump-probe geom-etry.60,75 Recently, femtosecond pulse shapersbased on spatial light modulators or acousto-optic programmable dispersive filters have be-come more widespread.33,34,39,43–46 These opti-cal components have the advantage of easilyproducing reliable coherence times, and can berapidly adjusted to allow phase cycling meth-ods and minimize waiting time for mechanicaldelay positioning. Interestingly, despite these

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advantages, a hybrid spectrometer that can useeither translation stage or pulse shaper-baseddelays was recently described by Tollerud andDavis.29 Their instrument exhibited several is-sues related to the pulse shaper under some con-ditions, particularly in the measurements withlong coherence times. Transmissive delays us-ing ROFs, to our knowledge, have been demon-strated only once before for use in 2DES.59

However, the design differs from that describedin this work due to the use of a single rotationstage and a folding mirror with two importantconsequences. First, the delay range was lim-ited to 80 fs, suitable only for generating coher-ence time delays. Second, the use of foldingmirrors introduces additional sources of phaseinstability.

The spectrometer detailed in this work ismost closely related to designs using the box-cars layout and translating wedges to con-trol pulse delays, thus it shares many of thesame advantages and disadvantages.28,29 Theprimary disadvantages are (1) the limited delayrange required to sample long population times,(2) the relatively slow acquisition times due towaiting on delay stage positioning, and (3) theneed for manual phasing of the processed data.The advantages include simplicity of design andintrinsic passive phase stability. In addition,the design presented here lowers the cost of a2D electronic spectrometer by making use ofthe ROF delay stages. Compared to the cost ofsuitable linear translation stages with controllerand wedged glass,40,64 the rotation stages andOF are competitive, while a pulse-shaper baseddesign is an order of magnitude more expensive.

While translating wedges and ROFs sharemany similarities, there are some key differ-ences. Clearly, as seen in Figure 2a, there isa nonlinear relationship between θ and the op-tical delay by the ROFs (Supporting Informa-tion), while the delay is linearly proportionalto stage position for the translating wedges.The varying precision of the programmed de-lay over the range of rotation angles is a poten-tial issue. The interplay of the OF thickness,rotation stage capabilities, plus required delayrange and interval must be considered to en-sure sufficient precision at the maximum delay

times where θ is large. Transmission throughthe OFs also varies with angle, and depends onthe polarization of the light. Using the hor-izontally polarized output of the compressor,the k1 or k2 beams are p- or s-polarized, re-spectively, relative to their ROFs (Figure 1b),and transmission through the OF pairs is de-scribed by the Fresnel equations,76 as shownin the Supporting Information. The linear re-sponse of the pump-probe experiment allowssimple correction of the data using the pre-dicted intensity change of the pump with OFrotation angle. Interestingly, because of the op-posing effects of the p- and s-polarized beams,the intensity of the third-order signal of the 2Ddata only changes by 5% for OF rotation anglesup to 40◦, and is negligible below ∼30◦ (Sup-porting Information). Despite commerciallyavailable OF possessing better surface flatnessand smoothness specifications than wedges, sig-nificant delay deviations from the expectedmodel are still observed during calibration (Fig-ure 2c). These imperfections are not isolatedto ROFs. Significant errors in wedge baseddelays attributed to surface roughness was re-ported by Augulis and Zigmantas,57 where adisplacement-to-delay lookup table scheme wassuggested as a means to overcome these de-fects. Wedge calibration issues were furtherdiscussed more recently by Bolzonello et al.,41

whose use of 4◦ CaF2 wedges required a morecareful scheme for determination of the calibra-tion factors. However, despite a rigorous multi-step calibration process, imperfections in thewedges still induced phase deviations which re-quired correction during data processing. Zhuet al. also investigated the suitability of single-parameter wedge calibration factors consideringthe influence of flatness and surface roughness,and discussed peak shifts or distortions whichmight result from calibration errors.58 Imper-fect optics are not only a problem limited totransmissive delays; Zheng et al. also showedthat the phase stability of an all-reflective inter-ferometric delay design was limited by surfaceflatness of the mirrors used.61 We suggest thatthe lookup table calibration method used in thiswork may improve any mechanically-based de-lay system by correcting for arbitrary system-

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atic imperfections in either optics or hardware,potentially leading to improved data qualityand allowing the use of low-cost motion controldevices.

Spectral dispersion, or pulse chirping, is aconsideration for any transmission-based delaysystem due to the broad spectral bandwidthused for 2DES. Insertion of varying amountsof dispersive material necessarily results in de-viations from the ideal, transform-limited pulseshape across the delay range. Brixner et al. cal-culated a pulse broadening factor of 1.6× 10−4

