Mitigation of thermal artifacts in 100 kHz ultrafast 2D IR spectroscopy

Abstract

Ytterbium lasers make possible shot-to-shot data collection of two-dimensional infrared (2D IR) spectra at 100 kHz and higher repetition rates. At those rates, the power absorbed by the sample is appreciable and creates a steady state temperature rise and an accumulated thermal grating artifact in the spectra that can obscure weak or low concentration IR chromophores. We report the magnitude of the temperature rise, the pulse ordering by which it is created, and ways to mitigate it. Using a calibrant molecule, we measured a steady-state temperature up to 32.5 and 45 °C for laser light at 4 µm in H₂O and 6 µm in D₂O, respectively, for a typical optical density used in 2D IR experiments. The temperature reached a steady state in ∼60 s. The temperature rise scales with the integrated optical density of the sample across the laser spectrum. By cooling the sample cell, we returned the steady state temperature to room temperature within the laser focus. For samples that undergo rotation, the accumulated thermal grating artifact is removed using a perpendicular ⟨XXYY⟩ polarization because the permuted time-orderings of the thermal grating artifact has the orientational response ⟨XYXY⟩, which decays to zero during the delay between consecutive laser pulses. The procedure described in this study can be used to characterize and minimize the thermal effects in experiments where repetition rate and/or pulse energy cause an appreciable temperature rise.

I. INTRODUCTION

Ultrafast non-linear spectroscopies are beginning to take advantage of the high power and high repetition rates of amplified ytterbium-based lasers.^1–10 Traditionally, ultrafast spectroscopies have relied on amplified Ti:sapphire laser technology, operating at 1–5 kHz. Yb:KGW lasers are now powerful enough to pump optical parametric amplifiers, providing tunable amplified pulses at hundreds of kHz repetition rates. Indeed, it is now the readout rate of cameras and linear array detectors that limit the shot-to-shot repetition rates of transient absorption and 2D spectroscopies to about 100 kHz. If all things were equal, operating at 100 kHz would produce spectra with 10-times the signal-to-noise. In fact, because of the difference in noise of the two types of laser systems, improvements beyond that expected from repetition rate alone have been observed.^3,11 To achieve maximum benefit from the repetition rate, shot-to-shot control of phase and pulse delay are necessary.³

Only a few ytterbium-based 2D IR and visible spectrometers exist at the moment, most of which operate at 100 kHz repetition rates to take advantage of shot-to-shot detector readout and shot-to-shot phase and delay increments with pulse shapers.^1–5 This article focuses on 2D IR spectrometers, but analogous effects and mitigation efforts might be expected for 2D visible spectrometers. On a shot-to-shot basis, mid-IR pulse energies are 1–3 µJ for Yb-based systems operating at 100 kHz compared to 5–15 µJ on traditional Ti:sapphire systems operating at 1–5 kHz.^1,12 The higher pulse energies of Ti:sapphire lasers is preferable for some experiments, such as coherent control.^12,13 However the higher signal-to-noise from Yb systems is generally preferable and accelerates the acquisition time for imaging methods.^1,3,11 Moreover, the high-repetition rates make possible new modalities of data collection, such as rapid scanning of dynamic processes and screening large sample sets.^1,14 It is also now possible to electronically time two different laser systems, such as a Ti:sapphire with a Yb laser, to provide an actinic pump for transient 2D experiments.¹⁵

There are two differences between mid-IR pulses generated by Yb amplifiers compared to a Ti:sapphire: power and repetition rate. At 100 kHz, the mid-IR power is about 270–480 mW, compared to 5–15 mW for 1 kHz Ti:sapphire. In a typical 2D IR spectrometer, 10%–20% of the light might be absorbed in a roughly 100 µm diameter × 25 µm thick sample volume. For a 1 kHz Ti:sapphire based spectrometer, the temperature rise caused by sample absorption is generally assumed to be minor and that the energy has fully dissipated before the arrival of the next laser shot 1 ms later.^16–18 In contrast, at 100 kHz, absorption causes a significant temperature rise, as we quantify here. At 100 kHz, the heat created by absorption for one particular laser shot persists longer than the 10 µs delay before the next laser shot, and thus accumulates, causing a temperature rise, which, in turn, creates a thermal grating artifact that appears along the diagonal in 2D IR spectra.^3,16,19 The thermal grating artifact was first observed by Farrell et al. in 100 kHz 2D IR spectra of neat D₂O.³ It was assigned to a transient grating signal and thermal relaxation of a solvent, both caused by the previous laser shot. The artifact signal decreased with repetition rate and was absent at 1 kHz. A similar accumulated grating signal was observed in 2005 by Hamm and coworkers in mid-IR pump–probe spectra of nitrous acid, caused by isomerization between laser shots.²⁰ Most recently, Donaldson and coworkers characterized a zeolite sample measured at 3.8 µm with a 10 kHz Ti:sapphire laser and observed a thermal grating signal as well as a laser-induced steady state temperature rise of ∼21 °C.¹⁹

