Methodology

A 2D experiment32 is comprised of three pulses with precisely controlled time-spacing between the pulses. Each pulse interacts with the sample up to 1st order in time-dependent perturbation theory. When there is a manifold of coupled excited electronic states, the effect of the first two “pump” pulses can be understood as preparing a superposition of excited (or ground) states, which is then allowed to evolve during the time interval between the second and third pulses, typically called the pump-probe waiting time. The third pulse probes the evolving superposition by generating a 3rd order macroscopic polarization in the sample at different pump-probe waiting times. In the presence of an ensemble of dipoles, the fields radiated by individual oscillating dipoles within the macroscopic polarization coherently add up to generate an experimentally detectable electric field signal along a specific phase-matched direction, which depends on a linear combination of the wavevectors of the individual pulses, that is, k sig,R = −k 1 + k 2 + k 3 and k sig,NR = + k 1 − k 2 + k 3 , where k sig,R and k sig,NR are rephasing and non-rephasing 2D signals, and k i , i = 1–3 are wavevectors of the three pulses. Phase-matching allows background-free detection, providing a route towards high signal-to-noise ratios. However, phase-matching also constrains the 2D experiment. The generation of a phase-matched signal intrinsically relies on probing dipole ensembles with volumes larger than λ3, where λ is the wavelength of light. In addition, background free detection through phase-matching requires that the pulses be non-collinear, making the experiment difficult to integrate with a microscope objective, thus constraining the possibility of spatially resolved measurements.

Fluorescence detected two-dimensional electronic spectroscopy (F-2DES) in a fully collinear geometry was first implemented by Warren and co-workers using a phase-cycled acousto-optic modulator (AOM) based pulse-shaping approach33. Fluorescence detection implies that sample volumes smaller than λ3 can be detected as the need for a macroscopic grating of dipoles radiating a detectable electric field is replaced by the detection of fluorescence from an excited state population that is produced by the addition of a 4th pulse. A fully collinear geometry implies that the setup can be integrated with a microscope objective, making spatially resolved measurements facile. In the fully collinear geometry, background-free detection can be achieved by replacing phase-matching with phase-cycling33 or phase-modulation34. Several phase-cycling approaches to F-2DES have been demonstrated33,35,36. To date, phase-cycling methods have been employed in spatially resolved 2D-infrared (2DIR) vibrational spectroscopy in the ground electronic state of a metal-carbonyl stained polystyrene bead37,38. Very recently, Goetz et al.39 performed phase-cycling-based F-2DES in a microscope. Some of the phase-cycling-based approaches that have been used for imaging applications have relied on a single AOM pulse-shaper to create multiple time-delayed pulses. Depending on the pulse-shaper, this may constrain the method to only a few tens of kHz laser repetition rates. In addition, control over the polarization and spectrum of each pulse, both of which have been routinely exploited to suppress unwanted signals32, may become difficult to implement. While better for use with high repetition rate lasers, spatial-light-modulator pulse-shapers have relatively slow switching times, making setups that employ them susceptible to laser noise. In addition, phase-cycling approaches often require that as many as 27 scans with different relative pulse phases be acquired to extract a single absorptive 2D spectrum35,39. For samples where photobleaching is significant, this requirement is particularly problematic.