for their 40 fs pulse duration with T = 300 fsand the use of fused silica wedges.25 After cor-recting for this dispersion they showed that itmade negligible impact on the resulting spec-tral shapes, a conclusion shared by other groupsusing translating-wedge delays.38,58 However,with increasing laser pulse bandwidth andlonger induced delays the dispersion effect canbecome significant, requiring either correctionduring the data processing stage,41 or the use ofall-reflective delay mechanisms.61,62,67 Interest-ingly, the ROFs outperform translating wedgesin terms of spectral dispersion. Although a pos-itive optical delay is achieved by increasing theoptical path length through glass and decreas-ing that through air, there is a notable differ-ence in the two approaches. Because the ROFsproduce a beam displacement between the OFpair, the reduction of path length through airis less than the increase in path length of glass(note the absence of beam displacement afterpassing through the pair). Consequently, whencompared to translating wedges, the same in-duced delay requires a smaller increase in paththrough glass, hence reducing the beam paththrough glass by up to 40%. This effect is par-ticularly significant with broadband ultrashortpulses such as the ones used in this work. Fur-ther details and calculations are shown in theSupporting Information. The reduced spectraldispersion also has an effect on the error of de-lay time. The spectral interferometry methodused to construct the delay lookup tables (Fig-ure 2) produces a calibration curve for each de-tection wavelength, thus the effect of varyingspectral dispersion with delay time can be di-rectly measured. We found a ±0.1% difference

in delay time across the spectral range usedin this experiment (Supporting Information),which is approximately half the error in thetranslating-wedge calibration factors measuredby Zhu et al. 58 The increased performance ofthe ROF-based design is consistent with thesmaller change in glass path length required forthe same optical delay time, as calculated in theSupporting Information.

In the boxcars geometry, positioning of thefour beams is crucial to obtain the correct phasematching conditions for the heterodyne sig-nal detection. Transmission through pairs ofwedges necessarily produces a permanent beamdisplacement (Supporting Information). Thiseffect can be minimized by having a small wedgeangle and ensuring the separation between thepair is as short as practicable. Displacementafter passing through a typical 1◦ fused silicawedge pair separated by a few mm can be ex-pected to be < 0.1 mm, but is linearly depen-dent on both cut angle and separation (Sup-porting Information). For this reason, the useof wedges with larger angles to increase de-lay range can introduce significant issues, asbeam displacement will change the vector ofthe emitted signal, ks, so that it is no longercollinear with the LO, reducing the quality ofthe obtained interferogram. For example, witha wedge angle of 4◦ and a separation of 10 mm,the beam displacement is estimated to be closeto 10% of the beam diameter of ∼3 mm. Withthis level of beam displacement, the spatial mis-match between ks and the LO can cause theinterferometric signal intensity to decrease by10% (Supporting Information).

Finally, we note that the spectrometer pre-sented in this work is a simple design for demon-strating the use of ROFs to produce pulse de-lays suitable for multidimensional spectroscopy.With additional hardware, improvements suchas dual-modulation may be made,41,42,62,66,67,77

which can reduce the influence of beam scat-tering and potentially collect pump-probe datain the same experiment. Rotating referenceframe heterodyne detection may also be usedto reduce the number of acquisitions required inthe τ axis and decrease total acquisition time,but it requires control of the LO arrival time

9

which may be implemented with additional de-lay stages.66,74 Increasing the achievable popu-lation time is also desirable, and is in-principlea straightforward task. The delay produced bythe ROFs is directly proportional to the OFthickness, but increasing the delay range in thisway comes at the cost of a decreased resolution.With the rotation stages used in this work, weexpect a population time delay of 1 ps to beachievable using ∼1.5-mm thick OFs while stillmaintaining sufficient coherence time accuracy.Alternatively, a conventional translating-mirrordelay stage may be installed to selectively delayk3 and the LO relative to k1 and k2, eliminat-ing a pair of ROFs. However, this approachinvolves breaking of the boxcars layout and re-balancing the relative pulse delays, thus caremust be taken when reassembling the boxcarsgeometry to ensure accurate re-imaging of thebeam pattern at the sample position. The de-lay range offered by the ROFs in this work issuitable for the study of systems with fast dy-namics, such as electron or metal–metal chargetransfer,3,4,78 as well as many molecular sys-tems.8,19–21 However, an extended delay rangemay be required for systems with long coher-ence times or where low frequency vibrationalor phonon modes are of interest.5,41 If a conven-tional delay stage is installed to control the pop-ulation times, and the ROFs are only requiredto produce the relatively short coherence timedelays, the issue of slow acquisition rate couldalso be addressed. The rotation stages used inthis work have the advantages of providing therequisite accuracy over a large rotation angle,but are slow to position. Galvanometer-typeactuators are fast to position and can offer therequired resolution, but only operate over a rel-atively small angle (and thus delay) range. Us-ing custom built driver circuitry to synchronizethe galvanometer positioning with the cameraframe rate, fast acquisition techniques could beemployed55 without requiring additional tracerbeams or electronics.79

Conclusions

In conclusion, we have presented a new methodto use ROFs to produce optical delays with in-terferometric precision suitable for use in mul-tidimensional electronic spectroscopy. Whencompared to translating wedge designs, theROFs offer a low-cost solution with reduced ef-fects from spectral dispersion due to varyingglass thickness. We have demonstrated the suc-cessful acquisition of 2D spectra of cresyl violetusing a spectrometer based on a pair of ROFdelay lines.

Acknowledgement PCT, TWK and GDSacknowledge the Australian Research Coun-cil for funding support (LE0989747 andDP160103797).

Supporting Information Avail-

able

Characterization of laser pulse and spectrome-ter stability, phasing of 2D data, influence oflaser spectrum on peak shape, full 2D data,rotating glass delay model, spectral dispersionand beam displacement compared to translat-ing wedges.

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