Flowing the sample, rotating the sample cell, and reducing the path length are the typical methods for minimizing temperature effects, but are not fully effective at 100 kHz repetition rates.^16,17,21 In this article, we calibrate the thermal response of two molecules, one that absorbs near 4 μm and one near 6 μm. Using these molecules, we then measure the magnitude of the thermal effects, the rate at which they equilibrate, and test methods to mitigate the temperature effects. We show that perpendicular polarization ⟨XXYY⟩ eliminates the transient thermal grating signal in samples that isotropically rotate on the microsecond timescale because the permuted time orderings of the thermal grating artifact has the orientational response ⟨XYXY⟩, which decays to zero during the 10 µs delay between consecutive laser pulses. To mitigate the change in the steady state temperature, we cool the sample cell so that it reaches the desired equilibrium temperature at the laser focus, which it does so in about 60 s. We also provide a protocol to characterize the steady state temperature for other spectrometers and samples, as well as measure changes induced by day-to-day fluctuations. Techniques such as these are helpful for achieving the full potential of new high repetition rate amplified spectrometers. For instance, control over the equilibrium temperature is important for biological samples and minimizing the accumulated thermal grating artifact is necessary for achieving background free spectra at micromolar concentrations.

II. EXPERIMENTAL METHODS

2D IR spectra were collected on two different 100 kHz spectrometers. One spectrometer generated mid-IR from a 20 W Yb:KGW regenerative amplifier (Pharos, Light Conversion) pumping a two-stage home-built optical parametric amplifier (OPA) and difference frequency generation (DFG) setup, as described in detail elsewhere.³ This spectrometer was used to collect data shown in Figs. 2, S3, and S4. All other data were collected using a spectrometer where mid-IR was generated from a 40 W Yb:KGW regenerative amplifier (Carbide, Light Conversion) pumping a commercial OPA and DFG setup (Orpheus MIR, Light Conversion). Briefly, both spectrometers utilized the pump–probe beam geometry and pulse shaping technology. The mid-IR is split along pump and probe paths. A mechanical stage delay is used to control their relative delay. The pump pulse pair is generated using a mid-IR pulse shaper in the horizontal 4f geometry.²² 2D IR spectra are detected at 100 kHz using a mercury cadmium telluride (MCT) linear array detector (infrared systems). Signal digitization is performed using high-repetition rate MCT detection electronics (Jackhammer, Phasetech Spectroscopy).³ Variations of four-frame phase cycling were calculated using custom MATLAB codes. The polarization was controlled using λ/2 waveplates designed for 6.1 µm. BaF₂ polarizers were placed after the waveplates to ensure linear polarization. Experiments were performed in a sample cell consisting of 2 mm thick CaF₂ windows separated by a Teflon spacer of 12.5–51 µm, unless noted otherwise. In experiments where the temperature of the sample cell is actively adjusted, a micro thermocouple was taped to the CaF₂ as close as physically possible to the laser spot. The thermocouple was calibrated externally with an ice bath and boiling water. The placement of the thermistor reflects the cell temperature to <0.5 °C since the CaF₂ temperature is constant to within 2 °C across its face.

FIG. 2.

Verification that background is a thermal grating artifact created by consecutive laser shots in neat D₂O by its dependence on the ordering of the phases ($\left.{\varphi }_1,{\varphi }_2\right)$ of E₁ and E₂ in the pulse train. (a)–(c) Experimentally measured artifact after processing data to isolate the E₂E₃ scatter term for three different orderings of relative pump phases. (d)–(f) Simulations of experiments performed in panels (a)–(c).

FT IR spectra were collected with a Nicolet iS10 FTIR spectrometer (ThermoFisher Scientific) equipped with a beam condenser (PIKE Technologies). Experiments were performed in the same sample cell described above at room temperature.

III. RESULTS

In this section, we report on two consequences that may occur in spectra measured at 100 kHz. First, is an accumulated thermal grating artifact that obscures the signal of weak or low concentration IR chromophores. The origin of the transient thermal signal is from hot ground states, which persist shot-to-shot, created by vibrational relaxation to low frequency solvent modes. The second is an elevated average temperature that reaches a steady state. Both effects occur because the energy deposited from each pulse does not have sufficient time to return to the temperature of the solvent outside the laser spot before the next laser shot, so the energy compounds and increases the local temperature at the laser focus.

