Resonance conditions, detection quality, and single-molecule sensitivity in fluorescence-encoded infrared vibrational spectroscopy

Single-molecule (SM) vibrational spectroscopy has emerged as a powerful class of tools for investigating chemical phenomena. Probing vibrations offers sensitivity to chemical connectivity and bonding, intermolecular contacts, and other angstrom-scale changes in structure—the molecular properties and events that drive chemistry. Simultaneously, SM detection accesses the individual characteristics of molecules that would otherwise be lost in the ensemble average for heterogeneous systems. From a time-dependent perspective, SM observation can reveal the trajectory of a molecular observable as it freely explores its configurational space. Provided sufficient time-resolution and sampling, such trajectory measurements represent the purest form of studying kinetics and dynamics in that the residence times within, transitions between, and overall history of states visited are directly accessible. While this combination of capabilities offers enormous potential, SM vibrational detection presents unique technical challenges that compound the difficulty of experiments and continues to be developed in many different forms.

The primary difficulties associated with the optical detection of molecular vibrations are their small cross sections and fast non-radiative relaxation. Currently, the most prevalent approaches employ near-field optical effects to both amplify the light–matter interaction and reduce the observation volume to the point where SM detection is possible. The most important examples are surface-enhanced Raman spectroscopy (SERS) and tip-enhanced Raman spectroscopy (TERS), which achieve near-field signal enhancement through nanometer proximity or direct adsorption to a metallic nanostructure and have been used extensively for SM spectroscopy for over two decades.^1–5 Infrared (IR) techniques based on scattering-type scanning near-field optical microscopy (IR s-SNOM), atomic force microscopy (AFM-IR), and other near-field schemes can isolate signals from small ensembles of oscillators at nanometer length scales^6,7 and are being developed toward SM detection with some recent success.⁸ Non-optical methods based on scanning tunneling microscopy (STM) have also been used to probe the vibrations of individual molecules and similarly rely on sub-nanometer localization with a metallic probe.⁹ However, the necessity for contact with a surface, nanostructure, or probe imposes severe restrictions on the types of samples that can be studied with these methods. Critically, molecular systems in solution or other condensed-phase environments where these requirements are too perturbative remain out of reach.

An alternative approach that circumvents the optical near-field is to couple the ground-state vibrational spectroscopy to a fluorescence read-out signal that can be detected at the SM level using the by now well-developed far-field microscopy methods of SM fluorescence spectroscopy. This idea long predates SM spectroscopy and was explored in the work of Laubereau, Seilmeier, and Kaiser, who introduced a double-resonance method employing a picosecond IR pulse followed by a picosecond UV/vis pulse to resonantly excite vibrations and then selectively bring those molecules to their fluorescent electronic excited state.^10–13 Critical to this approach is the use of pulses that are of similar duration or shorter than the typically picosecond vibrational lifetimes. A similar double-resonance approach using stimulated Raman excitation instead of IR absorption was proposed by Wright¹⁴ and later explored theoretically by Orrit and co-workers as a potential technique for SM vibrational detection.¹⁵ Min and co-workers successfully established this double-resonance Raman method—stimulated Raman excited fluorescence (SREF) spectroscopy—demonstrating SM vibrational detection operating entirely in the far-field.^16,17 Our group has built upon the original IR-pumped method—fluorescence-encoded IR (FEIR) spectroscopy—employing femtosecond pulses to perform ultrafast Fourier transform spectroscopy,^18–20 and recently showed that SM sensitivity can be achieved in solution.²¹ 

While our initial demonstration of SM sensitivity is encouraging, developing FEIR spectroscopy as a generally useful method will require a more thorough understanding of the optical and molecular factors involved in SM FEIR detection. Specifically, what makes a molecule a good FEIR chromophore, and given such a molecule, how is FEIR detection optimized? The first question can be initially addressed by considering the minimum requirements of a good, i.e., SM capable, FEIR chromophore from a heuristic standpoint: high fluorescence brightness, strong IR activity of the target vibration(s), and strong vibronic coupling of this target vibration to the electronic transition, e.g., Franck–Condon activity. Next, the double-resonance condition must be met: the IR frequency ω_IR is tuned to cover the vibrational transition, while the visible frequency ω_vis should “make up the difference” to bring the molecule to the electronic excited state, i.e.,

where ω_eg is the electronic transition frequency. Practically speaking, this relation suggests that the visible pulse should be pre-resonant with the electronic absorption band by an amount commensurate with the target vibrational frequency. However, given the typically broad electronic line shape in room-temperature solution with its interplay of intramolecular vibrational and solvation contributions, it is not a priori clear where this optimal resonance is located or even to what extent the equilibrium absorption line shape is a useful or predictive guide. Furthermore, direct excitation by the visible pulse produces an undesirable fluorescence background that degrades detection contrast and, therefore, must also be considered in the optimization of the resonance condition.

Motivated by these questions, in this paper we investigate the practical experimental factors that govern FEIR signal strength and detection quality with the objective of elucidating the requirements for achieving SM sensitivity. We introduce an experimental FEIR brightness metric that accounts for instrumental parameters to isolate the intrinsic molecular factors that control signal size and thereby facilitates a comparison between different chromophores. We will focus on the particular role of the resonance condition in optimizing FEIR brightness and the signal-to-noise ratio. Perhaps the most direct experiment to capture the effect of electronic resonance would be to excite a single vibration at fixed ω_IR while tuning ω_vis. However, our current instrument is limited to a fixed ω_vis, so here, we adopt the strategy of performing measurements across a series of dyes whose electronic spectra span a range of different frequencies. Motivated by our demonstration of SM sensitivity for coumarin 6 (C6) in acetonitrile-d3, we use a set of structurally similar coumarin dyes in the same solvent in order to keep the vibrational and vibronic aspects of the chromophores as similar as possible. Clearly, these vibration-specific factors are crucial for sensitive FEIR detection, and we will address mode-specific considerations, including normal mode character and molecular symmetry, with the aid of more detailed theory and electronic structure calculations in a subsequent publication.

Questions of signal strength, detection sensitivity, and “goodness” of chromophore are also fundamentally coupled to the spectroscopic information content of an experiment. As a nonlinear ultrafast technique, FEIR spectroscopy can be used to access information beyond linear vibrational spectra, including relaxation dynamics, relative orientation of the vibrational and electronic transition dipoles, and inter-mode coherence and dephasing. However, our analysis here is concerned with experimental photon count rates and the signal-to-noise ratio at a practical level. We find that the electronic absorption spectrum can predict the dependence of FEIR brightness on the resonance condition to a reasonable degree across the full frequency range considered. For bulk measurements, the signal-to-noise ratio is limited by background fluorescence from direct visible excitation, and therefore, detuning from resonance to decrease the overlap of ω_vis with the tail of the electronic band is often desirable. However, at SM equivalent concentrations, background is mostly of non-molecular origin and maximal resonance should be employed. We observe saturation of the vibronic encoding transition by the visible pulse, which ultimately limits the upper range of molecular emission rates that can be achieved.

