Abstract
Plasmon-enhanced stimulated Raman scattering (PESRS) microscopy has been recently developed to reach single-molecule detection limit. Unlike conventional stimulated Raman spectra, dispersive-like vibrational line shapes were observed in PESRS. Here, we propose a theoretical model together with a phasor diagram to explain the observed dispersive-like line shapes reported in our previous study. We show that the local enhanced electromagnetic field induced by the plasmonic nanostructure interferes with the molecular dipole-induced field, resulting in the dispersive profiles of PESRS. The exact shape of the profile depends on the phase difference between the plasmonic field and the molecular dipole field. We compared plasmon-enhanced stimulated Raman loss (PESRL) and plasmon-enhanced stimulated Raman gain (PESRG) signals under the same pump and Stokes laser wavelength. The PESRL and PESRG signals exhibit similar signal magnitudes, whereas their spectral line shapes show reversed dispersive profiles, which is in an excellent agreement with our theoretical prediction. Meanwhile, we verify that the nonresonant background in PESRS mainly originates from the photothermal effect. These new insights help the proper use of PESRS for nanoscale bio-imaging and ultrasensitive detection.
1 Introduction
Raman spectroscopy offers label-free contrasts for bio-imaging based on the vibrational information of biomolecules such as lipids, protein, DNA, and small metabolites [1]. However, spontaneous Raman spectroscopy suffers from its poor sensitivity due to inherent small cross-sections for most endogenous biomolecules. It needs a long exposure time to obtain a high-quality Raman spectrum. Owing to the generation of a coherent light field, stimulated Raman scattering (SRS) produces a signal that is many orders of magnitude larger than that of spontaneous Raman spectroscopy [2]. Because of its fast imaging speed comparable with fluorescence microscopy, SRS microscopy has been extensively utilized to capture chemical images of live cells, large-area tissues, living animals, and even human subjects [3].
Despite these attractive attributions, the imaging sensitivity of SRS is not sufficient for performing measurements on the single-molecule level without other enhancement processes [2]. To detect SRS signals from a single molecule, one approach is the involvement of electronic resonance which increases the nonlinear susceptibility of a molecule. Min and coworkers reported electronic pre-resonance SRS to achieve sub-micromolar-sensitivity detection for chromophores [4], [5]. Later, Min et al. reported a stimulated Raman excited fluorescence method that encoded the vibrational resonance into the fluorescence emission. This approach can obtain the Raman signal of the single chromophore by detecting its fluorescence signal [6]. Another route to achieving single-molecule detection is to enlarge the driving light field. Due to the localized surface plasmon resonance (LSPR) effect, the plasmonic nanostructure dramatically increases the intensity of the local electromagnetic field on and near the metal surface [7], [8]. The local enhanced electromagnetic field interacts with molecules close to the nanostructure surface to amplify the SRS signals. The Van Duyne’s group reported surface-enhanced femtosecond SRS (SE-FSRS) spectra, including stimulated Raman loss (SRL) and stimulated Raman gain (SRG) from molecules embedded in a SiO2-coated gold nanodumbbell colloid [9], [10], [11], [12]. Very recently, Cheng and coworkers demonstrated a label-free plasmon-enhanced SRS (PESRS) microscopy which is able to detect single molecules having extremely small Raman cross-sections (∼10−30 cm2 sr−1) with the aid of gold nanoparticles (Au NPs) and the pico-Joule high-repetition-rate laser pulses [13]. The reported PESRS microscopy opened a new window for ultrasensitive and ultrafast bio-imaging.
