1. Introduction

With the commercialization of pulsed laser systems, broadband transient absorption (TA) spectroscopy has become a common technique for measuring the excited state dynamics of chemical, material, and biological systems. As the attainable pulse durations have decreased from ns to ps to fs, the number of excited state processes that can be measured using TA have grown, from radical ion and triplet formation [1] to isomerization transitions [2], and now with fs-pulses, intermediate charge transfer pathways [3]. The improving time resolution has provided increasingly detailed insights into the behavior of photoexcited species in the moments following excitation. Since the excited state dynamics of a molecule or material can determine its utility for any application that involves excited species, TA has played an important role in the development of new materials for a variety of optoelectronic applications [4–7]. Solution-based methods for the synthesis and processing of such materials are highly attractive owing to the ease and low cost of these procedures. For example, semiconducting films of organic molecules can be prepared by molecular aggregation from solution [8], and luminescent colloidal nanocrystals can be grown through solution-based syntheses [9]. The ability to measure excited state dynamics during materials formation can give insight into the relationship between the pathway of formation and the resulting photophysical properties [10]. Except for a few examples [11–14], TA has previously been limited to materials systems that are at a structural equilibrium owing to the duration of a typical TA measurement. Here, we present a broadband TA instrument capable of measuring excited state dynamics during the complex processes that occur during materials formation.

TA spectroscopy is a pump-probe technique. The pump pulse, which is resonant with the sample, generates excited species in the sample. The probe pulse interacts with the excited sample after a controlled time delay. After passing through the sample, the probe is spectrally resolved by a spectrograph and directed to a wavelength-calibrated array detector. A transient spectrum is acquired by measuring the differential transmission, ΔT/T, of the probe with and without the excitation from the pump at a series of different time delays between the two pulses. The time delay is typically adjusted using a retroreflector mounted on a motorized translation stage. Positions on the translation stage are calibrated to time delays using the speed of light and a measurement of ‘time zero’, the translation stage position where the pump and the probe interact with the sample simultaneously. A full transient spectrum is acquired by collecting measurements at different time delay positions. Measurements at each position are repeated until a sufficient signal-to-noise ratio (SNR) is achieved, usually taking minutes to hours. TA signal is linearly dependent on the pump power when the fluence is sufficiently low. At higher pump fluence, non-linear processes such as exciton-exciton annihilation can impact the measured dynamics of the system. Unless these higher-order processes are the subject of study, the energy of the pump is typically lowered to eliminate/minimize these processes.

Single-shot transient absorption (SSTA) instruments are capable of acquiring a range of pump-probe time delays simultaneously. This is possible by spatially encoding the time delay range into either the pump or probe pulse. One approach [15–20] employs a large angle between the pump and probe wavefronts (Fig. 1) to spatially encode a time delay range onto the sample. The time delay range is determined by t_range = d sin(θ) / c, where c is the speed of light, d is the length of the pump-probe overlap region on the sample, and θ is the angle between the pump and probe wavefronts at the sample. Another common approach [13,14,21–24] uses reflective or transmissive echelon optics. These stair-step optics cause different spatial regions of the beam to have different travel times to the sample, generating the spatially encoded time delay. Previously, we have reported a single-color instrument using tilted beams to acquire a 45-ps time delay range [19]. This time delay range exceeded that of any previously reported instrument, enabled by the use of a spatial light modulator (SLM), discussed below. The acquisition time is dramatically decreased using single-shot techniques since the signal at all time delays is collected in parallel, without requiring the sequential movement of a motorized translation stage. Although these techniques have historically been referred to in literature as being ‘single-shot’, a sequence of laser pulses are required to calculate a transient and multiple transients are typically averaged to increase the SNR. More accurately, SSTA measurements enable the simultaneous acquisition of a range of time delays.

 

Fig. 1. The size, d, and tilted angle, θ, between the pump (blue) and probe (red) beams determine the spatially encoded time delay range used in single-shot transient absorption.

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In this work, we present a broadband single-shot TA (SSTA) instrument that enables the acquisition of a transient spectrum within a few seconds, depending on the photophysics, optical density, and quality of the sample. This is a significant advance from our previous work [19], which was limited to single-color measurements, and extends our time delay range to 60 ps. This is possible by acquiring a window of time delays simultaneously. Both the pump and the probe are focused into lines at the sample plane using cylindrical lenses. The incident angle between the pump and probe beams is larger than in a typical TA instrument, causing different regions of the pump to interact with the sample at different times, thus spatially encoding the time delay between the pump and probe. SSTA signal is then acquired by imaging the probe pulse through a spectrograph onto a 2D array detector, with one axis of the resulting image providing spectral resolution and the other axis reporting on the spatially encoded time delay. Here, we present the design and implementation of this novel spectrometer, along with the calibration approach required to convert the measured 2D image into time and wavelength resolved data. We discuss methods to optimize excitation density and pump-probe beam overlap in the sample. We demonstrate the instrument by measuring a number of materials systems. Our results demonstrate the robustness of the technique to non-uniform pump fluence and profile.