Ten commercially available 7-aminocoumarin dyes were obtained from Sigma (C30 and C153), TCI America (C314, C337, C334, and C7), Acros Organics (C343 and C6), and Exciton-Luxottica (C525 and C545) and used as received. For each coumarin dye, Fourier transform IR (FTIR) absorption measurements were performed in 1–5 mM acetonitrile-d3 solution at 100–500 μm path length using a Bruker Tensor 27 FTIR spectrometer at 2 cm⁻¹ resolution. Each FTIR spectrum was solvent-subtracted and converted to molar extinction units by dividing the measured absorbance by concentration and path length.

UV/vis absorption was performed with an Agilent Technologies Cary 5000 spectrophotometer using a 4 nm excitation bandwidth with 0.5 nm steps. Dye solutions in acetonitrile at 40 μM were measured in a 1 cm path length quartz cuvette, resulting in maximum absorbances <2, which was determined to be within the linear range of the spectrometer. Each spectrum was corrected by an independently measured solvent blank and converted to molar extinction units. An exponential fit to the low-frequency absorption wing was used to extract the extinction value at ω_vis for all coumarins but C545 (see Fig. S1 of the supplementary material).

Fluorescence spectra were measured with a Horiba Flouorlog-3 fluorimeter using right-angle collection from 1 cm path length quartz cuvettes. The concentration was adjusted (typically <2 μM) to keep the maximum absorbance below 0.1 to avoid inner filter artifacts. Excitation-emission surfaces were measured with 3 nm slit widths for both excitation and emission monochromators. The excitation spectra acquired by integrating over the emission axis were found to match the line shape of the UV/vis absorption, and fluorescence emission spectra were acquired by integrating over the excitation axis. Fluorescence quantum yields were measured relative to coumarin 153 in ethanol (ϕ = 0.53) as a standard using the procedure outlined in Ref. 22, and we estimate uncertainties of ∼10% for these values. All solutions were air-saturated.

FEIR measurements were performed with the experimental apparatus described previously.^20,21 Briefly, 230 fs IR pulses (center frequency ω_IR = 1620, 120 cm⁻¹ fwhm bandwidth) were generated with a home-built optical parametric amplifier (OPA) pumped by a 1 MHz repetition-rate Yb fiber laser (Coherent Monaco).²³ These pulses were sent through a Mach–Zehnder interferometer to create a collinear pulse-pair with controllable delay τ_IR and then focused into the sample from below using a ZnSe aspheric lens of numerical aperture (NA) ∼0.7. The visible encoding pulse [∼330 fs, center frequency ω_vis = 19 360 cm⁻¹ (=516.5 nm), fwhm bandwidth <80 cm⁻¹ (<2 nm)] was generated by frequency doubling the fiber laser fundamental, delayed with respect to the stationary pulse of the IR pulse-pair by τ_enc, and focused into the sample from above, collinear to the IR, with a 0.8 NA air objective. The IR and visible pulses were linearly polarized with parallel orientation in the sample. Fluorescence was collected with the same objective, separated geometrically from the visible excitation beam by a long-pass dichroic, sent through both a ω_vis-band rejection and selective fluorescence bandpass filter, and imaged onto a single-photon counting avalanche photodiode (SPAD) using its 50 μm diameter active area as a confocal aperture to remove out of focus light. Considering the NA and magnification (57×), the radius of this aperture corresponds to 4.2 optical units at ω_vis or equivalently ∼1.1 times the Airy disk radius. While slightly larger than the optimal size for the maximum signal-to-noise ratio in confocal microscopy (2.4–3.3 optical units), this aperture is close to that for producing an optimal signal-to-noise ratio in fluorescence correlation spectroscopy (∼4.5 optical units).^24–26 

Sample solutions (30–100 μM in acetonitrile-d3) were held between a 1 mm thick CaF₂ window (bottom, IR side) and either a 175 μm-thick glass or a 150 μm-thick CaF₂ coverslip (top, visible side), separated by a 50 μm polytetrafluorethylene (PTFE) spacer, and positioned so that the visible confocal volume was ∼20 μm below the coverslip. Detrimental thermal effects due to IR absorption by the conventional glass coverslips limited the upper range of IR power that could be used and reduced signal levels.²⁰ However, switching to the CaF₂ coverslips effectively removed these artifacts, yielding FEIR signals ∼3 times larger. In this work, both types of coverslips were used (glass for the data in Sec. IV C and CaF₂ in Sec. IV D); however, quantitative comparisons are only made among measurements using the same type.

The IR pulse energy at the sample during total constructive interference between the pulse-pair (τ_IR = 0) was kept constant at ∼50 nJ, although variations of ±5% occurred between measurements. Considering the pulse duration and 1/e² focal radius of ∼9 μm, the corresponding peak intensity is ∼160 GW/cm², with a pulse-train average intensity of ∼40 kW/cm². The visible pulse energy was varied between 10 fJ and 100 pJ depending on the concentration and resonance condition for each sample, which considering pulse duration and 0.34 μm 1/e² focal radius corresponds to peak intensities of 0.015–150 GW/cm² or average intensities of 0.005–50 kW/cm². In each case, the visible pulse energy was chosen to keep the total fluorescence count rate from exceeding 200 kHz (20% of the repetition-rate) to prevent pile-up distortions—caused by the arrival of multiple photons at the detector per excitation cycle, only the first of which can be registered—from being too severe (<10% error). The raw count rates were then corrected for pile-up using the relation x_corrected = −r ln(1 − x_raw/r), where r = 994.7 kHz is the exact repetition-rate (details provided in Sec. S2 of the supplementary material).

The total photon count rate F_tot (Hz) detected in an FEIR measurement consists of the following components:

Here, F is the desired FEIR signal, which depends on the pulse delays; F₀ is a constant background fluorescence due to the direct excitation of the target molecule by the visible pulse alone; and B encapsulates all other sources of background not arising from the target molecule, e.g., solvent Raman scattering, emission from impurities and optics, and detector dark counts. For the sake of this analysis, we will consider the IR pulse-pair delay fixed at τ_IR = 0, i.e., two-pulse experiments (one IR and one visible pulse). Previously, we have referred to such experiments as one-pulse²⁰ or one-IR-pulse measurements;²¹ however, here, we modify our terminology to reflect the total number of pulses. The two-pulse amplitude F(τ_enc) reflects the integrated response of all vibrations within the bandwidth of the IR pulse spectrum. The fractional contribution to the count rate from a distinct vibrational resonance can, in principle, then be calculated using the FEIR spectrum measured at that encoding delay, although we will not explore this strategy here. We will consider early, positive τ_enc, where F is near its maximum, and suppress the time argument for brevity. In general, successful FEIR detection requires the ability to distinguish the signal F against the background F₀ + B, and therefore, a practical figure of merit is the modulation ratio

i.e., the ratio of useful FEIR photons to all other detected photons. The presence of F₀—a fluorescence signal from the target molecule, yet contributing to the background—is an important aspect of the practical optimization of FEIR detection. As a signal to background ratio, M is a readily apparent feature of the raw data and, consequently, a convenient target for optimization. However, the more fundamental descriptor of detection quality is the signal-to-noise ratio (SNR),

defined here for the shot noise limit as the ratio of the number of FEIR photons accumulated during the integration time T relative to the Poisson noise of the total number of detected photons. Therefore, both the contrast M and the absolute magnitude of the signal F need to be considered to maximize the SNR.