Unlike the Lorentzian-line shape in traditional SRS spectroscopy, SE-FSRS spectroscopy and PESRS hyperspectral imaging both produced dispersive line shape spectra [9], [10], [11], [12], [13], [14], [15]. The dispersive line shape was attributed to Fano interference of the discrete molecular vibrational states on the continuum-like plasmon resonance [9], [11]. Ziegler et al. indicated that the cross term between the heterodyned SE-FSRS signal and the plasmon light emission resulted in the dispersive-like line shape [16]. Schatz et al. proposed that the asymmetric line shape resulted from the combination of two Fano contributions arising from the interference between both the real and imaginary components of the Raman local electromagnetic field and the plasmon field [17]. Both theoretical descriptions were based on reported SE-FSRS results and only discussed the SRG process. Yet, there are significant differences between the SE-FSRS measurement and PESRS imaging in experiment conditions, including the laser pulse duration, the modulation frequency, the laser excitation, collection approach, and the data processing. Besides, the recent wavelength-dependent SE-FSRS result did not match predictions of any proposed SE-FSRS theory, indicating an incomplete understanding of the plasmon-enhanced SRS process [12], [18].
In this article, we employ the classic light-matter interaction theory and the phasor diagram to elucidate the origin of dispersive shapes in plasmon-enhanced stimulated Raman loss (PESRL) and plasmon-enhanced stimulated Raman gain (PESRG) measurements. The phasor graphs provide an intuitive view of the origin of dispersion, which derives from an interaction between the plasmon-enhanced electric field and the molecular dipole field. We also develop a theoretical model to simulate both PESRL and PESRG spectra. Furthermore, PESRL and PESRG measurements using the same pump and Stokes laser wavelength are conducted to confirm our theoretical prediction.
2 Theory
We start with basic SRS in the absence of a plasmonic field. For details on the classical model of the SRS process, readers can read references [19], [20]. Assuming a pump field (
where
and
Here
For SRL, the first term and second term in

Phasor graphs of stimulated Raman scattering (SRS) and plasmon-enhanced stimulated Raman scattering (PESRS). Phasor representation of stimulated Raman loss (SRL) (a) and stimulated Raman gain (SRG) (b) without plasmon field, plasmon-enhanced stimulated Raman loss (PESRL) (c) and plasmon-enhanced stimulated Raman gain (PESRG) (d) at rigid plasmon resonance, PESRL (e) and PESRG (f) at plasmon pre-resonance, and PESRL (g) and PESRG (h) at plasmon post-resonance.
In the case of PESRS, the signal is from the interaction of a molecule with the local enhanced electromagnetic field. Thus, the PESRS intensity is rewritten as:
where
Here, the local enhancement fields are described as
where
Figure 1e and f presents the pre-resonance conditions (
Next, we discuss the origin of the nonresonant background in the PESRS microscopy. As shown in Figure S2, a strong nonresonant background, in the form of an intensity loss, is generated in the Au NPs substrates with and without adenine adsorption. The background also shows a broad and asymmetric profile in a delay time domain. Moreover, the strong backgrounds are observed in the negative delay time region. Thus, we assign the nonresonant background to the PT effect of Au NPs. The PT effect can be viewed as a scattering field (
Here, C is a constant which reflect the magnitude of PT contribution. We note that other pump-probe processes including XPM and TA may also contribute a small part of nonresonant background. Both XPM and TA can be considered to be wavelength independent [21], which does not impact the dispersive line shapes of PESRL and PESRG.
By inserting eq. (5) into eq. (4) and adding the PT contribution (eq. (7)), a full expression of PESRS is given by
The PESRS can be viewed as a linear combination of an asymmetric line shape (the real part of molecular susceptibility) and a symmetric line shape (the imaginary part of molecular susceptibility). The dispersive line shape of PESRS depends on the relative contribution of the imaginary and real components of the plasmonic field. The PT term normally is a negative constant value in a short spectral window. As shown in eq. (8), the interference between the molecular susceptibility and the plasmon enhancement coefficient leads to the dispersive line shapes in PESRS. When IPT = 0 and FP = FS = 1 (no plasmon resonance), eq. (8) is reduced to the normal SRG and SRL cases.