2. Experimental methods

2.1 Sample preparation

Cresyl violet and pseudoisocyanine (PIC) were dissolved in methanol and acetone, respectively. Concentrations were adjusted such that in a quartz cuvette with a 0.2 mm path length the optical density (OD) was ∼0.3 at the pump wavelength for TA measurements. A glass substrate (75 mm × 25 mm × 1 mm) was washed with methanol. A thin film of regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT) was formed by doctor blading a 0.07% by weight P3HT solution in chlorobenzene onto the glass substrate at 60 °C. The film was measured immediately after formation. Absorption measurements for cresyl violet, PIC, and P3HT are shown in Appendix A.

2.2 Single-shot transient absorption setup

Transient measurements are collected using a homebuilt broadband SSTA instrument, modified from a previously described one-color instrument [10,19,25]. A 1 kHz Ti:sapphire laser (Coherent) at 800 nm is split into two beam paths, Fig. 2. One path pumps an optical parametric amplifier to generate pump pulses at 520 nm. A prism compressor compensates for temporal dispersion yielding a pulse duration of 40 fs at the sample. A neutral density filter adjusts the power of the pump pulse. A half-wave plate and polarizer optimize the polarization for use with an SLM (Meadowlark). A broadband probe pulse is generated in argon. Argon is used instead of other common solid-state media for white light generation (WLG), such as sapphire or calcium fluoride, because it is capable of generating the higher pulse energies needed for SSTA measurements while maintaining a sufficiently broad spectrum with reasonable stability [26]. 800 nm pulses are focused approximately two-thirds of the way into a 1.6 m homebuilt argon gas cell using a concave mirror with a 2 m focal length. The cell, which is capped at each end by a 1.5 mm thick quartz window, is evacuated with a vacuum pump and filled with high purity argon to a differential pressure of 0.55 bar. An iris attenuates the beam before entering the gas cell to optimize WLG. The probe path length is controlled via a retroreflector mounted onto a translation stage (Newport). This is not moved during SSTA measurements but is used to calibrate the spatial time delay, discussed in Section 4. The pump and probe beams are modulated using optical choppers with chopping frequencies of 250 and 125 Hz, respectively. After resizing each beam, the SLM reshapes both beams to a flat-top intensity profile, further discussed in Section 2.3. A cylindrical mirror limits spectral dispersion caused by the SLM in the probe beam. Cylindrical lenses focus both beams into a 22 mm line at the sample with a spatially encoded time delay generated by the 42° angle between them. The probe beam at the sample is imaged onto the 20 µm entrance slit of a grating spectrograph (Princeton Instruments) coupled to a CMOS camera (Andor, 2160 × 2560 pixels). To increase the data acquisition speed from the detector array during SSTA measurements, the area of interest of the camera is set to 180 × 2560 pixels. The camera exposure time is set to 1.3 ms and is triggered such that, during each exposure, two probe pulses hit the detector. One axis (2560 pixels) of the images acquired by the camera captures the spatially encoded time delay between the pump and probe beams, and the other axis (180 pixels) is spectrally resolved. Transient transmission, ΔT/T, is calculated using four consecutively collected images from the camera. The camera is synchronized with the two choppers to yield images using the four possible exposure combinations by the pump and probe pulses, T₁₁, T₁₀, T₀₁, and T₀₀, where the first and second subscripts indicate the presence (1) or absence (0) of the pump and probe, respectively. Ambient background light (T₀₀) and signal arising from pump scatter and pump-induced fluorescence of the sample (T₁₀) can be subtracted using this combination of images [25]. Each transient image represents a broadband transient spectrum with a time delay range of 60 ps and spectral range of 100 nm.

 

Fig. 2. Schematic of SSTA instrument. Ar (g), pressurized argon cell; BS, beam splitter; CHP, optical chopper; CMOS, camera; CYL, cylindrical lens or mirror; HWP, half-wave plate; ND, neutral density filter; OPA, optical parametric amplifier; PC, prism compressor; POL, polarizer; RR, retroreflector; SLM, spatial light modulator.