Since the absolute size of an FEIR signal is ultimately governed by the molecular emission rate, we seek to relate experimental count rates to the overall probability of excitation, emission, and detection per molecule. Furthermore, accounting for the instrument-specific factors that influence these probabilities should, in principle, isolate purely molecular metrics that describe the propensity of a given vibration to be detected via FEIR. In conventional fluorescence spectroscopy, such a metric is the fluorescence brightness, which characterizes a fluorophore’s ability to emit a photon in response to optical excitation. From an external spectroscopic standpoint, brightness can be defined as the product of absorption cross section (at the excitation frequency) and fluorescence quantum yield (σ_el × ϕ).^22,27,28 Alternatively, fluorescence brightness has also been defined directly from experimental SM count rates, which can be related to σ_el × ϕ with the knowledge of the excitation beam photon flux and overall detection efficiency.²⁹ This concordance of definitions is made possible by the linear nature of the fluorescence excitation process, which facilitates a straightforward separation of molecular and optical factors.

In contrast, FEIR excitation is a nonlinear process consisting of IR excitation of the vibrational ν = 1 population followed sequentially by a vibronic transition to the excited electronic state (Fig. 1). To a first approximation, these two steps may be considered as the resonant absorption of one photon (IR, then visible), producing a linear dependence separately in the intensity of the IR and visible fields. Importantly, this process is distinct from two-photon absorption, where there is typically no resonant intermediate state and the transition must occur instantaneously, i.e., within the temporal profiles of the pulses. The overall FEIR excitation process competes with picosecond vibrational relaxation, and its efficiency is, therefore, sensitive to aspects of the temporal pulse profiles beyond peak or integrated photon fluxes. Additionally, multimode effects such as the coherent excitation of pairs of vibrational fundamentals within the IR bandwidth further complicate the interplay between molecular and optical factors.¹⁹ These effects can be properly incorporated into a theoretical description of FEIR excitation based on time-domain response functions for the electronic excited population to fourth order in the incident field but are beyond the scope of the current discussion.

Given these theoretical complexities, here, we take a practical route to defining FEIR brightness based on experimental count rates and a simple phenomenological model for how the signal scales with experimental parameters. We assume that the overall probability P_ex that a molecule is electronically excited in response to a pulse sequence follows the bilinear intensity dependence,

where I_IR and I_vis are peak pulse intensities (GW cm⁻²) and a plays the role of an FEIR cross section and is defined by this relation. While neglecting time-dependence and pulse duration effects, this relation is applicable to varying the energy of pulses with fixed time-delays and temporal profiles. The measured count rate is proportional to P_ex; specifically,

where r is the pulse repetition-rate, ⟨N⟩ is the average number of molecules in the probe volume, η is the overall photon detection efficiency, and ϕ is the fluorescence quantum yield.³⁰ We have previously verified this linear I_IR- and I_vis-dependence for bulk samples where P_ex ≪ 1 for any given molecule.²⁰ In analogy to fluorescence brightness, the FEIR brightness in the context of this model is a × ϕ.

Our approach is to extract this value, or a proportional quantity, from the measured count rate by dividing out the experimental and instrument-specific parameters in Eq. (6). Not all of these parameters can be directly measured, although reasonable estimates can be made. For example, the detection efficiency can be approximated as

Here, η_coll is the geometric collection efficiency of the objective lens and optical path coupling the photon onto the detector, which can depend on the specific details of the experimental configuration in complicated ways and is difficult to measure absolutely. The objective’s numerical aperture (NA) is the dominant factor, and for isotropic emission in a homogeneous medium of refractive index n, the objective’s collection efficiency is $sin212sin−1(NA/n)$⁠, which is 10% in our experiments. The frequency integral in Eq. (7) is the overlap of the molecule’s area-normalized fluorescence spectrum s_fl(ω), transmission function of the emission filters’ bandpass T_bp(ω), and detector quantum efficiency η_detector(ω). For our detector, η_detector(ω) is ∼45% and slowly varying over the emission frequencies considered.³¹ The factor that is significantly variable between different molecules is the fraction of the fluorescence spectrum transmitted by the bandpass filters,

which may be calculated directly from steady-state fluorescence and transmission measurements. Overall, using these estimates, η ≈ 0.045 × η_bp, although this is likely only an upper bound due to further unknown factors in η_coll.

Similarly, ⟨N⟩ is difficult to measure in general, but can be represented up to proportionality by the solution concentration C (mol l⁻¹). Previously, we have measured ⟨N⟩ directly from nM solutions of C6 by performing FEIR correlation spectroscopy (FEIR-CS), finding ∼0.65 molecules/nM, or assuming that this relation is scalable to any concentration ⟨N⟩ = 0.65 × 10⁻⁹ C.²¹ However, to ensure we only use parameters that are directly controlled or measured, we define FEIR brightness (mol⁻¹ l GW⁻² cm⁴) as

where the second approximate equality uses the estimates stated above to isolate the fully corrected FEIR brightness in Eq. (6).

The FEIR cross section a reflects the microscopic molecular factors governing the overall excitation process, shown in Fig. 1. While a complete description that includes the effects of vibrational relaxation, pulse durations and spectra, and multimode excitation is best handled by a response function calculation, here, we discuss the relevant quantities from a heuristic standpoint. For a single vibration within the Condon approximation and assuming early encoding delays where vibrational relaxation is negligible,

Here, ω₁₀ and μ₁₀ are the vibrational frequency and transition dipole moment, ω_eg and μ_eg are the pure electronic transition frequency and dipole moment, and ⟨1_g|0_e⟩ is the Franck–Condon factor describing the vibrational-electronic coupling. $Y=⟨[μ̂eg⋅ε̂vis]2[μ̂10⋅ε̂IR]2⟩$ is an orientational factor determined by the projection of the pulse polarization vectors $ε̂IR$ and $ε̂vis$ onto the transition dipole directions $μ̂10$ and $μ̂eg$⁠, averaged over the orientational distribution present in the experiment. Such orientational factors are common to coherent third-order nonlinear techniques, the most directly analogous being 2D-VE spectroscopy;^32,33 however, in terms of overall magnitude, this factor plays a minor role, and we will not discuss its contribution in detail here. The final factor Δ(ω_vis − (ω_eg − ω₁₀)) is a normalized resonance term that accounts for the spectral overlap of the visible pulse with the encoding transition, i.e., the vibronic transition from the ν = 1 state of the vibration being pumped to the excited electronic manifold. Here, we have assumed that the IR pulse is spectrally broad compared to the vibrational transition and tuned to resonance ω_IR ≈ ω₁₀ so that Δ describes the detuning from the resonance condition in Eq. (1). As an effective line shape function for the encoding transition, Δ should, in principle, be influenced by many of the same intramolecular vibrational and solvation coordinates that govern the line shape of the equilibrium electronic transition.