A. Accumulate thermal grating artifact

The accumulated thermal grating artifact has been described previously, which we rewrite here.^3,20 Figure 1(a) shows a diagram of the three electric field interactions [E₁, E₂, and E₃; $E_j(\vec{r},t)=e^{\pm i(\omega t\mp {\vec{k}}_j\cdot \vec{r}\mp {\varphi }_j)}$] created by using a 2D spectrometer for each of three consecutive laser shots, n, from the laser. The pulses are separated by relative time delays t₁, t₂, and t_RepRate, as shown in Fig. 1. t_RepRate = 10 μs for a spectrometer operating at a 100 kHz repetition rate. $E_1^n$, $E_2^n$, and $E_3^n$ represent the first pump pulse whose absolute time changes with t₁, the second pump pulse which stays fixed in time for a given t₂, and the probe pulse, respectively. They have wavevectors ${\vec{k}}_1$,${\vec{k}}_2$, and ${\vec{k}}_3$, respectively, and superscripts that note the laser shots from which they originate (e.g., n, n + 1, n + 2). The pulses that create the accumulated thermal grating artifact for n + 1 ($E_{\mathit{grating}}^n$) are highlighted in red. Figure 1(b) shows the double-sided Feynman diagram that we assign to the dominant contribution to the thermal background. There are two additional pathways shown in Fig. S1. The pump and probe pulses created by shot n ($E_2^n$ and $E_3^n$) create a population state. The population state of the chromophore relaxes into the solvent, presumably on a picosecond timescale, increasing the temperature of the sample to create a thermal grating. If the temperature of the sample does not re-equilibrate before the next laser shot t_RepRate later, the hot ground state (0_h) will be excited by the traveling pump from the next shot, $E_1^{n+1}$, thereby creating a signal in the phase matching direction of k₃, which we call $E_{\mathit{grating}}^n$. The $E_{\mathit{grating}}^n$ signal field is self-heterodyned by $E_3^{n+1}$. Unfortunately, the phase matching direction of the thermal artifact is the same as the third-order signal, and so beam geometry does not discriminate one against the other.

FIG. 1.

Origin and simulated artifacts created by accumulated transient thermal gratings. (a) Laser beam path overlayed with the pulse sequence. Pulses that generate the transient thermal grating (red) arise from two consecutive laser shots. (b) Feynman diagram of the most dominant pathway of the transient thermal grating. (c) Simulation of the 2D spectrum of the thermal grating artifact.

The equation describing the thermal grating artifact created by shot n is, in the limit of delta-function pulses,

$$\begin{array}{ll}\hfill E_{\mathit{grating}}^n(t)& \propto E_2^n{E}_3^n{E}_1^{n+1}{\mu }_{01}^4{e}^{-i\left({\phi }_1^{n+1}-{\phi }_2^n\right)}{e}^{-i\omega t_2}{e}^{i\omega \left(t_1+t_3\right)}\hfill \\ \hfill & \times e^{-{\mathrm{\Gamma }}_2\left(t_2+t_3\right)}{e}^{-{\mathrm{\Gamma }}_T\left(t_{\mathit{RepRate}}-t_1-t_2\right)}.\hfill \end{array}$$ (1)

In Eq. (1), Γ₂ is the dephasing time of the solvent modes and Γ_T is the relaxation time of the temperature jump. The thermal grating will deflect subsequent laser shots for as long as it is out of equilibrium, set by Γ_T, and so we perform a sum to calculate the “accumulated” thermal grating signal at 100 kHz,

$$\begin{array}{ll}\hfill E_{\mathit{grating}}^N(\text{t})& \propto {\mu }_{01}^4\sum _{n=1}^N{E}_2^n{E}_3^n{E}_1^{n+1}{e}^{-i\left({\phi }_1^{n+1}-{\phi }_2^n\right)}{e}^{-i\omega t_2}{e}^{i\omega \left(t_1+t_3\right)}\hfill \\ \hfill & \times e^{-{\mathrm{\Gamma }}_2\left(t_2+t_3\right)}{e}^{-{\mathrm{\Gamma }}_T\left(n\times 10\mu s-t_1-t_2\right)},\hfill \end{array}$$ (2)

where N is the number of laser shots that contribute to the thermal grating.