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For each sample, the 100-nm spectral range acquired by the array detector is set via the spectrograph software. Calibration of the spectral axis of the image is discussed in Appendix B. The pump and probe beams are reshaped to a flat-top profile and overlapped as described in Sections 2.3 and 3, respectively. The probe energy was set to 10 nJ. The pump energy was set to 1.1 µJ, 730 nJ, and 400 nJ for cresyl violet, PIC, and P3HT measurements, respectively. The pump fluence for each sample was in the linear regime. Measurements of P3HT were acquired while translating the film at a speed of 0.3 mm/s with a motorized linear actuator to average over any heterogeneity in the film. SSTA measurements are acquired at a range of translation stage positions corresponding to 120 ps of time delay typically with a step size of 1 ps. The spatially encoded time delay is calibrated, as described in Section 4. A correction for non-uniformity in the pump profile is performed following the procedures described in Section 5. Spectral calibration is only performed when the wavelength range of the spectrograph is adjusted. The remaining calibration procedures are performed once for each sample.

2.3 Reshaping the probe and pump beams using an SLM

The probe and pump beams are each incident on a different spatial region of a phase-only SLM. Each pixel of the SLM can be independently controlled to modify the phase of incident light. The imparted phase reshapes the approximately Gaussian incident spatial profile to a flat-top profile at the sample using geometric beam shaping [19,27]. This is important for both the probe and the pump beams. A uniform spatial profile for the probe beam enables a uniform saturation level on the array detector, allowing the full dynamic range of the detector to be leveraged to increase the SNR of the measurement. As discussed below, a uniform pump intensity at the sample facilitates a maximum excitation density across the spatial time delay range without causing many-body interactions that affect excited state dynamics.

In addition to a phase map that reshapes each beam, phase maps that emulate a prism and a lens provide further control over the incident beams [28]. The prism phase is ϕ_prism = a · x where the constant a imparts linearly varying phase along a spatial coordinate, x, with x = 0 at the center of the SLM. This corresponds to the effect of a small-angle prism and results in a shift in the pointing of the beam. This redirects the reshaped beam away from the zeroth order reflection from the SLM, preventing this reflection from interfering with the measurement. The lens phase is ϕ_lens = b · x² where the constant b changes the effective focal length of the lens. The beam focuses when b > 0 and defocuses when b < 0. The size of each beam at the sample is finely tuned by choosing two values of b to independently focus or defocus each beam.

The total phase mapped onto each beam by the SLM is simply the sum of the three phase components. Using both the prism phase and lens phase, the horizontal and vertical shift and focusing of each beam can be independently controlled. Additionally, the applied phase can be varied as a function of spatial location, resulting in variable focusing and shifting of the beam, shown in Section 3.2 to be particularly useful for correcting undesirable focusing effects in the pump beam inherent to the experimental setup.

3. Spatial overlap of the pump and the probe

3.1 Pump overlap through fluorescence imaging

The pump and probe beams must be spatially overlapped in the sample for TA measurements. When the angle between the pump and probe beams is relatively small both beams can be easily imaged using optics with a low numerical aperture onto a camera, enabling accurate control of the overlap. This is not possible in our SSTA apparatus owing to the large angle between the pump and the probe and their relatively large spatial profiles at the sample position. The pump could be directly imaged using a second camera [18], but the imaging planes for the pump and probe would necessarily be different and fiducial markers would be needed to overlap the pump and probe images collected using their respective detectors. To avoid these additional measurement complexities, we directly image the probe and use fluorescence to image the pump. The imaging optics are placed such that the sample plane is conjugate to the entrance slit of the spectrograph, with the long axis of the entrance slit coincident with the axis onto which the pump-probe time delay is spatially encoded. The plane of the entrance slit is also conjugate to the plane of the detector. When both beams are imaged onto the detector at each point along the long axis of the 20 µm slit, the two focal lines must be well-overlapped at the sample plane. The probe is directly imaged, with the pointing of the probe optimized to obtain a uniform saturation level on the camera for the wavelength range imaged by the camera. The steep angle of the pump prohibits it from being directly imaged at the sample plane. Instead, the profile of the pump beam is determined by fluorescence imaging using a resonant, highly fluorescent, and homogenous sample [29]. The pump intensity at the sample position is determined by integrating the fluorescence intensity along the spectral axis of the detector, and the pump pointing is adjusted to maximize the intensity of fluorescence at the spatial locations that are coincident with the directly imaged probe pulse.

