Doubly-resonant four-wave mixing (DR-FWM) is a nondegenerate four-wave mixing process in which four photons interact to coherently probe two distinct Raman resonances. We demonstrate DR-FWM microscopy as a label-free and nondestructive molecular imaging modality with high chemical specificity on the submicron scale by imaging alkyne-substituted oleic acid in both aqueous and lipid-rich environments. DR-FWM microscopy is contrasted to coherent anti-Stokes Raman scattering (CARS) microscopy and it is shown that the coherent addition of two simultaneously probed Raman resonances leads to a significant increase in signal without increasing the non-resonant background. Thus, this scheme enables the detection of weak Raman signals through amplification by a strong Raman resonance, potentially increasing the overall detection sensitivity beyond what has been demonstrated by either CARS or stimulated Raman scattering (SRS).
©2009 Optical Society of America
Over the past several years a number of optical techniques have been developed that provide label-free measurements of the dynamics and distribution of complex molecules with diffraction-limited spatial resolution. Linear processes such as the excitation of intrinsic fluorescence, elastic (Rayleigh) light scattering, and inelastic (Raman) light scattering have found widespread application since they are relatively straightforward to implement and measure. These processes have been utilized extensively to provide structural information on the micron length scale, with a focus on analyzing biological cells. Among these processes, Raman scattering is particularly attractive because it is arguably the most chemically specific. The small cross-section of Raman scattering events, however, typically requires long integration times to produce measurable signals. Therefore, nonlinear processes such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS) have been used to enhance the signal and enable high-resolution microscopic imaging [1–5].
In CARS, two pump photons, ωP, and a Stokes photon, ωS, interact simultaneously with a molecular vibrational mode to produce an anti-Stokes photon, ωCARS. The energy difference between the Stokes and pump photons, ℏωP−ℏωS, matches the vibrational energy of the molecular mode and the resulting anti-Stokes photon is produced at frequency ωCARS=(ωP−ωS)+ωP (see Fig. 1(a) , Case 1). While CARS microscopy, based on diverse Raman bands has been reported, the broad use of CARS across the entire chemical fingerprint region has been limited to just a few fairly strong resonances  since weak resonances are typically unable to produce sufficient contrast against a large electronic non-resonant background that is present in most multi-photon mixing spectroscopies. Various techniques have addressed this problem by minimizing the non-resonant background [1, 7–9]. Background suppression may, however, not be sufficient for the detection of a low density solute against the strong background produced by a solvent.
Here, we present a doubly-resonant four-wave mixing (DR-FWM) scheme that further improves the sensitivity of label-free microscopy by preferentially enhancing the signal while maintaining a constant non-resonant background. This scheme makes use of the fact that CARS is a special degenerate case of four-wave mixing, because it requires the simultaneous interaction of two identical pump photons, ωP. If, however, a third source is introduced with another, distinct frequency, ωP’, then several possibilities for four-wave mixing arise. In particular, the combination ωP’−ωS (Fig. 1(a), Case 3) can now probe another Raman resonance that is distinct from the original resonance ωP−ωS (Fig. 1(a), Case 2). If, in each of these processes the second pump photon is distinguishable from the first pump photon, then the signals generated in both these processes interfere constructively and lead to a stronger overall resonant signal, ωDR-FWM. As shown in detail below, this process can be utilized to amplify the signal from a weak Raman resonance in the presence of a much stronger Raman resonance.
2.1 Doubly-resonant four-wave mixing
DR-FWM occurs when ωp, ωp’, and ωs are non-degenerate. In this case, where ωp is distinguishable from ωp’, photons with these frequencies can mix with ωs in two ways to produce the same resulting photon, ωDRFWM =(ωp−ωs)+ωp’=(ωp’−ωs)+ωp (see Fig. 1(a), Case 2 & 3). Lotem et al. first observed that these two processes add coherently and showed that two resonant terms, χ(3)R and χ(3)R’, had to be considered in order to distinguish the Raman resonance probed by (ωp−ωs) as opposed to (ωp’−ωs) . The third-order non-linear susceptibility, χ(3), then becomes:Eq. (1) that as ωp−ωs and ωp’−ωs both approach Raman resonances the non-resonant cross-term (in the second line) approaches zero as χ(3)R and χ(3)R’ both become purely imaginary.
It should be noted that DR-FWM is a four-wave parametric mixing process in which two different resonances are independently probed by three distinguishable laser wavelengths. At least two different forms of DR-FWM processes may occur, including the probing of electronic  or Raman resonances. Names such as “three color CARS” have been used to distinguish between electronic and Raman resonances, but involve only a single Raman resonance . In this paper we describe a FWM process that probes two different Raman resonances. To stay consistent with the nomenclature adopted in the original papers we chose to call it DR-FWM despite its ambiguity .
2.2 Coherent anti-Stokes Raman scattering
It is instructive to compare DR-FWM with CARS since CARS may actually be considered a special, degenerate case of DR-FWM in which the two ωp photons are indistinguishable. In fact, in 2002 Volkmer et al. demonstrated time-resolved CARS microscopy by taking advantage of non-degenerate frequency mixing mediated by a single Raman resonance . In degenerate FWM (i.e. CARS), since ωp−ωs=ωp’−ωs both possible combinations of the three incident fields probe the same Raman resonance and the third-order nonlinear susceptibility contains just a single Raman-resonant term.