Figure 1(c) shows a simulation of the thermal artifact using Eq. (2) and equivalent equations for the other two Feynman diagrams shown in Fig. S1. Two narrow, out-of-phase, stripes are observed along the diagonal. The thermal artifact is phased twisted because the signal is measured as t₁ + t₃. The anti-diagonal widths of the stripes scale inversely with the largest t₁ delay measured and the diagonal linewidths scale with the laser bandwidth. In this work, we do not delve on the magnitude of the thermal artifact relative to signals of the solute, but in our prior publication, we reported experiments on chromophores at low concentrations where the thermal background was a non-negligible contributor to the 2D spectra.³

In a prior publication when the thermal artifact was first reported, it was not observed at repetition rates lower than 10 kHz.³ Thus, under those conditions, we estimated that it was negligible within 100 µs, in which case N = 10 for t_RepRate = 100 µs. Others have reported elevated temperatures for zeolite pellets, which cooled over 1–3 ms, and solution phase samples, which cooled to room temperature over a range of 140 µs–300 ms.^18,23–25 We also simulated thermal relaxation of the solvent within the laser spot by solving the heat equation using the finite difference method (see the supplementary material for more details).²⁶ The results predict that the thermal diffusion decays to 10% of its initial value within 10 ms (Fig. S2). Thus, we expect N to span many laser shots, with the exact number depending on the details of the sample and spectrometer.

We confirmed that the features are indeed caused by a thermal grating that lives beyond a single laser pulse by collecting three datasets whose only difference is the ordering of the phases in the pulse sequence. The intensity and phase of a normal 2D IR signal depends on the pulse phases, but not the ordering of phases from one shot to the next because the signal from each laser shot is independent of the next. In contrast, a thermal grating for shot n + 1 will depend on the preceding shot, n. Therefore, the signal generated by the exact same pulse sequences, but in a different order, will alter the spectral signature of the artifact.

Figures 2(a)–2(c) shows experimental 2D spectra of E₂E₃ scatter measured for three different orderings of the phases (Schemes 1, 2, and 3 presented in Table I). Each scheme lists the phases for pulses E₁ and E₂ used for four consecutive laser shots, n to n + 4. The scheme then repeats the same four phases for the next t₁ delay and the process is repeated until all t₁ delays are measured. The E₂E₃ scatter was calculated by phase cycling the shot-to-shot 2D IR data, $S_{{\varphi }_1,{\varphi }_2}$, for each time delay through

$$S_{E_2{E}_3}={\log }_{10}\left(\frac{S_{0,0}{S}_{\pi ,0}}{S_{0,\pi }{S}_{\pi ,\pi }}\right),$$ (3)

which suppresses other signals and isolates the E₂E₃ scatter signal that depends on the phases of $E_2^n$ and $E_3^n$. As the experimental data in Figs. 2(a)–2(c) shows, the phase and intensity of the signal depends upon the scheme, confirming that this signal is generated by more than a single laser pulse and thus is created by a thermal response that lasts at least 10 µs. The third phase cycling scheme eliminates the interference signal, demonstrating that the artifact is an E₂E₃ process, although E₁E₃ scatter survives and so this scheme is not a viable approach to mitigate the artifact.

TABLE I.

Schemes for 4-frame phase cycling (ϕ₁, ϕ₂).

	Frame 1	Frame 2	Frame 3	Frame 4
Scheme 1	(0, 0)	(π, 0)	(0, π)	(π, π)
Scheme 2	(π, π)	(0, π)	(π, 0)	(0, 0)
Scheme 3	(0, 0)	(π, 0)	(π, π)	(0, π)

In addition, Figs. 2(d)–2(f) show simulations using Eq. (2) and additional thermal artifact pathways given in the supplementary material for the three schemes. We simulated thermal grating artifacts that survive phase cycling, as shown in Fig. S1, which accumulate due to sample heating from consecutive laser shots. The thermal grating signals were scaled by the temperature decay profile based on the sample's thermal diffusivity, as shown in Fig. S2. The simulation accounted for the phase dependence and interference between laser pulses and the thermal grating signal, Eq. (2). The resulting total detected signal was then processed as if it were experimentally obtained. The simulated spectra are nearly identical to the experiment, confirming a long-lived thermal background. Simulations agree reasonably well with the experiment for any t_RepRate $\le 100\mu \text{s}$. Above this, the thermal artifact is present in the simulations but not in experimental data, likely because it is below the noise floor.³

To collect a 2D IR spectrum, both the pulse phases and delays are varied. In the above-mentioned sample, the t₁ delay was incremented after the phases were cycled through their entirety. Alternatively, the phases could have been incremented after all t₁ delays had been scanned. Since the thermal grating exists across multiple laser shots, the two orderings may not be equivalent. However, the thermal grating is unchanged in the 2D IR spectrum, Fig. S3. Figure S4 shows the experimental 2D IR spectra collected using the typical four-frame phase cycling scheme of (ϕ₁, ϕ₂) = (0, 0); (0, π); (π, 0); (π, π) with (a) phases set shot-to-shot, followed by an increment in t₁ delay, and (b) t₁ delays are incremented shot-to-shot, followed by a change in phase. The shape of the thermal artifact in both scenarios is very similar, but the former scheme results in an artifact that is five-times weaker than the latter. Since the artifact is created by the summation of signal from several consecutive laser pulses, the intensity of the artifact is impacted by the relative ordering of the phases in the pulse sequence. Thus, scanning the full set of phases for a given time delay is preferable for this particular phase cycling scheme. Therefore, 2D IR spectrometers with shot-to-shot phase control are preferable to those that can only chop and/or scan their delays, so that a beneficial pulse ordering can be chosen.