3.2 Non-uniform focusing of the pump

The steep incident angle of the pump beam at the sample also results in non-uniform focusing at the sample position. The cylindrical lens focuses the pump to a line that is not parallel with the sample plane, Fig. 3(a). The entire spatial profile of the pump pulse on the sample plane can be imaged by using a fluorescent sample, as described above, opening the entrance slit to the spectrograph such that it does not impede any part of the imaged fluorescence, and directing the zeroth order reflection from the grating to the array detector. As shown in Fig. 3(b) (blue), the pump beam produces a bowtie-shaped area of excitation at the sample plane, resulting in a non-uniform energy density. We correct for this by using the SLM to apply a phase map that emulates a lens with a focal length that varies along the long axis of the pump beam,

 

Fig. 3. Pump beam focus correction. (a) Pump beam focused onto the sample plane using a cylindrical lens with each side of the beam traced to its projection on the sample. Inset: Projection of pump onto sample, viewed from top. (b) Spatial profile of the pump beam on the sample plane without (blue) and with (red) focus correction. Colored pixels indicate locations where measured fluorescence intensity, ${I_f}$, was above $\max ({I_f}) \cdot {e^{ - 2}}$ where $\max ({I_f})$ is the maximum intensity for each column of pixels. Dashed lines mark the spectrograph entrance slit when set at 20 µm. (c) A three-peaked pump intensity profile through the 20-µm slit integrated along each column of pixels from (b) without focus correction (blue) and with focus correction (red).

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In practice c and d are determined as follows. The pump profile is modified to consist of three peaks of equal intensity via geometric beam shaping using the SLM. With the spectrograph slit set at 20 µm [Fig. 3(b), dashed lines], the integrated intensity of the uncorrected pump fluorescence for the edge peaks are lower than the central peak due to the bowtie shape, shown in Fig. 3(b) (blue). Note that curvature of the imaged slit results from minor optical aberrations in the spectrograph and does not significantly impact results. The values of c and d are adjusted until the three peaks are of equal size, Fig. 3(c) (red). The zeroth order image of the corrected beam, shown in Fig. 3(b) (red), minimizes the bowtie shape. The three peaks are removed to yield a pump with a near-rectangular spatial profile and flat-top intensity profile at the sample plane, ideal for SSTA measurements.

4. Calibration of the spatially encoded time delay

Each pixel in an acquired image reports on a particular pump-probe time delay when the probe beam is imaged onto the array detector. A uniform change in these time delays can be imparted by changing the path length of either the pump or the probe beam using a retroreflecting mirror on a translation stage, a mechanism used in typical TA instruments. SSTA measurements performed at a series of translation stage positions are used to calibrate the spatially encoded time delay since the delay imposed by the translation stage can be precisely determined, as can the pixel at which time zero occurs [12,15,16,23,24,30]. We have previously reported the methodology for calibrating the time delay for a one-color SSTA measurement [19]. Since temporal chirp causes time zero to vary as a function of wavelength, a careful two-dimensional calibration must be performed to determine the relative pump-probe time delay of every pixel in the acquired images of spectrally resolved probe pulses. Minami et al. reported time delay calibration with spectral chirp using signal from a Kerr medium [22]. We demonstrate a calibration method that can be performed with any resonant sample.

SSTA measurements are performed at a series of different retroreflector positions. A broadband SSTA measurement at a particular retroreflector position (arbitrarily assigned to be 0 ps) is shown in Fig. 4(a). Temporal chirp affects the horizontal pixel at which time zero is observed, resulting in the curve shown in Fig. 4(a). At any particular wavelength, the pixel location of time zero shifts as the retroreflector is translated, Fig. 4(b). The pixel at which time zero occurs is determined for each retroreflector position by finding the maximum of a step function (simulating time zero) convoluted with the signal along the pixel axis. The location of the maximum for this convolution corresponds to the best overlap between the simulated step function and the signal. This analysis is performed for each wavelength across the entire range of time delays induced by the retroreflector. Figure 4(c) shows a 30-pixel strip of SSTA data around time zero for a few retroreflector positions. Using the identified pixel locations of time zero, a 3D surface correlating spatial pixels and wavelength to retroreflector time delays can be fit using a bivariate polynomial. This fit is then applied to the entire image, assigning a relative spatial time delay to each pixel at each wavelength. Agreement between the time delay imparted by the translation stage with the spatially encoded time delay is shown in Fig. 4(d).