As ωp−ωs approaches a Raman resonance the CARS intensity yields:
Assuming ωp, ωp’, and ωs are all far from electronic resonances, a comparison of Eqs. (1) and 3 shows that there should be no difference in non-resonant background levels for DR-FWM and CARS regardless of the number of mixing processes that are coherently adding up to produce the resulting signal. Therefore DR-FWM microscopy should improve the signal to non-resonant background ratio when compared with CARS microscopy.
2.3 Double resonance enhancement
The signal intensity of the doubly resonant process, IDR-FWM, can be compared with the signal intensity of the singly resonant process, ICARS. If we ignore the non-resonant background terms in Eq. (1) (i.e. taking just the last line of the equation), χ(3) R can be factored out to give the expression:Eq. (4) it can be seen that a strong |χ(3) R’|2 of one Raman resonance, based on e.g. high bond density or large Raman cross-section, could be used to enhance the much weaker χ(3) R of another Raman resonance. For example if |χ(3) R|/|χ(3) R|≈10 then |χ(3) R|2 will be enhanced by approximately 2 orders of magnitude. Even a situation in which |χ(3) R’|2≈|χ(3) R|2 will still lead to an approximately 4x increase in signal strength over the signal intensities of either singly resonant process.
3. Methodology and Results
3.1 Spectral dependence
As described by Lotem et al., a DR-FWM peak is best described in a 2D parameter space where the two independent variables, (ωp−ωs) and (ωp’−ωs), determine the value of χ(3) . In order to positively verify the nature of the DR-FWM signal we show the dependence of the signal on these two parameters. An aliquot of alkyne-modified oleic acid exhibiting strong Raman resonances at both the 2845 cm−1 C-H stretch and 2115 cm−1 alkyne stretch vibrations (see the spectrum in Fig. 1(b)) was dried onto a glass coverslip and then submerged in water. Imaging was achieved with a modified CARS microscope, described in detail elsewhere, where a 1064 nm Stokes pulse and ~817 nm and ~869 nm pump pulses are used to match the appropriate Raman resonances .
Nine images were then obtained in which (ωp−ωs) and (ωp’−ωs) were tuned between 2845 and 2871 cm−1 and 2101-2116 cm−1, respectively (see Fig. 2(a-i) ). It is important to note that resonant FWM peaks are often calculated for the ideal case in which the resonances involved are narrow and well isolated. This, however, is not always the case. Therefore, to illustrate this process and its favorable properties for molecularly specific imaging, we probed a single spectral quadrant within the 2D parameter space (see highlighted region in Fig. 3(a) ). Figure 1b shows that, while the 2115 cm−1 peak is narrow and isolated, the 2845 cm−1 line is clearly much more complex and includes multiple tightly packed spectral lines. CARS images were also acquired from 2846 to 2872 cm−1 (Figs. 2(j-l)) and compared with the DR-FWM images. The images are normalized to the laser input power so that each image represents the magnitude of |χ(3)|2 at a particular spectral location.
When (ωp−ωs) and (ωp’−ωs) are both tuned away from their respective Raman resonances, the DR-FWM signal and the CARS signal are roughly equivalent in strength and dominated by non-resonant background contributions as can be seen in Figs. 2(a) and 2(j). As (ωp−ωs) and (ωp’−ωs) are simultaneously tuned to their respective Raman resonances a significant increase in the DR-FWM signal compared to the CARS signal can be observed, see Fig. 2(i and l). This increase in signal is consistent with the inclusion of an additional resonant χ(3) term. Substituting the average intensity over a small region of the image, <IDR-FWM>, for both Figs. 2(i) and 2(l) into Eq. (4), we obtain |χ(3)R|/|χ(3)R|≈0.5. This value, along with the ratio of the Raman peaks, which we found to be approximately 6.5, suggest that the ratio of the line widths ΓR/ΓR’≈3.2 and the ratio of the differential Raman cross-sections (∂α/∂Ω)/(∂α/∂Ω)’≈4.6. These relationships are valuable for comparison with theory.
3.2 Comparison with theory
A DR-FWM surface plot was calculated for two Raman resonances with the inferred relationships for Γ and ∂α/∂Ω, see Fig. 3a. In order to fit the theoretical surface to the data it was necessary to model the 2845 cm−1 line as the superposition of two resonances at 2845 cm−1 and at 2860 cm−1 with a combined ∂α/∂Ω that maintained the necessary relationship, which is consistent with the convoluted nature of the aliphatic Raman peak. Using the average intensity over a small region of the image, <IDR-FWM>, from Fig. 2(g), (h), and (i), Fig. 2(c), (f), and (i), and Fig. 2(a), (e), and (i) as data points and plotting them with corresponding cuts through the parameter space, Figs. 3(b-d) demonstrate excellent agreement between the theoretical DR-FWM line shapes and the collected data. For comparison, <ICARS> from Fig. 2(j), (k), and (l) was fit with a CARS line probing the same 2845 cm−1 resonance as in the DR-FWM case. This resulted in Fig. 3(e), which also shows excellent agreement with the measured values.