B. Orientational response of thermal grating signal and its elimination using polarization

In this section, we describe the orientational response of the accumulated thermal grating artifact and demonstrate the use of polarization to remove it from the 2D IR spectra. The signal strength for third-order signals is scaled by the four-point orientational correlation function.^27–29 The pulse time ordering for 2D IR signal and accumulated thermal grating artifact signal are not the same. The pulse ordering for 2D IR is $E_1^n$, $E_2^n$ and then $E_3^n$, whereas the pulse ordering for the thermal artifact is $E_2^n$ and $E_3^n$, followed by $E_1^{n+1}$. Therefore, setting the relative pulse polarizations to ⟨θ₁, θ₂, θ₃, θ_LO=3⟩ = ⟨XXYY⟩ scales the 2D IR signal by the ⟨XXYY⟩ orientational correlation function and the thermal artifact signal by the ⟨XYXY⟩ orientational correlation function. The orientational correlation functions for a diagonal peak measured using ⟨XXYY⟩ and ⟨XYXY⟩ polarization schemes are shown in the following equations:²⁷

$$⟨XXYY⟩=\frac{1}{45}\left[5-2e^{-6DT}\right],$$ (4a)

$$⟨XYXY⟩=\frac{1}{15}{e}^{-6DT}.$$ (4b)

Equation (4) holds for isotropic conditions and includes the effect of molecular rotations occurring after the second field interaction. D is the orientational diffusion coefficient, and T is the time delay between the second and third field interactions. As shown in Fig. 1(a), T = t₂ for the 2D-IR signal and T = n x t_RepRate −t₁ −t₂ for the thermal artifact. D is often on the order of ps⁻¹ to ns⁻¹ in solution. Therefore, since T ≫ D, the artifact will decay to zero and the 2D IR signal will survive. Cross peaks have different orientational responses than the diagonal peaks, but the result holds true.²⁷ The polarization approach only works for samples in which heating becomes isotropically distributed, whether by the solvent physically rotating or by energy flow leading to heating whose ensemble average is isotropic. It will not work for anisotropic solids with domains larger than the laser spot size. Indeed, Donaldson et al. observed that the thermal artifact was not fully removed in ⟨XXYY⟩ for an anisotropic sample of zeolites.¹⁹

We verified the prediction that ⟨XXYY⟩ polarization removes the accumulated thermal grating artifact. Figure 3(a) shows the 2D IR spectrum of neat D₂O measured in ⟨XXXX⟩. The thermal artifact appears along the diagonal and is roughly 100× larger than the noise after 5 min of averaging. Figure 3(b) shows the 2D IR spectrum of the same sample measured in ⟨XXYY⟩. The artifact is suppressed below the noise floor. The broad peaks in Fig. 3(b) result from the HOD bending vibration, which is not apparent in Fig. 3(a) because it is completely obscured by the thermal artifact. Thus, collecting spectra in ⟨XXYY⟩ may often be useful for measurements on weak or low concentration chromophores.

FIG. 3.

Removal of the thermal grating artifact using perpendicular polarization. (a) Neat D₂O sample measured in ⟨XXXX⟩. (b) Neat D₂O sample measured in ⟨XXYY⟩. Z axis is scaled 10×.

C. Elevated steady-state temperature, equilibration time, and temperature compensation

While the accumulated grating artifact in the 2D IR spectra can be eliminated with polarization, the sample is still heated by the laser pulses. This section reports the magnitude of the temperature rise, the time required for temperature equilibration, and a method for counteracting the temperature rise. We study the effects at 4 and 6 µm, since those are two commonly used wavelengths for 2D IR data collection. To determine the solution temperature at 4 µm, we use a probe molecule of 43.5 mM 4-cyanophenol (4CNPh) in H₂O with a 51 µm spacer. Other relevant experimental parameters are presented in Table II.

TABLE II.

Laser pulse parameters.