 

Fig. 4. Spatial pixel time delay calibration. Each marker represents the pixel location of time zero for a particular wavelength at a specific retroreflector stage time delay position. Time zero when the stage time delay is 0 ps is shown by stars, all other stage time delays are marked as circles. Time zero for 604 nm is shown by black symbols, all other wavelengths as blue symbols. (a) Broadband ΔT/T signal with the retroreflector stage set to a time delay of 0 ps. For each wavelength, the location of time zero corresponds to a different spatial time delay pixel (horizontal axis). (b) ΔT/T signal at 604 nm as function of spatial location and retroreflector positions. For each retroreflector position, the location of time zero corresponds to a different spatial time delay pixel (horizontal axis). Inset: Expanded region at stage positions near 0 ps. (c) Spatial ΔT/T signal where each strip (separated by grey) represents the signal around time zero at specific retroreflector positions (labels). (d) Analogous plot to (c) after spatial time delay calibration.

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5. Pump profile correction and validation

5.1 Effect of the pump profile on SSTA measurements

In order to obtain an accurate transient spectrum of the sample, the pump pulse must cause the same excited state dynamics throughout the entire excitation volume. The SLM in our instrument reshapes the pump pulse such that the excitation density across the spatial time delay range is consistent, but any remaining imperfections in the uniformity of the resulting pump profile will impact SSTA measurements. For example, a flat-top target pump profile [Fig. 5(a), grey] was used to generate a phase map to reshape the pump profile. SSTA measurements were acquired using a retroreflector stage position that caused the entire spatially encoded time delay range to be after time zero [Fig. 5(b), grey]. This signal should report the dynamics of the excited state population in cresyl violet as a function of time, but small residual deviations from a perfectly flat pump profile result in small amplitude differences in the SSTA signal since the intensity of the pump beam determines the intensity of the measured ΔT/T signal. The effect of the pump profile on SSTA measurements is more clearly demonstrated by using a pump profile modified to include three peaks [Fig. 5(a), black], resulting in larger ΔT/T signal at pump-probe delay times that are measured in areas exposed to higher pump intensity [Fig. 5(b), black]. This SSTA signal clearly does not accurately report the excited state dynamics of cresyl violet.

 

Fig. 5. Pump profile reshaping and correction for SSTA measurements of cresyl violet at a probe wavelength of 615 nm. (a) Target pump profiles used to reshape the pump beam with 3 peaks (black) and flat-top (grey). (b) Actual pump profiles measured using SSTA with target profiles in (a). (c) SSTA signal at 615 nm at different retroreflector time delay positions, where each vertical slice represents a traditional transient measured by each pixel and each horizontal slice is a spatially encoded TA signal using the 3-peaked pump profile from (b). The TA signal with corresponding relative time delays from each pixel in the blue box is averaged in the direction of the arrow. (d) The averaged TA signal (blue) is fit to a tri-exponential function (black) from 5 to 55 ps. (e) TA signal from (c) normalized by the tri-exponential fit from (d). The normalized signal in the green box is averaged for each pixel in the direction of the arrow to obtain the spatially dependent pump profile, (f). (g) The raw SSTA signal (c) is corrected using the extracted pump profile (f) to factor out the effects of a non-uniform pump profile.

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5.2 Normalizing the spatially encoded transient

We have developed a method that normalizes the ΔT/T signal by the pump intensity profile to reveal a transient spectrum that accurately describes the sample. Previously reported methods to normalize the signal by the pump intensity profile have drawbacks, such as requiring a separate detector [18] or requiring samples that are sensitive and exhibit particular behaviors at the pump wavelength [20]. We have found that fluorescence detected images of the pump profile do not exactly match the strength of the measured ΔT/T signal. One correction strategy is to use signal from a long-lived dye at a time delay significantly after time zero assuming that changes in the signal are negligible over the time range of the spatially encoded signal [16,17]. This approach is valid for single-color SSTA with a small spatial time delay of 1 ps, but is insufficient when a longer time delay range of 60 ps is used. Herein, we demonstrate that our correction method is robust to significant deviations from a perfectly flat pump profile by using the pump profile with three peaks shown in Fig. 5(a) for broadband SSTA measurements of cresyl violet in methanol. This correction method is shown for the transient at 615 nm and was repeated for each wavelength in the acquired broadband spectrum.