We performed simulations of PESRS based on eq. (8). The Raman peak is centered at 731 cm−1 with a 7 cm−1 HWHM. The pump and Stokes beam wavelengths are centered at 969 nm and 1040 nm, respectively. The plasmon peak is kept at 800 nm. The HWHM of the plasmonic peak is set as 5000 cm−1. The PT constant C is set as −10,000, indicating an intensity loss in the probe beam. The simulated PESRL and PESRG results are shown in Figure 2. Figure 2a and b presents the PESRL and PESRG spectra as a function of the enhancement factor A. As we expected, without plasmon enhancement (A = 0), the SRL and SRG spectral profiles are determined by the imaginary part of χ, both showing symmetric Lorentzian-line shapes with a negative and a positive peak, respectively. With the plasmonic effect, SRL and SRG both show dispersive line shapes. All PESRL spectra show a strong negative peak at lower wavenumber and a weak positive peak at higher wavenumber. All PESRG spectra show a strong positive peak at higher wavenumber and a weak dip at lower wavenumber. As we predicted, the asymmetric profiles of PESRL and PESRG are opposite. In addition, PESRL and PESRG acquire more prominent dispersive characters as the enhancement factor increases. Similar results were reported by Ziegler [16]. While we find that the dispersive characters do not increase when the enhancement factor reaches a point that is large enough. As we discussed above, the dispersive line shape depends on the plasmon resonance frequency relative to the pump/Stokes frequency. As is evident in Figure 2c and d, the increasing dispersive line shapes and more negative PT backgrounds are shown when the plasmonic peak approaches the pump or Stokes wavelength. Intriguingly, under the plasmon post-resonance condition (e.g., first rows in the panel c and d), as predicted by our phasor diagram, PESRL appears as a gain at post-resonance condition, i.e., the positive peak becomes stronger than the negative peak. Similarly, PESRG appears as a loss, i.e., the negative peak dominates.

Simulation results. (a–b) Simulated plasmon-enhanced stimulated Raman loss (PESRL) (a) and plasmon-enhanced stimulated Raman gain (PESRG) (b) as a function of the plasmonic enhancement factor, A. The plasmon peak is kept at 800 nm. (c–d) Simulated PESRL (c) and PESRG (d) as a function of the plasmon peak
3 Result and discussion
We have experimentally investigated the line shapes of PESRL and PESRG predicted by our theoretical model above. The hyperspectral SRS data are collected by using a spectral-focusing SRS microscope which has been previously described [13]. Figure 3 presents the scheme of the hyperspectral SRS microscope. In brief, an 80 MHz tunable femtosecond laser (InSight DS+, Spectra-Physics) provides the pump (969 nm, ∼120 fs) and Stokes (1040 nm, ∼200 fs) lasers. Two acousto-optic modulators are installed in the pump and the Stokes beams for implementing SRL and SRG, respectively. The pump and the Stokes beams are collinearly overlapped and sent to an upright microscope with a 2D galvo mirror system for the laser scanning. To obtain spectral-domain information, the pump and the Stokes pulses are stretched by 5 and 6 glass rods, respectively. In this way, about 7 cm−1 spectral resolution is achieved. The laser powers (the pump ∼ 150 μW and the Stokes ∼ 150 μW at the sample) are sufficiently low to ensure no damage of molecules or nanostructures during the experiments. A water immersion objective (Olympus, NA = 0.8, 40×) is used to focus the pump and the Stokes lasers on a sample. An oil condenser (Olympus, NA = 1.4) is used to collect the laser light in the forward direction. To obtain SRL signals, the Stokes beam is modulated at 2.2 MHz. Two 1000 nm short-pass filters block the Stokes laser before a photodiode with a lab-built resonant amplifier. To obtain SRG signals, the pump beam is modulated at 2.2 MHz. Two 1050/50 nm band-pass filters and two 1000 nm long-pass filters block the pump beam before the photodiode. A lock-in amplifier demodulates the SRS signals and the R channel is used to read out SRS signals. The hyperspectral PESRS datacube contains 200 × 200 pixels with 120 Raman channels. Each datacube took about 2 min with a 10 µs dwell time per pixel. The image area (30 µm × 30 µm) and pixel size (150 nm) are the same in all experiments. We note that Van Duyne’s group used pump/Stokes and pump/anti-Stokes pulses to obtain SE-FSRG and SE-FSRL signals to sample different portions of LSPR of nanodumbbell colloids [12]. Here, we used the same pump and Stokes pulses and exchanged the modulated beam to obtain PESRL and PESRG to probe the same LSPR portions of the nanoparticle aggregation.