Instead of phase-cycling, we adopt the alternative phase-modulation approach to F-2DES demonstrated by Marcus and co-workers34 for our implementation of SF-2DES. A simplified layout of the setup is shown in Fig. 1. Four time-delayed pulses are created using interferometers, MZ1 and MZ2, and the carrier-envelope phase of each pulse, Ω i is scanned by its respective AOM, over the laser pulse train. Thus, each pulse is tagged with a unique radio-frequency Ω i , which replaces the unique wavevectors, k i of a 2DES experiment. The resulting rephasing and non-rephasing 2D signals are contained in a four-wave mixing (FWM) population which modulates at the linear combination of radio frequencies of the individual pulses, that is, Ω R = −Ω 1 + Ω 2 + Ω 3 − Ω 4 and Ω NR = Ω 1 − Ω 2 + Ω 3 − Ω 4 , for rephasing and non-rephasing signals, respectively. The two signals are demodulated and detected in parallel lock-in channels using phase-sensitive lock-in detection40. The signal is physically undersampled through detection relative to a reference wavelength of 826 nm, generated from REF1 and REF2 outputs of MZ1 and MZ2, respectively (see Methods, Supplementary Figure 2 for details). The reference frequencies are chosen close to the electronic energy gap, such that the signal phase oscillates at (ω eg − ω R1(2) ), where ω eg is the electronic energy gap which is sampled during time delay t 1(3) , and ω R1(2) are reference frequencies generated using REF1(2). Undersampling makes the measurement insensitive to phase noise caused by mechanical delay fluctuations in the interferometer arms, thus avoiding the need for active-phase stabilization41. In contrast to the approaches mentioned above, there is no constraint of kHz pulse repetition rates, and the polarization and spectrum of each pulse can be independently controlled with ease. Use of a lock-in amplifier for phase-sensitive signal detection is another major advantage that allows high signal detection sensitivity over a wide dynamic range. Modulation of the resulting signal at high frequencies implies that 1/f noise can be minimized, and frequency filtering by lock-in detection enables minimization of white noise. Moreover, phasing of the 2D signal is done in the time-domain at t 1 , t 2 , t 3 = 0 by the lock-in amplifier, making it substantially easier than many other approaches to 2DES32. Importantly, in the phase-modulation approach34, the phase-cycling happens in “real time” as each AOM sweeps the carrier-envelope phase over the laser pulse train. This obviates the need in the phase-cycling approach33,35,36,39 for combining multiple separate phase scans during which time photobleaching and laser fluctuations will reduce the signal-to-noise ratio with which the desired signal can be extracted.

Fig. 1 Spatially resolved fluorescence-detected 2DES spectrometer (SF-2DES). Further details of the spectrometer are provided in Supplementary Figure 2. A given pulse in the compressed laser pulse train is split 50:50 by a beamsplitter (BS1), and each half is routed into a Mach-Zehnder (MZ) interferometer (MZ1 and MZ2). Each of the four interferometer arms (two per MZ) contains an AOM which sweeps the carrier-envelope phase of the pulse by frequency Ω i , i = 1−4. The time intervals between the four pulses, t 1 , t 2 , and t 3 are controlled by mechanical delay stages. One output port from each MZ is used to generate a reference signal REF1(2), which is utilized by the lock-in amplifier for signal detection. The other output port from each MZ is combined at BS6, generating four collinear time separated pulses (pump and probe pulse pairs), which are optically filtered by a shortpass filter (SP), and routed into a confocal microscope. A dichroic mirror (DCM) in the microscope transmits the collinear pulse train towards a water objective (WO), which focuses it on an immobilized sample. The sample is mounted on an XY scanning piezo stage (PZ). The fluorescence collected by the WO is separated from the excitation light at the DCM, and can be either routed for fluorescence imaging, or for generating a 2D map. An example of the fluorescence image, and the 2D spectrum at a desired XY location is shown in the figure. The 2D spectrum corresponds to zero waiting time between pump and probe pulse pairs (t 2 = 0), and shows absorptive changes in the refractive index of the sample in the form of distinct 2D peakshapes. Cross peaks at t 2 = 0 indicate that the absorption and detection frequencies of the system are different. This implies that the transitions corresponding to the positions of the two diagonal peaks correspond to excitonic transitions between sites which are electronically coupled on the excited state, and therefore connected via a common ground electronic state, and a common doubly excited electronic state manifold Full size image

To perform SF-2DES, the collinear phase-modulated pulse train generated by MZ1 and MZ2 is routed to a confocal microscope as shown in Fig. 1. First a fluorescence map of the sample is generated, followed by acquisition of F-2DES spectra at the desired XY locations.