Each pixel on the detector can measure a separate transient by scanning the position of the retroreflector on a translation stage to achieve time delays from -60 to 60 ps, shown in Fig. 5(c). The signal can be represented as

To avoid effects resulting from any time-dependent component in the pump profile, ${S_{measured}}({x,t} )$ could be normalized by ${S_{sample}}(t )$. ${S_{sample}}$ is not directly known, but averaging the signal from all of the pixels using the same relative translation stage time delay range [Fig. 5(c), blue box and arrow] results in an average transient signal, ${\bar{S}_{measured}}$, [Fig. 5(d), blue] that is dependent on ${S_{sample}}$ but not on the spatial pump profile. The process for calculating the average transient signal is described in Appendix D, resulting in

5.3 Determining the pump profile from normalized SSTA measurements

The normalized pump profile correction factor is acquired by averaging over a time delay range using the following equation

5.4 Comparison of SSTA and traditional TA measurements

Through this process, the impact of the three peaks in the pump profile has been corrected, resulting in spatially encoded transient signal representative of the sample. SSTA measurements of cresyl violet are compared with the extracted traditional transient spectra to validate this correction method. Figure 6(a) shows the corrected SSTA spectra for cresyl violet. Horizontal slices represent transients at particular wavelengths. Vertical slices are transient spectra at particular time delays. Single-shot transients at different wavelengths [Fig. 6(b), grey] are compared with ${\bar{S}_{measured}}(t )$ from Eq. (5) [Fig. 6(b), dashed]. The different dynamics measured at these two wavelengths is accurately captured by SSTA. A comparison of these transients with the three peaks in the pump profile show that the regions of the transients with poor SNR correspond to regions of the sample that are excited with lower pump intensity. This noise can be minimized by using a uniform pump profile. Single-shot transient spectra at 250 fs, 10 ps and 40 ps [Fig. 6(c), solid] are compared with transients measured in a traditional manner [Fig. 6(c), dashed], showing that SSTA accurately reports the red shift in the peak location during the first 10 ps [31]. The SNR for a transient measured using a single pixel is 25 after 55 min. of data collection. The SSTA transient has a SNR of 18 after 20 s of data collection.

 

Fig. 6. Comparison of SSTA and traditional TA signal of cresyl violet in methanol. SSTA and traditional TA measurements were acquired in 20 s and 55 minutes, respectively, where the traditional TA signal is a composite of signal collected by all 2560 pixels of the detector. (a) Broadband SSTA signal with transients (horizontal) at 575 (dark grey) and 615 (light grey) nm compared with corresponding traditional TA measurements (b, black) at the same wavelength. Transient spectra (vertical) at time delays of 0.25 (blue), 10 (green), and 40 ps (purple) are compared with corresponding traditional TA measurements (c, black) at the same time delay. Vertical dashed lines in (a) and (b) denote a change in the time delay scale. Signal in (b) and (c) are offset by 0.001 for clarity.

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In this section, we have shown a method that corrects for spatial deviations in the pump intensity. While the SLM does generate a relatively uniform pump profile, raw SSTA data demonstrate that there are still artifacts that arise from subtle deviations from a perfectly uniform profile. This method compensates for such deviations, even when they are significant, as demonstrated by using a pump profile with three distinct peaks. Despite this robustness, a uniform pump profile is ideal because it maximizes the signal response across the transient spectra while staying in a linear excitation regime, which prevents noisy regions in the measured transients evident in Fig. 6(b). The pump profile acquired using this process can be used for in situ SSTA experiments, where the sample is constantly changing during data acquisition.

6. SSTA of organic materials

A comparison between traditional and SSTA measurements for two additional material systems is presented. The pump profile correction method was utilized to correct non-uniformity in each case. Unlike the measurements of cresyl violet, the target pump profile was a flat-top beam. The excited dynamics of PIC, shown in Fig. 7(a), are notably faster than that of cresyl violet and change significantly at different wavelengths. The signal changes sign at wavelengths greater than 535 nm. The fast dynamics and changing sign limit the method represented by Eq. (4) for obtaining the pump profile, as described in Appendix C. The pump-probe time delay range used to determine the pump profile was 3 to 25 ps. Through normalization by ${\hat{S}_{measured}}$, the negative component and fast decay of ${S_{measured}}$ are factored out and a pump profile is calculated. Time delay regions where the signal is near zero result in high noise upon normalization, but these regions have little impact on the calculated pump profile because their weighted contribution is minimal as determined by Eq. (8). Figures 7(b) and 7(c) demonstrate agreement between traditional (dashed) and SSTA measurements (solid). The SNR for a transient measured using a single pixel is 30 after 55 min. of data collection. The SSTA transient has a SNR of 17 after 20 s of data collection.