In analogy to Eq. (6), the directly excited fluorescence background F₀ can be written as

where a₀ is the coefficient relating the probability of one-photon electronic excitation to the visible peak pulse intensity. Specifically, a₀ is related to the absorption cross section and visible pulse duration t_vis as a₀ = σ_el(ω_vis)t_vis/ℏω_vis. Higher-order contributions in I_vis, e.g., two-photon absorption, can also become significant in cases when ω_vis is sufficiently off-resonance from the electronic absorption band. We define the direct excitation brightness (mol⁻¹ l GW⁻¹ cm²) as

When linear absorption is the dominant contribution, q₀ ∝ ϕa₀ with the same estimated proportionality factor as Eq. (9) and represents the conventional fluorescence brightness excited at ω_vis. The nonlinearity of the FEIR excitation process spatially localizes signal generation to the product of the IR and visible intensity profiles. However, because the size of the IR focus is at least an order of magnitude larger than the visible, the spatial distribution of FEIR signal generation within the 50 μm-thick solution layer is essentially the same as the one-photon fluorescence background, which precludes the use of more aggressive confocal filtering to selectively suppress F₀.

The sources of background not originating from the target molecule can be numerous and naturally become increasingly prevalent in the low concentration regime of SM experiments. However, these contributions to the non-molecular background B can be decomposed by its excitation power dependence,

The constant d represents the detector dark count rate (∼40 Hz in our experiments), while the term linear in I_vis describes Raman scattering from the solvent and fluorescence from the optics or undesired impurities. In principle, higher-order terms such as multiphoton-excited fluorescence could contribute but do not appear to be important under our experimental conditions. We have not observed any background signal due to excitation with the IR pulse alone.

The series of 10 coumarin dyes used in this study is shown in Fig. 2(a). Our naming convention follows the Kodak catalog, with the exception of C525 and C545, which are Exciton catalog names.³⁴ The electronic spectroscopy of the S₀ → S₁ transition is influenced by the charge-transfer character of the S₁ excited state, which is modulated by the electron-donating and electron-withdrawing abilities of the amino group (shown in blue) and substituent on the lactone ring (shown in red), respectively.^35–37 The variation of the electron-withdrawing group and degree of alkylation of the amino group consequently tunes the absorption and fluorescence spectra [Figs. 2(b) and 2(c), respectively] across a frequency range of ∼3000 cm⁻¹. We illustrate the resulting span of FEIR excitation resonance conditions by overlaying the visible pulse spectrum and convolution of visible and IR pulse spectra on the absorption bands in Fig. 2(b) (spectral distributions shown in gray, with respective center frequencies ω_vis and ω_IR + ω_vis denoted by dashed lines). The IR/visible spectral convolution, formally the distribution of all IR + visible frequency sums accessible between their bandwidths, nominally indicates the breadth of double resonance around ω_IR + ω_vis that can be supported by the pulse spectra and has a fwhm of ∼140 cm⁻¹. Notably, both this distribution and the visible pulse spectrum are narrowband with respect to the coumarins’ electronic absorption line shapes. Figure 2(d) shows ω_vis and ω_IR + ω_vis against various metrics characterizing the electronic absorption frequency (see also Table I): ω_mean, first moment of the band, ω_max, frequency of the band maximum, ω_1/2, frequency of the half-way point up the low-frequency edge, and ω_0–0, an approximation of the 0–0 transition frequency given by the crossing point of the normalized absorption and fluorescence line shapes. The coumarins have been ordered by decreasing ω_1/2 values. For C30, the most blue-shifted coumarin under consideration ω_IR + ω_vis falls ∼1500 cm⁻¹ below ω_0–0, while the three reddest—C6, C525, and C545—have ω_IR + ω_vis > ω_0–0, notably with ω_IR + ω_vis ≈ ω_max for C545.

While each of these electronic frequency metrics is influenced to some degree by the band’s shape, they nevertheless cannot adequately account for the breadth of the line shape. As a potentially more direct characterization of FEIR resonance, we will investigate ɛ_el(ω_IR + ω_vis)—the value of the extinction coefficient at the double-resonance frequency. Figure 2(e) shows the same absorption spectra on a logarithmic y axis to better show the extent of the low-frequency edge, with ω_IR + ω_vis and ω_vis indicated by dashed lines. From the bluest to reddest coumarins in the series, ɛ_el(ω_IR + ω_vis) spans nearly 3 orders of magnitude. In principle, this metric describes both detuning, through position on the line shape, and electronic transition strength, through the extinction magnitude. Maximum extinction values, as well as oscillator strengths calculated from the molar decadic extinction spectra via the numerical relation f = 4.32 × 10⁻⁹∫ɛ(ω)dω with ω expressed in cm⁻¹,^38,39 are listed in Table I and vary by a factor of ∼3 across the series. In the context of the heuristic expression for FEIR cross section in Eq. (10), ɛ_el(ω_IR + ω_vis) should supply information on |μ_eg|² by proportionality with f, while we would also expect similarities with the ω_vis-dependence of the encoding line shape function Δ in the presence of shared line-broadening mechanisms.

Linear absorption of the visible pulse is controlled by ɛ(ω_vis), which also varies dramatically by over 3 orders of magnitude across the coumarin series. Below a few percent of the band maxima, the low-frequency absorption tails exhibit an exponential frequency dependence, apparent as linear slopes in the logarithmic scaling of Fig. 2(e) (exponential fits shown in Figs. S1 and S2 of the supplementary material). This so-called “Urbach tail” is a well-known feature in the band-edge spectra of solid-state materials,^40,41 but is also frequently observed for organic molecules in solution, often with a 1/k_BT-dependent decay constant.^42–45 For molecules, this exponential tail and characteristic temperature dependence have been interpreted as the cumulative effect of hot-band transitions originating from the sparsely thermally occupied excited levels of Franck–Condon active vibrations on the ground state. For all the coumarins, with the possible exception of C545, ω_vis falls within this Urbach region.

The fluorescence quantum yield ϕ and fractional spectral bandpass η_bp are listed in Table I. The optimal location of the instrument’s emission bandpass depends on the interplay between the fluorophore’s Stokes shift, fluorescence line shape, and the pre-resonant shift on the order of ω_IR ≈ ω₁₀ required for FEIR resonance [i.e., Eq. (1)]. A detection band on the Stokes side of ω_vis can, in general, only access a smaller portion of the emission spectrum than in a conventional one-photon resonant fluorescence excitation scheme due to this pre-resonant shift. For fluorophores with small Stokes shifts, placing the detection band on the anti-Stokes side of ω_vis could, in principle, allow for larger η_bp, with the added benefit of contending with the weaker anti-Stokes solvent Raman background. In this work, we use a Stokes-side bandpass [Fig. 2(c)] that relies on the relatively large Stokes shifts of the coumarin dyes (Table I), which for the most part greatly exceed ω₁₀ for the vibrations under consideration. The decrease in η_bp from ∼0.4 to ∼0.1 when moving red to blue across the coumarin series is a consequence of the increasingly off-resonant FEIR excitation with Stokes-side detection. C153 is notable by its large ∼5000 cm⁻¹ Stokes shift, which results in the second-highest η_bp in the series despite its position in the blue side of the series.