Laser center wavelength	4 µm	6 µm
Pump (μJ)	0.2–0.3	0.03–0.04
Probe (μJ)	0.6–0.7	0.1–0.2
Spot size (μm)	48	64
Sample concentration (mM)	43.5	100

Figures 4(a) and 4(b) show 2D IR spectra of the C≡N stretch, with v(CN) measured under identical conditions except that the laser repetition rate is set to 1 and 100 kHz, respectively. Each spectrum was an average of 100 000 2D IR spectra. The center frequencies were determined with a Gaussian fit to the diagonal slice of 2D IR spectra, as shown in Fig. 4(c), which gives v(CN) = 2230.1 ± 0.1 and 2229.5 ± 0.1 cm⁻¹ for 1 and 100 kHz, respectively. The 0.6 ± 0.2 cm⁻¹ frequency shift reflects the increase in solution temperature.

FIG. 4.

Temperature-induced frequency shift of 4CNPh. (a) 2D IR spectrum of 4CNPh collected at 1 kHz where laser-induced temperature increase is negligible. (b) 2D IR spectrum of 4CNPh sample collected at 100 kHz. All other conditions are unchanged. (c) Diagonal slices (solid lines) of 2D IR spectra (a) and (b) with Gaussian fits (dashed lines). (d) Center frequencies of 4CNPh Gaussian fits under active heat/cooling with temperature control sample cell. Change in center frequencies was linear for both 100 and 1 kHz data (yellow, blue, respectively). Linear fit (dashed red line).

To determine the temperature change required to create a 0.6 cm⁻¹ shift in frequency, we measured the frequency of 4CNPh from 5 to 55 °C using a temperature-controlled sample cell and repetition rate of 1 kHz. Figure 4(d) shows the center frequency of 4CNPh as a function of temperature as measured by a thermocouple taped to the CaF₂ window beside the laser spot. The frequency shifts linearly with temperature with a slope of −1 cm⁻¹ per +19.1 ± 0.1 °C. Thus, the −0.6 ± 0.2 cm⁻¹ frequency shift reported in Figs. 4(a) and 4(b) corresponds to a +12 ± 3 °C increase in temperature.

We repeated the measurements at 100 kHz using the same temperature-controlled sample cell. Once again, the change in frequency is linear with temperature, albeit spanning lower frequencies. Shifting the 1 kHz spectra by +11.8 ± 0.1 °C overlaps the trend with that of the 100 kHz data, as shown in Fig. S6. Thus, we conclude that, under the conditions utilized here, there is a ∼12 °C increase in temperature for data collected at 1 vs 100 kHz.

We also characterized the kinetics of the temperature rise at 100 kHz by monitoring the intensity change of the linear signal after the removal of a beam block, as shown in Fig. 5(c). The procedure was repeated ten times and the data averaged. The intensity rises rapidly over the first ten seconds and then stabilizes after approximately one minute. Therefore, at 100 kHz under our conditions, the sample reaches a steady state temperature in about 60 s.

FIG. 5.

Control of steady state temperature at focal spot. (a) Without active cooling, sample temperature at focal spot is elevated. (b) With active cooling, the sample was returned to room temperature. (c) Laser-induced change in optical density of 4CNPh to infer the thermal response at the focal spot. Biexponential fit (red) demonstrated rapid increase in temperature (<10 s) and then slow rise to a steady state (60 s).

Since the kinetics of the temperature rise plateaus within a minute, it is relatively straightforward to compensate by actively cooling the sample cell, as shown here in an experiment where we cool the sample cell so that data are collected at room temperature (21.5 °C in our laser laboratory). Figure 5(a) shows 2D IR spectra of 4CNPh collected at 100 kHz without actively cooling the sample. It has a frequency of 2229.5 ± 0.1 cm⁻¹, which, according to the frequency calibration shown in Fig. 4(d), corresponds to a +11 ± 3 °C elevation in temperature above that which would be measured at 1 kHz. This is a slightly smaller temperature rise than for the data above due to differences in pulse power and focusing conditions from the week prior. Figure 5(b) shows the 2D IR spectrum collected for the same sample after it has been actively cooled to 7.1 °C. It has a frequency of 2230.1 cm⁻¹, which, according to the frequency calibration shown in Fig. 4(d), is 21 ± 4 °C. Thus, one can set the ambient temperature of the cell to adjust for the temperature change created by absorption at high repetition rates, at least for the conditions used to perform these experiments.