SF-2DES on unmixed samples

Chromatic adaptation in a number of species of purple photosynthetic bacteria involves both a growth in the size of the photosynthetic unit through an increase in the number of peripheral light-harvesting antenna complexes (LH2) per reaction center core (RC-LH1 complex)42, as well as synthesis of LH2 complexes with modified spectral properties43. Under high light (HL) conditions the LH2 complex contains a monomeric ring of 9 bacteriochlorophyll a (BChl a) pigments which absorbs at ~800 nm (B800 ring), and a dimeric ring of 18 BChl a pigments which absorbs at ~850 nm (B850 ring) at 300 K. The pigments are held together by nine αβ polypeptide pairs whose composition is light-intensity-dependent, and is dictated by which of the multigene family of puc genes are expressed44. Rps. palustris presents an interesting case because under lower light (LL) intensity conditions, the B850 ring loses oscillator strength and a band around 810 nm appears. This has been attributed to the polypeptide inhomogeneity within an LH2 ring, causing a blue-shift in the site energies of certain BChl a pigments45.

Figure 2 shows in vivo measurements illustrating how the growth-condition-dependent perturbation of the electronic structure of purple bacteria manifests in the SF-2DES spectra. Figure 2a shows fluorescence images collected from a bacterial colony in unmixed samples of LL (upper panel) and HL (lower panel) bacteria. Multiple XY locations on these fluorescence maps were chosen to collect fluorescence-detected 2DES spectra. Figure 2b shows the averaged absorptive fluorescence detected 2DES spectra for LL and HL bacteria. The positions of the two diagonal peaks correspond to the B800 (upper diagonal) and B850 (lower diagonal) excitonic manifolds of the LH2 antennae within the bacterial cells. The effect of growth conditions on spectral properties is reflected by the varying strength of the lower (B850) diagonal peak. This is better seen in Fig. 2d, which compares slices through the maxima of the diagonal peaks for the LL and HL cases. The measurements show that between HL and LL conditions, the 2D diagonal peak strengths change by a factor of four, that is, the ratio of B850/B800 diagonal peak changes from 2:1 to 1:2. The measured changes are well above the error bars of the measurement, emphasizing that the SF-2DES spectrometer is able to distinguish between the two kinds of cells with a respectable signal-to-noise ratio. Higher error bars near the peak slopes in Fig. 2d reflect the fact that any index shifts in the 2D spectra, resulting from trial-to-trial variations, are averaged over. Averaging the 2D spectra would also lead to broader than ideal 2D peakshapes. The strength of a 2D peak is a product of the absorption and emission transition strengths12, such that it depends on ~μ4, where μ is the electronic transition dipole magnitude. Thus, a factor of 4 change on the diagonal peaks from HL and LL cells suggests that the absorption strength (μ2) for the B850 manifold decreases by a factor of 2 under low light (LL) conditions. The cross-peak strengths are less perturbed than the diagonal peaks because they depend on the product of B800 and B850 absorption strengths. The 2D cross-peaks also highlight the fact that despite the strong perturbation of the site energies of the BChl a pigments on the B800 and B850 rings, the BChl a transition dipoles at B800 and B850 sites remain coupled through Coulomb interactions. Figure 2c compares the absorption spectrum of HL and LL grown cells. It is seen that the spectral changes highlighted by the absorption spectrum, which reflect the strength μ2 of a given electronic transition, are less than that indicated by the 2D peaks because, as mentioned above, the 2D peak strengths depend on μ4, and thus are more sensitive to changes in the excitonic structure. Both LL and HL absorption spectra show a shoulder around 875 nm (B875 band), which corresponds to the absorption of the LH1 complex. The laser spectrum (shown as solid gray area) overlaps dominantly with the blue part of the B850 band, and excitation of the B875 band is minimal.