FTIR spectra of the coumarin series are shown in Fig. 3. The IR pulse spectrum used in each FEIR measurement is superimposed to indicate the vibrations being excited. The pulse is broadband with respect to the vibrational linewidths and spans multiple modes in each case. Below 1650 cm⁻¹ in the spectral range shown are C=C ring vibrations localized predominantly on the coumarin core, while the lactone carbonyl stretching band appears above 1700 cm⁻¹. In many cases, this carbonyl band shows a considerable structure (e.g., the splitting especially prominent for C153 and C525), which is likely due to a Fermi resonance.^46,47 C334, C314, and C343 contain another carbonyl group in the electron-withdrawing substituent, which appears between 1650 and 1700 cm⁻¹. The center of the IR pulse spectrum ω_IR = 1620 cm⁻¹ was chosen to maximize the coverage of the highest frequency ring modes, which have similar character across the coumarin series and, as shown below, are typically the most strongly FEIR active. In contrast to the large variation in electronic resonance created by the range of absorption frequencies, here, the collection of vibrational modes being pumped are fairly similar in frequency and extinction. Nevertheless, the vibrational transition strength is a critical factor for FEIR brightness via Eq. (10), and any differences in IR-vibrational cross section should be reflected in the strength of the signal. To characterize these differences given the spectrally broad excitation, we compute the overlap,

where ɛ_vib(ω) is the vibrational extinction spectrum and S_IR(ω) is the normalized IR spectral intensity profile. As shown in Fig. S10 of the supplementary material, ɛ_IR only varies by a factor of ∼2 across the series.

Bulk FEIR measurements on three representative coumarins are shown in Fig. 4 (complete series shown in Fig. S5 of the supplementary material). High concentrations (30–100 μM) were used to keep the non-molecular background B negligibly small compared to the coumarin fluorescence. Panels (a)–(c) of Fig. 4 show the total detected photon rate F_tot from two-pulse measurements in brightness units, that is, divided by rCη_bpI_vis. Instead of additionally dividing the FEIR component F by I_IR to recover q as in Eq. (9), it will be convenient for our analysis to work with an effective FEIR brightness where the IR intensity dependence has not been removed,

which has the same units as q₀, facilitating a direct comparison of their respective magnitudes. Furthermore, because I_IR is held constant in this study, q_IR can still be compared between measurements on different molecules, and we will also refer to this quantity as the FEIR brightness unless further distinction is required. As B is negligible, q₀ is given by the constant offset (blue arrows) for τ_enc < 0 where F = 0 by causality.

F reaches a maximum at early τ_enc before decaying away on a picosecond timescale due to vibrational relaxation processes (see Sec. S3 of the supplementary material for a note on the assignment of τ_enc = 0). However, the details of the τ_enc-dependence near the maximum, notably the peak position, vary for the different coumarins. As F(τ_enc) measures the integrated response of the multiple vibrations within the IR bandwidth, some aspects of these differences reflect the variation in frequency spread, vibronic activity, and relaxation kinetics of the modes being sampled. To show which vibrations are contributing to the response in each case, Figs. 4(d)–4(f) show the corresponding FEIR spectra at selected early encoding delays superimposed on the IR pump-scaled FTIR spectra. In all cases, the high frequency ring modes between 1570 and 1620 cm⁻¹ have the largest contribution to the F amplitude. Multimode coherence produces the strongly damped oscillatory behavior present in some two-pulse transients, which to some extent also plays a role in the location of the signal maximum. However, in the vicinity of τ_enc = 0, the signal may also contain pulse-overlap artifacts, for example contributions from improperly ordered interactions of the IR and visible fields or vibrationally nonresonant IR + visible two-photon absorption. We note that even in these cases, the signal amplitude is still determined by the molecular response—one of the benefits of fluorescence detection that precludes non-resonant pulse-overlap contributions from the solvent or windows. Nevertheless, to avoid these potential complications, we will use the average value of F(τ_enc) between 400 and 800 fs[gray region in Figs. 4(a)–4(c) with the red arrow indicating the average] to define q_IR for our analysis. While this window safely avoids the pulse-overlap region, in many cases the excited vibrational population has already undergone partial relaxation, which may result in artificially lower measured FEIR brightness (Sec. S5 of the supplementary material compares these FEIR brightnesses with those using the maximum F values).

The coumarins in Fig. 4 were chosen to represent the full range of FEIR resonance conditions across the series: C314 being one of the bluest, C7 being one of the intermediate, and C545 being the reddest. As evident from the y axis scales of Figs. 4(a)–4(c), the brightness of the overall fluorescence (F + F₀) increases dramatically for the redder coumarins. However, for C545, the direct excitation background has become larger than the FEIR signal. This reduction in contrast is evident in a much smaller modulation ratio of M = 0.35 for C545, compared to M = 35 for C7 and M = 6.8 for C314.

In Fig. 5, we investigate how brightness and contrast are explicitly influenced by the FEIR resonance condition discussed in Sec. IV A. To normalize out variations in emission probability, we divide the FEIR and direct excitation brightnesses by quantum yield ϕ. The resulting quantities q_IR/ϕ and q₀/ϕ are proportional to aI_IR and a₀, respectively, with the same proportionality constant. The quantity aI_IR may be interpreted as the effective cross section seen by the visible pulse after vibrational excitation of the molecule with the IR pulse in our instrument. Figure 5(a) shows that these proxies for the FEIR and direct excitation cross sections are linearly related to the electronic extinction coefficient evaluated at ω_IR + ω_vis and ω_vis, respectively, over several orders of magnitude. Logarithmic scaling is used to conveniently represent the multiple decades in each axis (same data on linear axes are shown in Fig. S8 of the supplementary material).

The strong linear relationship between ɛ_el(ω_vis) and q₀/ϕ indicates that linear absorption of the visible pulse is the primary contributor to the direct excitation background F₀ across the range of resonance conditions studied here, and we will consequently, also refer to F₀ as the one-photon background. However, we note that for the bluest coumarins C30 and C314, the I_vis-dependence of F₀ becomes super-linear beyond the intensities used in Fig. 5 (see Fig. S16 of the supplementary material), implying a crossover to two-photon absorption being the dominant source of F₀ background for these deeply pre-resonant excitation conditions where ɛ_el(ω_vis) is exceptionally small.