 

Fig. 7. Comparison of SSTA and traditional TA signal of PIC in acetone. SSTA and traditional TA measurements were acquired in 20 s and 55 minutes, respectively, where the traditional TA signal is a composite of signal collected by all 2560 pixels of the detector. (a) Broadband SSTA signal with transients (horizontal) at 523 (dark grey) and 559 (light grey) nm compared with corresponding traditional TA measurements (b, black) at the same wavelength. Transient spectra (vertical) at time delays of 0.25 (blue), 10 (green), and 40 ps (purple) are compared with corresponding traditional TA measurements (c, black) at the same time delay. Vertical dashed lines in (a) and (b) denote a change in the time delay scale at 5 ps. Signal in (b) and (c) are offset by 0.005 and 0.0025, respectively, for clarity.

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One assumption of SSTA is that the dynamics measured is spatially uniform through the excitation region. This is a reasonable assumption for well-mixed solution measurements, such as PIC and cresyl violet, but films often exhibit some spatial heterogeneity. Heterogeneity in films may appear in SSTA signal as non-uniformity in signal intensity due to variations in film thickness at different measurement locations or in the excited state dynamics due to different molecular aggregate structures. To overcome such effects, P3HT film measurements, shown in Fig. 8, were acquired while translating the film through the excitation region. Agreement between ${\bar{S}_{measured}}$ [Figs. 8(b) and 8(c), dashed] and SSTA measurements of P3HT [Figs. 8(b) and 8(c), solid] confirm that heterogeneity in the film does not affect SSTA measurements. The SNR for a transient measured using a single pixel is 20 after 55 min. of data collection. The SSTA transient has a SNR of 20 after 20 s of data collection.

 

Fig. 8. Comparison of SSTA and traditional TA signal of a P3HT film. The film was translated during SSTA measurements. SSTA and traditional TA measurements were acquired in 20 s and 55 minutes, respectively, where the traditional TA signal is a composite of signal collected by all 2560 pixels of the detector. (a) Broadband SSTA signal with transients (horizontal) at 570 (dark grey) and 615 (light grey) nm compared with corresponding traditional TA measurements (b, black) at the same wavelength. Transient spectra (vertical) at time delays of 0.25 (blue), 10 (green), and 40 ps (purple) are compared with corresponding traditional TA measurements (c, black) at the same time delay. Vertical dashed lines in (a) and (b) denote a change in the time delay scale at 5 ps. Signal in (b) are offset by 0.002 for clarity.

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7. Summary and conclusions

This work reports a broadband SSTA instrument with a 60 ps spatially encoded time delay range. An SLM enables this by reshaping the pump and probe beams and compensating for the non-uniform focusing of the pump on the sample to produce near-uniform pump intensity within the measured region of the sample. A method to calibrate the spectral and pump-probe time delay axes of the images acquired by the array detector are presented. Even with the use of the SLM, the pump intensity is not perfectly uniform across the spatially encoded time delay. We report a correction method that removes the impact of these variations in the pump profile on SSTA measurements. This method is resilient to deviations in spatial uniformity provided that the excitation density does not exceed the threshold for many-body interactions in the excited species. This was demonstrated using a far from ideal pump profile, an organic molecule in solution with fast, wavelength-dependent dynamics, and a film of an organic polymer. Time delay calibration and pump profile correction procedures take less than an hour and are performed before in situ SSTA measurements. The broadband SSTA instrument established in this work can be employed in future studies to measure the changing excited state dynamics of chemical and materials systems as they evolve.

Appendix A. Absorption of organic dyes

Absorption spectra of cresyl violet in methanol, PIC in acetone, and a P3HT film (Fig. 9, solid) are measured using a broadband light source (ThorLabs) and spectrometer (Ocean Optics).

 

Fig. 9. SSTA measurements use a pump at 520 nm (grey). Absorption of cresyl violet in methanol (blue), PIC in acetone (green), and a film of P3HT (purple).

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Appendix B. Spectral calibration of the array detector

A HgAr calibration source (Ocean Optics) is collimated from an optical fiber and focused to a line at the sample plane, which is imaged through a spectrograph onto a 1000 × 2560 area of interest on an array detector. Minor aberrations in the imaging optics [Fig. 10(a)] require that wavelength calibration be performed for each column of pixels [32]. A central column of pixels is spectrally calibrated by visual inspection. This initial calibration is then propagated from the center column to the edges of the image, shown in Fig. 10(a). To determine the position of each peak with sub-pixel resolution, the five pixels nearest to the assigned peak position in the neighboring column are averaged, weighted by their intensities. Figure 10(b) shows the intensity profile for a spectral line at 763.511 nm from two pixel columns with symbols marking the intensity of the five pixels closest to the peak assignment from its respective neighboring column. A 3D surface correlating both pixel axes to wavelength is fit using a bivariate polynomial using the identified calibration peak locations across the image. This fit is then applied to the entire image, shown in Fig. 10(c).