Fig. 2 SF-2DESon unmixed cells of Rps. palustris grown under high and low light (HL and LL). a Confocal fluorescence images of a drop-dried film of photosynthetic bacteria Rps. palustris. The bacteria were grown under LL (top panel), and HL (bottom panel) conditions. A 10 μm scale bar is shown for reference. The OD of the live cell solution from which the samples were prepared is shown in panel (c) and the drop volume was measured to be ~0.08 μL through gravimetric analysis (Supplementary Note 3, Supplementary Figure 7). b Absorptive 2D spectra at t 2 = 0 fs obtained by averaging 2D spectra from 5 different XY locations on the LL and HL fluorescence images, as shown in the left and right panels, respectively. The spectra show distinct cross-peaks at t 2 = 0 fs. The LL and HL 2D spectra are normalized relative to the B800 and B850 bands, respectively, to more clearly emphasize their spectral differences. Contours are drawn at 10–90% in steps of 10%, with additional contours at 95 and 100% to highlight small differences in maxima. The frequency ω corresponding to the axes labels on the 2D plots corresponds to ω = |ω′|/2πc, where ω′ is in rad/fs. c Linear absorption spectrum for LL and HL grown Rps. palustris overlaid with the laser spectrum (gray area). The OD for the LL sample is scaled by a factor of 0.37 such both samples have the same OD at the B800 band. Note that the LL and HL cell concentrations are different. d Slices through the maxima of the upper and lower diagonal peaks of the LL and HL 2D spectra shown in panel b. The error bars are obtained from averaging LL and HL 2D spectra at 5 different locations on the fluorescence images of panel a. The solid black line across the 2D plot corresponds to the diagonal. All measurements were conducted at 300 K Full size image

SF-2DES on mixed samples

The measurements discussed above establish that spectral differences in the LL and HL cells can be clearly differentiated by a SF-2DES experiment. In order to demonstrate the spatial-resolution and ability to characterize complex samples provided by the SF-2DES spectrometer, we performed measurements on bacterial colonies with a spatially heterogeneous composition of the LL and HL cells. The idea behind these measurements was to simulate what one might expect in a heterogeneous thin film sample, such as those known in mixed halide perovskites28,29,46, and polymer-fullerene blends23. In a mixed sample, the overall 2D signal from a given point in space will be averaged over the HL and LL constituent cells. In order to deduce the ratio of HL:LL cells contributing to the 2D signal, the averaged HL and LL spectra in Fig. 2b are chosen as the 2D basis spectra, and a linear least squares fit of the mixed 2D signal is performed. Such an analysis assumes that the HL and LL cells are equally fluorescent. Thus a given HL:LL ratio indicates the ratio of FWM signal from HL versus LL cells, rather than the ratio of the number of HL to LL cells. Supplementary Figure 14 presents a possible calibration scheme for calibrating the measured FWM signal to number of cells.

Figure 3a shows the confocal fluorescence image obtained from a bacterial colony which has spatially heterogeneous composition of HL and LL cells. A 2D spectrum was collected at several points on this image, marked in red squares. The points are separated horizontally by ~5 μm. Three such 2D spectra, from the locations corresponding to the red, blue, and green solid dots, are shown in Fig. 3b. A fit of the 2D spectrum from each location as a linear combination of the 2D basis spectra is shown in the middle frame of Fig. 3b, and the residual is shown in the right frame. The plots for all other locations, and the fitting details, are provided in Supplementary Figures 3–5. The three chosen locations approximately show the extremes of the expected spatial variations, that is, a dominantly HL (middle) or LL (bottom) spectrum, as well as a spectrum which is an equal mixture (top). The fits and the residuals are shown on the same scale as the data, and show average fit errors of ~10%, across all the locations marked in red squares in Fig. 3a, emphasizing the capability of SF-2DES to spatially resolve the excitonic structure differences manifested in 2D peakshapes and amplitudes, into their heterogeneous constituents. Morphological variations in the pump-probe signal are already known for a number of systems11,23,28,29. However, in terms of resolving such variations into 2D cross-peaks so as to infer electronic transitions connected through a common ground state, the capability provided by SF-2DES is highly complementary to conventional 2DES.