D. Procedure for setting the desired equilibrium temperature using the integrated absorbance

Section III C establishes that the equilibrium temperature within the focal spot can be set to a desired temperature by adjusting the temperature of the sample cell. Upon irradiation, equilibration within the focal spot takes place within about a minute for our sample cell geometry. This conclusion was reached by using a reporter molecule dissolved in the solution. In this section, we outline a procedure to set the temperature for a generic sample that does not contain a reporter molecule. Our procedure utilizes the integrated area of the probe pulse to estimate the sample temperature, which can then be offset by cooling the sample cell. In this section, data were collected in the 6 µm region using 100 mM N-methylaceteamide (NMA) as the reporter molecule, with a 25 µm spacer, while varying the concentration of H₂O in D₂O to alter the optical density and thus the temperature of the sample. The temperature equilibrates within 60 s (Fig. S5) for this NMA sample like it did for 4PhCN [Fig. 5(c)].

Figure 6(a) shows the spectrum of the probe pulse for a series of samples that contain 100 mM NMA in D₂O with varying amounts of H₂O. H₂O broadly alters the optical density across the infrared spectrum and has a strong absorption at 1620 cm⁻¹ with a 75 cm⁻¹ fwhm.³⁰ Thus, increasing H₂O concentration increases the amount of mid-IR laser light absorbed by the sample. As shown in Fig. 6(b), the integrated area of probe absorption is linear with H₂O concentration, although absorption is non-uniform across the frequency range of the laser.

FIG. 6.

Temperature change scales with integrated absorbance of probe light. (a) Absorbance of probe light of 100 mM NMA with increasing concentrations of H₂O in D₂O. (b) Integrated area over probe frequencies scales linearly with H₂O concentration. (c) Laser-induced temperature change, obtained from 100 kHz 2D IR spectra, scales linearly with integrated absorbance of the probe light. Temperature change is relative to room temperature at 1 kHz. (d) NMA calibration curve used to determine temperature change at focal spot as measured by a shift in fitted frequency.

We then determined the temperature within the focal spot using the frequency of NMA in a similar manner to Sec. III C using 4CNPh. To do so, we created a calibration curve analogous to Fig. 4(d) by measuring the 2D IR spectra of NMA across a wide range of temperatures at both 1 and 100 kHz, Fig. 6(d). Similar to that for 4CNPh, the relationship between frequency and temperature is linear.

Using this calibration curve, we determine the temperature within the focal spot for each of the H₂O/D₂O mixtures, which are plotted in Fig. 6(c), relative to NMA in pure D₂O measured at 1 kHz, which we assumed to be room temperature. We find that the relationship is linear with respect to the integrated area of the probe pulse. The integrated area is plotted, not the absorbance at a given frequency, because it is the absorption across the entire pulse that dictates the amount of light absorbed and thus the temperature rise. Indeed, H₂O is a good test molecule because it absorbs both broadly across the 6 µm region and intensely at 1620 cm⁻¹. Thus, for a given integrated optical density, the temperature of the sample can be determined using Fig. 6(c) for the conditions under which the experiment is being performed.

The linear relationship between the integrated area of the probe pulse and the temperature of the sample means that the probe pulse can be used to estimate the temperature of an unknown sample. The procedure is as follows: the 2D IR (or linear IR spectrum) of a calibrant molecule, such as NMA or 4CNPh, is measured for a series of solutions across the range of optical densities expected for the yet-to-be-determined (unknown) sample using an identical sample cell, spacer thickness, and laser intensity. A plot such as that shown in Fig. 6(c) is created that relates the integrated probe spectrum to the frequency and temperature of the calibrant molecule. To do so, the relationship between the frequency and temperature of the calibrant molecule also needs to be known from measurements such as those shown in Figs. 4(d) and 6(d). The unknown sample is then inserted, the integrated area of the probe pulse is measured, and the solution temperature determined using Fig. 6(c). The sample cell is then cooled to the appropriate amount to set the desired temperature within the focal spot. Data collection is started 60 s after the pump and probe pulses impinge on the sample. In this manner, the precise characteristics of the laser and sample need not be known. All that is needed at the time of the experiment is the integrated intensity of the probe pulse and the previously measured calibration curve.

IV. DISCUSSION AND CONCLUSIONS

The availability of high repetition rate mid-IR lasers is making possible new experiments because higher signal-to-noise is achievable and/or data can be collected more rapidly.^1,31–33 However, there are two effects created by high wattage and repetition rate. First, a coherent signal is created that extends across multiple laser shots, causing a thermal grating artifact. That artifact spectrally overlaps with features in the 2D IR spectrum and becomes problematic at moderate to low sample concentrations. Second, the average temperature of the sample rises. Some experiments, such as ones involving protein structure, need to be carried out at precise temperatures.^18,23,34,35 However, even for experiments where precision is not necessary, it is almost always important to know the sample temperature, since pretty much all molecular and chemical dynamics is temperature-dependent.^36,37

In this article, we have characterized the thermal grating and the temperature rise and provided methods for alleviating both. If the sample undergoes molecular rotations and/or energy transfer that assumes an isotropic distribution with the time between laser pulses, then the thermal grating artifact can be removed by collecting data in the ⟨XXYY⟩. Regarding the temperature rise, we find that the temperature equilibrates within about a minute and that cooling the sample cell will set the temperature within the laser focus.