Schematic of spectral-focusing hyperspectral stimulated Raman scattering (SRS) microscope for stimulated Raman loss (SRL) and stimulated Raman gain (SRG) measurement.
First, we compared the SRL and SRG responses of non-plasmonic enhanced SRS. Figure S3a shows SRL and SRG images of a solid adenine sample at the same location. The SRL and SRG spectra of adenine that are equal in the bandwidth and the Raman peak position are shown in Figure S3b. In principle, the SRL and the SRG signal are equal in magnitude. However, due to the wavelength-dependent quantum efficiency of the photodiode and different transmittances of filter sets, the SRL response in our microscope is about three times larger than the SRG response. The SRL and SRG response correction will be considered in the following results to ensure the PESRS spectra which could be compared accurately in magnitudes.
Next, we examined the PESRL and PESRG signals of the adenine adsorbed on Au NPs. 5 μL of a 1 mM aqueous adenine solution was added to 2–4 μL of concentrated 60 nm Au NPs colloid sol. Then, the Au NPs were dropped on a cover glass followed by vacuum drying. Crucially, the analytes induced the aggregation of Au NPs before drying, creating hot spots occupied by the analyte itself. We randomly measured three locations on the aggregated Au NPs substrate. Both PESRL and PESRG signals were collected in every location to avoid the interference of aggregation states. To decrease the intensity variation, the PESRS spectra from all pixels in the whole image were averaged. The raw PESRL and PESRG spectra of adenine are displayed in Figure 4. The resulting PESRL spectra (Figure 4a) from the adenine-adsorbed Au NPs aggregates consists of a narrower feature at 727 cm−1 on the top of a strong and broad nonresonant background with a high end on the left. A penalized least squares fitting was used to subtract the broad spectral background [27]. The fitted backgrounds of PESRS are shown in Figure 4 as the same color dash lines. All PESRG spectra (Figure 4b) showed a broad background with a high end on the right and a sharp negative peak at 735 cm−1. The end-for-end reversed backgrounds in PESRL and PESRG can be explained as following. For the PESRL measurement, the 969 nm laser is the “probe” beam and the modulated 1040 nm laser is the “heat” beam for the PT process. The “heat” and “probe” beam are exchanged with each other for the PESRG measurement, and relative delay time turns end for end. In this way, the PT decay profiles under two different conditions are just reversed. Additionally, the SRL and the PT effect both produce an intensity loss in the “probe” beam. Thus, the raw data of PESRL are the sum of the PT signal and the SRL signal. While the SRG is a “probe” beam gain process, the total signal is the subtraction of the SRG signal from the PT signal. Consequently, the PESRG appears as a negative peak on a broad PT background.

Three raw plasmon-enhanced stimulated Raman loss (PESRL) (a) and plasmon-enhanced stimulated Raman gain (PESRG) (b) spectra of adenine adsorbed on aggregated Au NPs which are obtained from different locations. Fitting backgrounds are displayed as dash lines.
Figure 5 shows the vibrational resonant components of the PESRL and PESRG spectra obtained from the subtraction of the fitted backgrounds from the observed PESRS signals. For a better comparison, we set the strong peak of PESRG data as a positive peak. Due to our experimental conditions, the intensity of PESRL is about three times larger than that of PESRG. After the correction of the system response, the signal intensities are nearly identical between PESRL and PESRG. Remarkably, the PESRG result shows a blue shift in peak positions from the PESRL result and with an oppositely phased dispersion. In the PESRL result, the vibrational feature is characterized by a dip on the high wavenumber side and a peak on the low wavenumber side. While, in the PESRG result, the dip is on the low wavenumber side and the peak is on the high wavenumber side. This is an excellent agreement with our theoretical prediction of opposite dispersive line shapes between PESRL and PESRG.