Fig. 3 SF-2DES on mixed cells of Rps. palustris grown under high and low light (HL and LL). a Confocal fluorescence image from a mixed, LL and HL, drop-dried film of photosynthetic bacteria Rps. palustris. Red squares correspond to all the locations where a 2D spectrum was collected, and is shown in Supplementary Figures 3–5. The red, blue and green solid dots indicate locations for which the corresponding 2D spectra are shown in panel b. A 10 μm scale bar is shown for reference. b Normalized t 2 = 0 fs absorptive 2D spectra collected at the three solid dot locations shown on the fluorescence image in panel a. The three horizontal frames show the measured 2D spectrum (left frame), a linear least squares fit obtained by using the LL and HL 2D spectra (in Fig. 2b) as the basis spectra to describe the spectrum collected from a mixed sample (middle frame), and the resulting residual (right frame). All the frames in a panel are normalized to the left frame. The middle frame also displays the ratio of purely HL and LL 2D basis spectra (shown in Fig. 2b), which best fits the measured spectrum. c Absorptive t 2 = 0 fs 2D spectra for the HL and LL samples obtained by recirculating a live cell solution through a 200 μm pathlength sample cell using a peristaltic pump. These spectra represent the ideal scenario (represented as LL i , HL i ), where there is no measurable photobleaching. The OD of the sample in 1 mm pathlength corresponds to that shown in Fig. 2c. Contours are drawn at 10–90% in steps of 10%, with additional contours at 95 and 100% to highlight small differences in maxima. The frequency ω corresponding to the axes on the 2D plots corresponds to ω = |ω′|/2πc, where ω is in rad/fs. The solid black line across the 2D plot corresponds to the diagonal. All measurements were conducted at 300 K Full size image

Figure 3c shows the LL and HL 2D spectra from unmixed sample solutions of live cells which were recirculated using a peristaltic pump. These spectra are considered “ideal cases” (LL i and HL i ) because they exhibit no photobleaching artifacts. Changes in the sample OD and FWM signal before and after these experiments were not measurable beyond trial-to-trial variations. Normally, Mie scattering encountered in flowing similar colloidal solutions31,47 becomes a dominant source of noise in interferometric detection. However, despite the all-collinear geometry, the combination of spectrally separating the fluorescence from the laser, and high-frequency lock-in detection, allows us to make in vivo measurements with relative ease. A comparison of LL i and HL i spectra to the basis 2D spectra in Fig. 2b, and with the 2D spectra on mixed samples (Fig. 3b), shows vertical distortions in the spectra collected from immobilized samples. This distortion is partly caused by FWM signal degradation due to photobleaching of BChl a pigments within the cells (see Discussion).

SF-2DES theoretical resolution

A diffraction-limited optical imaging system images an ideal point as a three-dimensional light intensity distribution also called the point spread function (PSF)48. For a conventional fluorescence imaging system, the PSF is defined as H id,conv = I(r, z), where I(r, z) denotes the excitation light intensity distribution at the focus, and the subscript “id” denotes that it is an ideal diffraction-limited PSF. Here r and z are lateral and axial coordinates, respectively48. For confocal microscopy, the PSF depends linearly on the excitation intensity, as well as on the size of a point detector, and is given by H id,conf (r, z) = I(r, z)[I(r, z) ⊗ D(r)]. The second term results from a two-dimensional convolution of the excitation intensity with a detector D(r), such as a pinhole, and is responsible for optical sectioning in confocal microscopy. When the pinhole is large compared to the size of the Airy disc, the second term becomes constant, such that H id,conf is approximately the same as conventional PSF H id,conv , that is, \(H_{{\mathrm{id}},{\mathrm{conf}}}(r,z)\sim H_{{\mathrm{id,conv}}}\)48. This is also true for the confocal imaging part of the current experiment because a large detection pinhole (200 μm pinhole diameter compared to a sub-micron Airy disc diameter) renders the effect of a detection pinhole on the confocal PSF negligible.

Assuming a large detection pinhole, for the case of two-photon (TP) microscopy, the excitation point spread function (PSF) depends quadratically on the excitation intensity, that is, \(H_{{\mathrm{id,TP}}}(r,z)\sim H_{{\mathrm{id,conf}}}^2(r/2,z/2) = I^2(r/2,z/2)\)48. The functional dependence of intensity on r, z is different in the TP case due to the difference of 1/2 in the excitation wavelength. In analogy, the FWM signal in a fluorescence-detected 2DES experiment is generated by one light-matter interaction of the sample with each pulse in sequence of pump and probe pulse pairs, and therefore depends linearly on the pump and probe intensities. Thus, the volume of the FWM excitation PSF, which dictates the volume of the sample contributing to the FWM signal, will be a product of pump and probe intensities, that is, \(H_{{\mathrm{id,FWM}}}(r,z)\sim I^2(r,z)\). Note that unlike in the case of TP microscopy, the FWM process and fluorescence detection happens at approximately similar wavelengths, and therefore, r, z do not have a factor of 1/2. Consequently, the spatial resolution dictated by H id,FWM will be better than that provided by TP microscopy.