On the other hand, the linear relationship between ɛ_el(ω_IR + ω_vis) and q_IR/ϕ (and by proportionality a), though more diffuse, is a more striking and a priori less obvious result. Taken exactly, a perfect linear relationship would indicate that the effective line shape function of the encoding transition is simply given by the equilibrium absorption line shape red-shifted by the vibrational frequency, i.e.,

where g_el(ω) is the normalized electronic line shape function. While intuitive and in line with the heuristic double-resonance picture evoked by Eq. (1), this association cannot be formally exact, as, in general, both the initial and final states involved in the encoding transition are different from the bare electronic transition. The equilibrium line shape g_el(ω) is composed of multiple vibronic transitions involving the Franck–Condon active intramolecular coumarin vibrations—including, but importantly not limited to, the vibrations being interrogated by FEIR—as well as being broadened by overdamped solvation coordinates. While the vibronic contribution to Δ(ω) from the mode being pumped is certainly different because the initial state is ν = 1 rather than ν = 0, it is reasonable to expect a similar contribution from the solvent, as, from the solvent’s perspective, vibrational excitation on the ground state is a small perturbation compared with electronic excitation. As the FEIR resonance conditions explored here probe the red-side of the transition where the breadth of the line shape is likely dominated by the solvent contribution, Eq. (16) could, therefore, be a reasonable approximation. For coumarins on the blue side of the series, ɛ_el(ω_IR + ω_vis) falls within the Urbach region of the line shape, and it is possible that initial thermal population of low-frequency modes is important. A similar correspondence between signal size and resonance condition for ω_vis < ω_0–0 − ω_IR was found in some of the original experiments of Kaiser and co-workers, although the vibrations being pumped were likely combination bands.⁴² From a computational perspective, Δ(ω) is related to the line shape of the vibrationally pre-excited absorption spectrum introduced by Burghardt and coworkers to model the closely related excitation process in vibrationally promoted electronic resonance (VIPER) spectroscopy.^48,49 Although their approach only investigated the effect of the intramolecular modes and did not treat broadening from the solvation environment explicitly, their results typically show a peak red-shifted from the 0–0 transition by roughly ω₁₀ primarily due to the pre-excited mode’s 1–0 vibronic transition. These computational results support the frequency shift in Eq. (16) and the simplified energy-level diagram in Fig. 1.

The scatter in the ɛ_el(ω_IR + ω_vis) vs q_IR/ϕ trend is likely influenced by variations in the other terms in Eq. (10), i.e., the vibrational transition dipoles, Franck–Condon overlaps, and orientational factors. In fact, given that these factors are not accounted for, it is perhaps somewhat remarkable that a linear regression of this quality is even observed. This may be explained in the following ways. First, as the a values here reflect the collective response of multiple vibrations, the differences in these unaccounted factors are potentially smoothed out between dyes, thereby isolating the electronic resonance dependence for an “average” coumarin. Second, the structural similarity between the dyes likely precludes very large variations in these factors for the dominant core ring modes, while in contrast, ɛ_el(ω_IR + ω_vis) varies by almost 3 orders of magnitude. As mentioned in Sec. IV B, one way to account for the vibrational transition strength is by the factor ɛ_IR [Eq. (14)]. However, using ɛ_IR · ɛ_el(ω_IR + ω_vis) as the x values does not substantially improve the linear relationship (Fig. S10 of the supplementary material), perhaps because the remaining factors play the dominant role. Uncontrolled differences in the instrument’s alignment and errors in experimental parameters between measurements also contribute to uncertainty in the measured brightness values. We characterized day-to-day differences in q_IR and q₀ for C6 and found a coefficient of variation (standard deviation over mean) of 12% and 10%, respectively (Sec. S4 of the supplementary material). We expect this experimental uncertainty to be representative across the coumarin series, and it is smaller than the size of the data markers in Fig. 5(a). Therefore, we believe that this scatter is predominantly reflective of differences in the vibrational mode-specific factors, of which the vibronic coupling is likely the most important.

Figure 5(b) shows the corresponding modulation ratios M [Eq. (3)] from the FEIR measurements in Fig. 5(a). As B is negligible, M can be written as

which is manifested graphically as the signed distance (in log units) between respective y values in Fig. 5(a), (indicated for C314). The vertical error bar for C6 shows two standard deviations for the experimental uncertainty stated above. The M values are plotted against the extinction coefficient ratios,

thereby effectively combining both trends in Fig. 5(a). The relationship between these quantities describes the extent to which the equilibrium absorption line shape alone can predict the contrast in an FEIR experiment for given IR intensity. The resulting correlation is quite diffuse (Pearson correlation coefficient r = 0.49) primarily because the scatter in the q_IR/ϕ vs ɛ_el(ω_IR + ω_vis) trend caused by the unaddressed vibrational and vibronic factors is magnified. Additionally, noise on the small ɛ_el(ω_vis) values for the bluer coumarins likely amplifies the uncertainty in their κ values, although we do not estimate the corresponding error bars. While M is correlated with κ, the relationship is not sufficiently good to be widely predictive in a quantitative sense, most likely due to the importance of the vibrational mode-specific factors.

However, some general observations about how the contrast depends on the relationship between ɛ_el(ω), ω_vis, and ω₁₀ can still be made. The order of magnitude smaller M value for C545 compared to the rest of the series is clearly due to the large one-photon background produced by ω_vis falling substantially higher on the absorption band tail (ω_vis at ∼6% of the band maximum). Even though C545 has the highest FEIR brightness in the series—which assuming that Eq. (16) holds corresponds to fully maximized FEIR resonance—in practice, measurements on this molecule suffer from a lower signal-to-noise ratio caused by the large shot noise introduced by F₀, requiring longer averaging times (Fig. S5 and S6 of the supplementary material). Evidently, for the frequencies of vibration under consideration, the electronic absorption edge is not sufficiently steep (quantified, e.g., by Δω_edge in Table I and Figs. S1 and S2 of the supplementary material) to allow for maximal FEIR resonance without excessive one-photon background. How much direct band overlap, i.e., ɛ_el(ω_vis)/ɛ_el(ω_max), can be tolerated in practice depends on how much slower a grows with ɛ_el(ω_IR + ω_vis) than a₀ grows with ɛ_el(ω_vis). This comparison may be quantified by the trend line slope ratio α/β = 2.0% [dashed line in Fig. 5(b)]. Because the detuning dependence is accounted for, this value describes on average the relative efficiency of FEIR excitation vs direct one-photon excitation for a prototypical coumarin dye with the IR pulses of our instrument. Specifically, this value suggests that FEIR vibrational detection at maximal resonance is overall ∼50 times less efficient in these experiments than conventional fluorescence detection at maximal resonance. In terms of contrast, this implies that κ should be at least greater than ∼50 to achieve M > 1.

Even if the absorption edge is too broad to support maximal FEIR resonance with low one-photon background, detuning slightly could produce a workable compromise. For example, C6 has a similarly steep absorption edge as C545, but is detuned from maximal FEIR resonance by ∼900 cm⁻¹, putting ω_IR + ω_vis and ω_vis at 63% and 0.19% of the band maximum, respectively (κ = 340). The resulting FEIR cross section is ∼0.7 times the size of that for C545, but with a ∼40-fold decrease in one-photon background, leading to an excellent signal to background of M ∼ 10.