The experimental and simulated plasmon-enhanced stimulated Raman loss (PESRL) (a) and plasmon-enhanced stimulated Raman gain (PESRG) (b) spectra of adenine. The background-corrected PESRL and PESRG spectra are presented as solid lines (black, red, and blue). The Fano-like fitting spectral profiles based on eq. (9) are presented as the same color dash lines. Simulated PESRL and PESRG spectra based on eq. (8) are presented as green dot lines.
Then, we simulated the spectra of adsorbed adenine on Au NPs based on eq. (8). The vibrational peak of adenine is at 731 cm−1 with a HWHM of 7 cm−1. The PESRS spectra were simulated by using a plasmon response with
In the literature, the Fano function has been used to describe a dispersive line shape of SE-FSRS [11]. As shown in eq. (8), the PESRS can be viewed as a linear combination of a Fano-line shape (the real part of the molecular susceptibility in which Fano parameter value is one as shown in eq. S1) and a Lorentzian line shape (the imaginary of the molecular susceptibility). For a better comparison with the Fano line shape, we insert eq. (3) into eq. (8) and the eq. (8) are reformatted into a Fano-like line shape as following:
where
As shown in eq. (9), the PESRS profiles are the subtraction of two Fano profiles where the Fano parameter (q) of the first Fano function term depends on the real part and the imaginary part of plasmon enhancement coefficient and the Fano parameter of the second term is zero. The signs of the Fano parameters of PESRL and PESRG are opposite.
To valid this relation, we used the eq. (9) to fit the experimental spectra. We can obtain excellent agreements using q = −1.7 and q = 2 for all of the vibrational features in PESRL and PESRG, respectively. The fitting results are displayed in Figure 5 as the same color dash lines. The fitting results of the peak frequency, the bandwidth, and the amplitude are reported in Table S1. The reversal of the sign of q indicates an opposite change in the phase of dispersion between the PESRL and the PESRG process. Similar absolute values of q for PESRL and PESRG indicate approximate plasmonic responses due to the close wavelength of the pump and the Stokes beams in our experiments.
It is interesting to compare our phasor diagram and theoretical model to the SE-FSRS theories published by Ziegler and Schatz who only discussed the SRG process. In Ziegler’s theory, the interference between Raman susceptibility and a stimulated surface plasmon emission results in asymmetric line shapes, and the increasing enhancement factors result in increasing dispersive line shapes [16]. In Schatz’s theory, the Fano parameter depends on the ratio between the real part and the imaginary part of the square of the plasmonic field enhancement factor [17]. Different from Schatz’s and Ziegler’s work, our model makes an important prediction about the plasmonic enhancement factor which is given by
4 Conclusions
A theoretical model is developed to describe dispersive-like vibrational line shapes in PESRS microscopy. The plasmon-induced local electromagnetic field interacts with the molecular dipole, resulting in the dispersive line shapes of PESRS. The spectral feature further depends on the phase in the plasmonic field. Under the same laser and molecular conditions, an intensity loss in pre-plasmon resonance could become an intensity gain in post-plasmon resonance. At the same pump and Stokes wavelength setting, we experimentally observed PESRL and PESRG signals with reversed dispersive profiles, which fall into line with our theoretical prediction. We also verified that the nonresonant background in PESRS mainly originated from the photothermal effect. Together, we provided new insight into the nature of PESRS profiles and the mechanism of plasmonic enhancement of coherent Raman scattering. Results reported here can be used to improve signal enhancement in nanoscale coherent Raman imaging towards ultrasensitive detection of molecules.
Funding source: National Institute of General Medical Sciences
Award Identifier / Grant number: GM118471
Funding source: W. M. Keck Foundation
Funding source: National Institute of Allergy and Infectious Diseases
Award Identifier / Grant number: AI141439
Acknowledgments
We thank Lawrence D. Ziegler for his valuable suggestions in theory. We also thank Yurun Xie for his assistance with PESRS measurement.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This work was supported by NIH R01 grants GM118471, AI141439, and a Keck Foundation grant to J.X.C.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2020-0313).
© 2020 Cheng Zong and Ji-Xin Cheng, published by De Gruyter, Berlin/Boston
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