For the water objective (NA 1.2) used for SF-2DES experiments at a peak laser wavelength of ~820 nm, the ideal FWM PSF H id,FWM (r, z) is shown in Fig. 4, left panel. The lateral and axial FWHMs from Fig. 4, left panel are ~0.25 μm and ~0.69 μm, respectively. These represent the diffraction-limited spatial resolution obtainable from a SF-2DES spectrometer. As with confocal TP microscopy48, the use of a smaller pinhole could further improve the spatial resolution of SF-2DES.

Fig. 4 Ideal and experimental four-wave mixing (FWM) point spread function (PSF). (left panel) The expected ideal diffraction-limited FWM PSF for the case when the pump-probe laser beams with 820 nm peak laser wavelengths, are focused to a point in the sample using a water objective of NA 1.2, and a peak laser wavelength of 820 nm. (right panel) The non-ideal FWM PSF calculated from the ideal FWM PSF by convoluting it with a 0.54 μm diameter bead to approximate the measured experimental broadening. Contours are drawn at 0.1%, 1%, 2%, 5%, and 10–90% in steps of 10, 95, and 98% Full size image

Experimental determination of SF-2DES resolution and sensitivity

In order to estimate the sensitivity of SF-2DES compared to conventional heterodyne-detected 2DES studies, we perform an order of magnitude estimation of the number of cells contributing to the FWM signal measurements on bacterial colonies, and compare to recent in vivo studies31,47 on cells using conventional 2DES.

A confocal fluorescence image of a 0.5 μm bead measured with the imaging part of the SF-2DES spectrometer shows an average FWHM lateral diameter of 0.83 μm. The fluorescence image, fitting, and PSF estimation details are provided in Supplementary Note 4 and Supplementary Figures 8–10. However, the expected FWHM, obtained by convoluting the diffraction-limited lateral confocal PSF with a 0.5 μm bead, is ~0.52 μm. This implies that the experimentally broadened lateral confocal PSF deviates from the ideal case by a factor of ~0.83/0.52 = 1.6. Based on this deviation, in order to estimate the experimental non-ideal FWM PSF, we first convolute the ideal confocal PSF H id,conf , with a bead of a given diameter, such that the resulting confocal PSF has a lateral width of 1.6× the ideal lateral width. A bead diameter of 0.54 μm approximates this experimental broadening, and the resulting non-ideal confocal PSF is denoted as H nid,conf , where the subscript “nid” denotes the non-ideal case. The non-ideal FWM PSF H nid,FWM is then calculated as \(H_{{\mathrm{nid,FWM}}}\sim H_{{\mathrm{nid,conf}}}^2\). Figure 4b shows the estimated H nid,FWM , which dictates the experimental spatial resolution. As discussed above, the FWM PSF in Fig. 4 (right panel) approximates the experimental lateral broadening of the PSF measured through the confocal image. We note that the above analysis assumes that the experimental broadening of the diffraction-limited PSF along the axial direction is also affected in the same way as measured along the lateral direction, which is a reasonable assumption for an order of magnitude estimation.

The volume enclosed by the 10% contour in the FWM PSF in Fig. 4, defines the region inside which the excitation probability of a FWM signal is >10% of the maximum excitation probability in the experiment, that is, the sample volume from which >90% of the FWM signal contributes. For the ideal case in the left panel, the enclosed 90% volume is ~0.19 μm3, and increases to ~0.55 μm3 (0.55 femtoliters) when the FWM PSF is non-ideal (right panel). In comparison, in a conventional 2DES experiment with a 200 μm pathlength and a 100 μm diameter spot size, the pump-probe overlap volume is ~1.6 × 106 μm3, which is over six orders of magnitude larger than in our SF-2DES setup. Assuming the same starting OD for the experiments, we estimate ~25 cells/μm3 of the solution. This gives an upper estimate of ~103 cells in a dried drop of ~0.08 μL initial volume contributing to the FWM signal in SF-2DES. This estimate is detailed in Supplementary Note 3.