The analysis in Sec. IV C made use of high concentration measurements where essentially all of the detected light is dye fluorescence. As a per-molecule quantity, the construct of FEIR brightness is transferable to SM investigation, as is the brightness of the direct excitation background. However, in the low concentration regime where SM experiments operate, sources of background independent of the target molecule, i.e., B, will usually play the dominant role in influencing the contrast and signal-to-noise ratio. To investigate the impact of B and how the practical considerations for the contrast and signal-to-noise ratio differ in the SM limit, we perform concentration-dependent measurements for two members of the coumarin series: C6 and C7. These molecules have similar FEIR spectra that are dominated by a single ring mode just below 1600 cm⁻¹ and likewise show similarly shaped two-pulse transients (Fig. S5 of the supplementary material). C6 was previously used to demonstrate SM sensitivity in Ref. 21 and produces the second-brightest FEIR signal in the series. With the fixed resonance conditions of our instrument, C7 is $∼1/3$ as FEIR bright as C6, but displays an approximately threefold higher B-free modulation ratio. As such, at high concentrations where I_vis can be varied to set the total fluorescence output at will, C7 is technically the better FEIR chromophore in terms of detection quality, although M is sufficiently high for both to be excellent. As mentioned in Sec. II B, the CaF₂ coverslips employed for the measurements in this section allowed for an approximately threefold increase in FEIR brightness relative to the experiments in Sec. IV C and Ref. 21, while maintaining a similar background size (cf. high concentration M values in Figs. 5 and 6).

Figure 6(a) shows the concentration dependence of the FEIR signal size F/I_vis and background (F₀ + B)/I_vis from 100 μM to 1 nM for both molecules (complete FEIR data are provided in Sec. S6 of the supplementary material). In this representation, the effect of increasing I_vis to achieve reasonable count rates as C is lowered is normalized out to isolate the C-dependence across 5 orders of magnitude. For both dyes, the FEIR component decreases roughly linearly with C. The lowest concentration points fall slightly below a linear dependence, which may be due to a saturation effect as discussed below, or could be caused by systematic error in the concentration from the serial dilution procedure. On the other hand, the background is linear in C at high concentrations, but in the low-C limit approaches a C-independent value, which is the same for both coumarins: ∼15 Hz GW⁻¹ cm², which can be assigned as the b coefficient in Eq. (13). This reflects the change from the background being dominated by F₀ at high C to being almost entirely composed of B in the nM range. As shown in Ref. 21, the distribution of photon arrival times for measurements in the nM range is dominated by a prompt component absent at high C, which suggests that solvent Raman scattering is likely the major contributor to B. As shown in that work, time-gating photon detection to exclude this prompt component can, therefore, increase M and the SNR; however, we will not discuss this approach further here.

The C-dependence of the corresponding modulation ratios is shown in Fig. 6(b). At high concentrations, M is C-independent because F₀ ≫ B [i.e., Eq. (17) holds] and the empirical contrast guidelines discussed in Sec. IV C apply. However, below a certain concentration, M begins to fall as the dye’s fluorescence must compete with the C-independent B background, and at SM equivalent concentrations (∼1 nM; see below), M is 1–3 orders of magnitude lower than its high-C limit. The threshold concentration below which M decreases is notably lower for C6 than C7 and results in a crossing of their M vs C curves at ∼100 nM. As a result, C6 is distinctly the better SM FEIR chromophore under these resonance conditions, although C7 can still be detected at SM equivalent concentrations due to the approximately threefold increase in the FEIR signal facilitated by the updated sample configuration. This difference in bulk vs SM signal to background reflects a crossover from prioritizing a large F vs F₀ contrast to prioritizing the brightness of overall fluorescence F + F₀ against B. As long as the high-C limit of the modulation ratio is sufficiently large, say M > 1, we can define a limiting concentration C_lim where the F and B rates are predicted to be equal based on FEIR brightness, and below which FEIR detection becomes increasingly impractical,

The potential for SM detectability of an FEIR chromophore can then be simply assessed from a high concentration measurement by how close the calculated C_lim is to the SM equivalent concentration (Fig. S14 of the supplementary material). For example, we predict that C525 and C545 would also be possible SM FEIR candidates under the current resonance conditions, as at high-C, we expect an increase to M ∼ 1 for C545 with the new sample configuration.

In the range where F, F₀, and B each grows linearly with visible intensity, the signal-to-noise ratio of a measurement may be improved by increasing I_vis, while M remains constant, e.g., Eq. (4) predicts improvement by $∼Ivis$⁠. In practice, however, saturation effects in the encoding transition set a limit on how large I_vis can usefully be made while still increasing the SNR. Figure 7 shows the I_vis-dependence of the FEIR signal size, here represented as F/C, for C6 and C7. Data from the entire concentration range in Fig. 6 have been used in order to access both very low and high I_vis while keeping F_tot within the linear range of photon counting, and dividing F by C collapses the points onto a common saturation curve for each coumarin (log-scale plot in Fig. S15 of the supplementary material). Figure 6 uses the lowest I_vis point for each concentration, which at the lowest concentrations, nevertheless, lies near the onset of saturation, which may partially explain the deviation from a linear F/I_vis vs C relationship in Fig. 6(a) mentioned above.

In general, the intensity-dependent form of saturation is influenced by the temporal characteristics of excitation. For a two-level system with cw pumping, the steady-state upper level population, and hence the emission rate, saturates with the hyperbolic form

where the saturation intensity is I_S = ℏω_vis/(2στ_fl), τ_fl is the fluorescence lifetime, and σ is the absorption cross section.⁵⁰ However, for pulsed excitation where the pulse duration t_vis is much shorter than τ_fl while the repetition period τ_rep is simultaneously much longer than τ_fl, the excited population immediately after each pulse is

where I_S = ℏω_vis/(2σt_vis).^51,52 The lower level population fully recovers before the next pulse arrives, and the average fluorescence output is, therefore, proportional to p_max. Our experiments operate in this short pulse limit (t_vis ≈ 300 fs, τ_fl ≈ 1 ns, τ_rep ≈ 1 µs), and fits to the measured saturation curves using this exponential model are shown in Fig. 7 with fit parameters listed in Table II. In line with their relative FEIR brightnesses, F saturates at ∼3 times higher count rates for C6 than C7. However, the threshold intensities I_S extracted from the fits are the same within error, which is surprising, given that I_S should be inversely proportional to the cross section of the transition and aI_IR is ∼3 times smaller for C7 compared to C6. Other photophysical mechanisms that sequester population, such as intersystem crossing to triplet states, could also be playing a role in the saturation threshold.⁵³ Perhaps more importantly, treating the initial and final states of the encoding transition as a simple two-level system is likely not a reasonable assumption to describe the observed saturation behavior. So far, we have not observed a similar saturation behavior in I_IR, although a more careful investigation is needed.