 

Fig. 10. Spectral calibration of the array detector. (a) Spectral lines of HgAr light source with aberrations. A central pixel column (black) is spectrally calibrated. The calibration is propagated to the edges of the image (arrows). Red and blue lines highlight pixel columns 633 and 1942, respectively, of the spectral line at 763.511 nm. (b) Pixel intensity profile of 763.511 nm spectral line for pixel columns 633 (red) and 1942 (blue). The central pixel position of each peak (lines) is determined by the weighted average of the marked pixels. (c) Spectrally calibrated image from (a).

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Appendix C. Impact of translation stage step size and excited state dynamics on determining the pump profile

To determine the pump profile, SSTA measurements are taken at a range of translation stage positions, d_i, with a time delay step size of ${\Delta }{t_{step}}$, modeled in Fig. 11(a). Transient signal is measured by each pixel, x, at time delays $t({x,{d_i}} )$. Each pixel's time delay is shifted as a result of the angle between the pump and probe pulses. As Eq. (4) notes, the pump intensity is calculated by averaging signal within a particular time delay range which is chosen to be the same for each pixel and is denoted here as t₀ to t₁, shown in Fig. 11(b). However, unless ${\Delta }{t_{step}}$ is smaller than the time delay difference between adjacent pixels, the actual time delay range $t({x,{d_{m(x )}}} )$ to $t({x,{d_{n(x )}}} )$ for some pixels can be shifted up to ${\Delta }{t_{step}}/2$ from the target time delay range. This is evident in Fig. 11(b), where the measured time range for the blue pixel is significantly shifted from the time range measured by the green pixel. As a result, the average signal will not be calculated from the exact same time delay range, which causes sawtooth artifacts in the calculated pump profile. This is shown in Fig. 11(c), where the average signal from the blue pixel is calculated using a time delay range that is slightly earlier than the time delay range used to calculate the average signal from the green or purple pixels. The magnitude of the artifacts is dependent on Δt_step and the change in signal over Δt_step. Decreasing Δt_step will reduce the effect, but can dramatically increase the data acquisition time for this calibration step and still may not fully remove the artifacts.

 

Fig. 11. The effect of the translation stage step size, Δt_step, on the pump profile calculated from Eq. (4). (a) Simulated ΔT/T signal (false color) for pixels at time delays $t({x,{d_i}} )$ imparted at translation stage positions d_i. The translation stage time delay step size is Δt_step. Transients at different pixels (blue, green, purple) are compared in (b). (b) Transients from (a) are marked by symbols onto the full transient (black). Data outside the time delay range from t₀ to t₁ (gray) are excluded from Eq. (4). (c) The pump intensity calculated from the data in (b) using Eq. (4).

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Appendix D. Extracting an averaged transient signal from SSTA measurements

The average transient signal, ${\bar{S}_{measured}}$, of all of the pixels is determined using SSTA measurements conducted at a series of translation stage positions that impose time delays in steps of Δt_step, typically 1-3 ps, from -60 to 60 ps. This time delay range is double the spatially encoded time delay range of the instrument, 60 ps, which ensures that every pixel has 60 ps of data after time zero. To determine the average transient signal, a new array of time delays from -5 to 60 ps with a resolution of ${\Delta }t_{step}^\ast $, typically 0.1 ps, is defined where ${\Delta }t_{step}^\ast < {\Delta }{t_{step}}$. For each time point in the array, a fraction of the pixels (approximately ${\Delta }t_{step}^\ast{/}{\Delta }{t_{step}}$) have a data point that is within ${\Delta }t_{step}^\ast{/}2$ of that time point. The signal from these pixels is averaged and assigned to that time point. Every time point in ${\bar{S}_{measured}}$ then consists of signal from pixels that are evenly distributed across the image. The SNR in this transient is significantly higher than the SNR for a transient from any individual pixel, ideal for use in normalizing the spatially encoded transient. For cresyl violet, the SNR of ${\bar{S}_{measured}}$ is ∼270 vs. ∼25 for an individual pixel.

Funding

National Science Foundation (1752129).

Disclosures

The authors declare no conflicts of interest.

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