In principle, it should be possible to determine the temperature at which the sample will equilibrate from the characteristics of the sample and laser. However, we have found that estimating the temperature rise a priori is difficult because many of the variables are difficult to quantify. Some of the variables that dictate the temperature include: the absorbance spectrum of the solution, the frequency and bandwidth of the laser pulses, the intensities of the pump and probe spectrum, and the thermal diffusivity of the substrate. It might be possible to determine temperature by simply measuring the amount of light absorbed by the sample using a power meter, but even the sample thickness and the thermal conductance of the windows alter the equilibrium temperature.^16,18,25 The purpose of the calibrant molecule is to normalize for those variables in a single measurement. Of course, the calibrant molecule should be measured under conditions as close as possible to the desired experiment.

Ideally, the calibrant molecule should be very sensitive to the temperature. The molecules used here, 4CNPh and NMA, have frequency dependences of −19.1 ± 0.1 and +10.80 ± 0.07 °C/cm⁻¹, respectively. The temperature-dependent frequency shift is quite small, which is why the standard deviation of our temperatures is typically 3 °C in the above-mentioned measurements. We did not do an extensive search for temperature sensitive molecules and so other molecules might be better choices.^21,25 We imagine having a series of calibrated molecules that are routinely used to calibrate the temperature of each given experiment.

The temperature rises reported here are specific to our apparatus, sample cell, solute, and solvent. The rise may differ for other setups. Indeed, Donaldson and coworkers characterized a zeolite sample measured at 3.8 µm with a 10 kHz Ti:sapphire laser and observed a steady state temperature rise of ∼21 °C.¹⁹ Others have use continuous wave laser or pulsed laser to heat condense phase samples up to 75 °C to measure refolding dynamics.^17,18,21 In the amide I region, we have observed temperatures rises of 6–24 °C, based on the conditions described here. A temperature rise larger than 20 °C cannot be compensated by lowering the sample temperature, at least for water, because the solution would freeze. In principle, the rate of cooling should scale inversely with the path length since heat diffuses faster in CaF₂ than water, but we did not observe a systematic trend in equilibrium temperature when we compared heating in samples to 12, 25, and 51 µm spacers. When performing experiments with a large temperature rise, we typically reduce the repetition rate.

Regarding the thermal grating artifact, measuring spectra using ⟨XXYY⟩ polarization is a simple way of eliminating it. ⟨XYXY⟩ should also eliminate the thermal grating artifact, but not ⟨XYYX⟩, although we did not experimentally test these hypotheses. Ideally, one would be able to measure spectra free of thermal grating artifacts for any pulse polarization. In addition to the methods reported here, one can use a more brute force approach and subtract off the thermal artifact using a separately measured reference spectrum, such as a sample of solvent that lacks the solute. The anti-diagonal width of the thermal artifact scales inversely with the maximum t₁ delay, so by measuring t₁ to an exceptionally long delay, it can be much narrower than a natural linewidth of a molecule and thus more easily distinguished. If exceptionally narrow, it might be subtracted using a fitting routine and a functional form, or perhaps, a filter function. Of course, longer delays means longer data acquisition times and subtraction is not always ideal, so we did not test these brute force methods here. We are currently investigating if phase cycling and/or altering the t₂ delay can remove the thermal grating artifact.

Many 2D IR spectrometers are now being built to operate at both high pulse powers and high repetition rates. We hope that procedures like the one reported here will help alleviate the deleterious effects of high repetition/high power experiments and enable new experiments that take advantage of higher signal-to-noise and shorter data acquisition times.

SUPPLEMENTARY MATERIAL

The supplementary material contains details on the thermal grating artifact simulation, experimental data of the thermal grating artifact with different phase orderings, the temperature rise of NMA, least square analysis of the temperature offset, and relative absorption of the probe molecules to the solvent.

AUTHOR DECLARATIONS

Conflict of Interest

MTZ is an owner of PhaseTech Spectroscopy, Inc., which sells products related to ultrafast 2D spectroscopies, such as those used here.

Author Contributions

Harrison J. Esterly: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Shivani T. Shivani: Methodology (equal); Resources (equal). Kieran M. Farrell: Conceptualization (equal); Software (equal); Visualization (equal); Writing – original draft (equal). Martin T. Zanni: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.