The background continues to grow roughly linearly in I_vis over the same range of intensities (Fig. S15 of the supplementary material). Therefore, the contrast degrades as I_vis is increased into the saturating regime, leading to an eventual decrease in SNR. We find that a practical compromise is to operate near the saturation threshold I_S. Regardless of the mechanism, saturation leads to an increase in the effective size of the visible probe volume because the spatial distribution of excitation efficiency flattens out near the center of the focus but continues to increase in the wings.⁵⁴ At a given concentration, the average number of molecules ⟨N⟩ in the probe volume, therefore, increases with I_vis, and determination of ⟨N⟩ by FEIR-CS is intensity-dependent. We measure ⟨N⟩ = 0.7 for 1 nM C6 via FEIR-CS at the saturation threshold I_vis = 42 GW cm⁻², which from the two-pulse transient at the same intensity yields an F count rate per molecule of 480 Hz (see Figs. S17 and S11 of the supplementary material, respectively). While FEIR-CS was not performed on the 1 nM C7 solution, assuming equivalent ⟨N⟩ at the same I_vis gives a lower count rate per molecule of 150 Hz and the signal-to-noise ratio of the two-pulse signal is also correspondingly lower (cf. Figs. S11 and S12 of the supplementary material). To facilitate a comparison with existing SM optical methods, it is useful to estimate the overall excitation probability P_ex. Considering our estimate for the total detection efficiency of fluorescence from C6 (η ≈ 1.3%), its quantum yield (ϕ = 0.89), and the repetition-rate (994.7 kHz), this measured count rate per molecule corresponds to P_ex ≈ 4.2%. If this is, indeed, at the saturation threshold for the encoding transition [i.e., at (1 − 1/e) of the saturated transition probability of 50%], this P_ex value implies a 13% IR-vibrational excitation probability. In this case, we would expect that meaningful improvements to the overall excitation efficiency can still be made with larger IR fields.

In this work, we have examined some of the practical spectroscopic aspects of optimizing an FEIR experiment for bulk and SM vibrational detection. For a given molecule and vibration, the FEIR resonance condition is the most important aspect of experimental optimization. As ω_IR must always be tuned to cover the vibrational transition, this resonance condition amounts to a selection of ω_vis that efficiently brings the vibrationally excited molecule to the electronic excited state. Our experimental results indicate that the electronic absorption spectrum is a useful guide for this selection and, specifically, that the brightness of the FEIR signal scales linearly with ɛ_el(ω_IR + ω_vis) on the low-frequency side of the band. However, optimizing the resonance condition is also constrained by the background fluorescence from direct visible excitation, which for all but the most deeply pre-resonant cases is caused by linear absorption and, hence, is proportional to ɛ_el(ω_vis). For bulk measurements, keeping this fluorescence background small compared to the FEIR signal is the primary consideration for high signal-to-noise data acquisition. To this end, depending on the shape of the electronic absorption edge and particularly the fall-off of its red wing, bulk FEIR detection can be improved by detuning the resonance condition. In the SM regime, however, background is dominated by sources independent of the target molecule and signal photons are scarce, so the resonance condition should be adjusted to increase the absolute brightness of the FEIR signal at the expense of more one-photon background. Saturation of the encoding transition in the visible intensity limits the maximum photon count rates that can be achieved, although further improvements to the IR-vibrational excitation efficiency are likely still available.

Although the experiments presented here utilized a series of dyes with variable electronic spectra against a fixed ω_vis, we have framed the discussion of resonance conditions from the perspective of a tunable ω_vis. Indeed, our results indicate that being able to freely adjust ω_vis to carefully optimize resonance for the chromophore at hand will significantly improve the versatility of FEIR spectroscopy and represents an important technical step toward its application to more general SM vibrational investigation. Additionally, a wide tuning range will facilitate the selection of fluorophores across the entire visible spectrum as potential FEIR candidates. While the equilibrium electronic spectrum can be used to predict the effect of resonance, our results also show that it is alone not sufficient to predict FEIR brightness and that substantial variations occur even for similar-character vibrations of the structurally related coumarin dyes we studied. Therefore, a more detailed understanding of vibrational mode-specific factors will be crucial for predicting which vibrations on different families of fluorophores can be used as FEIR probes. In particular, we are interested in understanding the symmetry and structural properties required for a fluorophore to exhibit FEIR bright vibrations and to what extent various spectroscopically useful probe vibrations, e.g., local carbonyl stretching modes, can be made sufficiently FEIR active to yield SM sensitivity.

The largest SM signal count rates (480 Hz) achieved with our current implementation of FEIR spectroscopy are still low compared to the few to hundreds of kHz rates commonly encountered in modern solution-phase SM fluorescence experiments.^55–58 From the perspective of photon budget, further improvement beyond this level would likely be required to successfully implement SM dynamics measurements based on the direct analysis of signal intensity trajectories. With our current signal levels, however, one route toward accessing kinetic information from real-time SM fluctuations is through correlation spectroscopy (CS) methods analogous to fluorescence correlation spectroscopy and related techniques.^59,60 These methods measure ensemble-averaged kinetic timescales via time-correlation functions of signal fluctuations that arise from the dynamics of individual molecules transiently occupying the probe volume. Because the time-resolution of a correlation function is not degraded by time-averaging, CS methods can use longer data acquisition times when signal levels are small and are also less susceptible to photobleaching as diffusion replenishes the probe volume with new molecules. The FEIR-CS measurements used here and in Ref. 21 to characterize SM sensitivity demonstrate the basic feasibility of this approach. Potential FEIR-CS experiments could leverage changes in a molecule’s vibrational spectrum to isolate the persistence of specific chemical structures or follow how reactants and products interconvert on microsecond timescales. For example, local-mode vibrational probes could be used to address the impact of site-specific interactions, such as hydrogen-bonding or ion association, on molecular transport in complex environments. Similarly, FEIR-CS experiments could track the formation and breaking of specific intermolecular contacts between reactive partners during the initial diffusive encounter and subsequent binding in diffusion-limited bimolecular reactions.

Multiple routes exist for increasing SM FEIR signal sizes. Increasing the pulse repetition-rate beyond the current 1 MHz would have the greatest impact on accessing higher count rates. While the repetition-rate scalability of generating nJ-level sub-ps mid-IR pulses has technical challenges, increases by a factor of ∼10 with reduced pulse energy and bandwidth are feasible. When coupled with higher NA focusing of the IR, sufficiently large IR-vibrational excitation rates should still be achievable. Important gains in detection efficiency are also expected through increasing the NA of fluorescence collection, which at 0.8 is currently low compared to typical SM fluorescence experiments. With these improvements, we believe more useful kHz-level SM FEIR count rates should be accessible.

See the supplementary material for details on the coumarin low-frequency electronic absorption edges, photon pile-up correction, complete coumarin series FEIR data and acquisition details, estimation of experimental uncertainty in brightness, comparison of alternative brightness values, concentration and visible intensity-dependent FEIR data for C6 and C7, and determination of ⟨N⟩ for C6 by FEIR-CS.

This work was supported by a grant from the National Science Foundation (Grant No. CHE-1856684). Steady-state electronic absorption and fluorescence characterization made use of the shared facilities at the University of Chicago Materials Research Science and Engineering Center, supported by the National Science Foundation under Award No. DMR-2011854.

The authors have no conflicts to disclose.

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