3.3 Signal enhancement
The original DR-FWM spectroscopy work by Lotem et al. relied on fixed angles between the three input fields to satisfy the necessary phase matching conditions [10, 15–17]. This initial work also focused heavily on the interference effects between two Raman resonances and dismissed the doubly-resonant enhancement as insignificant. However, in the context of microscopy, this enhancement can present a significant advantage. Under the tight focusing conditions employed in high-resolution microscopy the phase matching conditions are relaxed due to the short interaction length making DR-FWM microscopy experimentally simpler to realize than free-space spectroscopy schemes [1, 18, 19]. This provides us with the added benefit that we can readily collect all signals produced at different phase matching conditions simultaneously (e.g. DR-FWM and CARS).
By comparing signals from DR-FWM and CARS, the signal enhancement can be further explored. In order to demonstrate this enhancement a mixture of the alkyne-substituted oleic acid was embedded in unmodified oleic acid and then imaged. The modified oleic acid used in these experiments forms a gel-solid phase at room temperature, allowing it to separate from the fluid unmodified oleic acid in the form of micron-sized structures. Imaging these amorphous crystal-like structures in an environment of pure oleic acid provides a demonstration of the ability of DR-FWM to extract and amplify a weak Raman resonance. Note that in this situation the entire space probed during imaging is filled with oleic acid species that all have a strong 2845 cm−1 vibration. Only the modified oleic acid, however, exhibits the 2115 cm−1 Raman resonance (Fig. 1(b)). Figure 4(a) shows a DR-FWM image of these modified oleic acid crystal-like structures in regular oleic acid. The structures appear as bright features on the submicron to micron length scale and are visible throughout the field of view above the combined resonant and non-resonant background from the aliphatic CH vibration of all oleic acid species. Figure 4(b) shows the same region imaged at the 2845 cm−1 CARS signal. Note the overall weaker signal obtained when imaging just a single resonance. Figure 4(c) again shows the same region imaged in CARS mode at 2115 cm−1. The signals were normalized consistently across all three images resulting in the apparent lack of background in Fig. 4(c). Lastly, by subtracting Fig. 4(b) from Fig. 4(a) the enhancement of the weak 2115 cm−1 signal by DR-FWM can be visualized (see Fig. 4(d)). According to Eq. (1) and Eq. (3) this difference image should be free from non-resonant background and represent the 2115 cm−1 resonance including an enhancement factor, as shown in Eq. (4).
4. Discussion and Conclusions
Clearly, based on Fig. 4(a) DR-FWM is able to provide strong, chemically specific contrast for the weak alkyne vibration. Removing the resonant CH and non-resonant background contributions as demonstrated in Fig. 4(d), allows us to visualize significantly more of the amorphous alkyne-containing oleic acid structure than what is possible by imaging with just the weak 2115 cm−1 mode by itself. It is also interesting to compare these results with Fig. 3(d) and Fig. 3(e). Although spontaneous Raman spectroscopy (Fig. 1(b)) shows that the intensity of the 2845 cm−1 Raman peak is more than a factor of 5 times greater than the intensity of the 2115 cm−1 peak (based on the area under the peak), the inclusion of the 2115 cm−1 alkyne resonance still more than doubles the intensity of the signal without increasing the non-resonant background. In other words it can be seen from our results that not only does a strong Raman resonance enhance a weaker one but a weaker resonance can also be used to significantly enhance a much stronger one.
In conclusion, we have demonstrated that even small modifications to χ(3), through the introduction of additional resonant terms, can yield significant changes in signal output that can increase the signal-to-background ratio and improve the sensitivity of Raman-based FWM microscopies. Other coherent Raman techniques, such as SRS microscopy have been shown to be free of non-resonant background contributions and enable higher sensitivity for detecting weak Raman resonances. SRS, however, is a non-parametric process with no known enhancement schemes utilizing multiple Raman resonances. We anticipate that DR-FWM microscopy, in combination with existing background suppression schemes, will eventually enable the label-free detection of Raman-active molecules at concentrations well below the current limit of detection [4, 7]. This could further support related efforts towards label-free super-resolution optical microscopy. Here, the signal intensity of Raman-based FWM processes decreases as r6 as the radius of the focal volume shrinks and sensitivity to just a few molecules could be necessary. Future implementations of DR-FWM may provide the appropriate sensitivity for such applications.
We would like to thank Drs. Kit Lam and Sheng Liang for the gift of the alkyne-modified oleic acid, and a reviewer for insightful comments. This work was supported by the American Heart Association through the Grant-in-Aid program. This work was also supported in part by funding from the National Science Foundation. The Center for Biophotonics, an NSF Science and Technology Center, is managed by the University of California, Davis, under Cooperative Agreement No. PHY 0120999. Support is also acknowledged from the UCD Clinical Translational Science Center under grant number UL1 RR024146 from the National Center for Research Resources (NCRR).
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