Abstract

We introduce a new coherent anti-Stokes Raman scattering (CARS) suppression scheme based on measuring a non-resonant CARS loss signal by three-beam (pump-Stokes-depletion) double stimulated Raman scattering (SRS) processes, which can be potentially of use for super-resolution Raman microscopy. In the converging configuration with employing both pump-depletion and Stokes-depletion SRS processes, we obtained approximately 94% suppression of non-resonant CARS signal, which is about 1.5 times more efficient than that with the parallel configuration with pump-Stokes and pump-depletion SRS processes. Such an enhanced suppression efficiency in the converging configuration results from a simultaneous loss of photons both in the pump and Stokes beams by double SRS processes, leading to an efficient suppression of the pump-Stokes-pump CARS signal. Based on the present method, we further propose two potential applications: (1) non-resonant background-free CARS imaging and (2) label-free super-resolution Raman imaging, and carry out simple numerical simulations to show their feasibility.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Raman scattering spectroscopy is a commonly used vibrational technique in various research fields for elucidating chemical structures of materials. However, a weak signal of spontaneous Raman scattering and a huge fluorescence background sometimes limit its routine use or more in-depth applications requiring a high signal-to-noise ratio (SNR). Coherent Raman scattering (CRS) techniques such as stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS) are advanced versions of the Raman method capable of enhancing a very weak Raman signal by several orders of magnitude [1–6]. Due to their enhanced SNR and inherent ultrafast time-resolvability, the SRS and CARS techniques have been extensively used for investigating ultrafast vibrational dynamics in the electronic excited state or label-free bio-imaging of lipids, proteins, organelle structures, drug penetration and delivery, etc. in live cells and tissues [2,3,6–14].

In a typical third-order CRS process, two incident laser fields called pump and Stokes beams interact with a material to generate the SRS and CARS signals when the frequency difference (Δω) between the pump (ωp) and Stokes (ωs) beams matches a vibrational frequency (ωv) of the material, i.e., Δω = ωpωs = ωv. This CRS process involves both dissipative and parametric energy redistributions. First, an energy exchange occurs between the incoming light fields and the material via the SRS process in such a way that a pump photon is used to generate a Stokes photon and a vibrational excitation of the material. Consequently, the interacting light fields overall lose their energy to the material via a non-parametric process. Second, combined energy of the pump and Stokes beams is split into new field energy of a CARS (ωCARS = 2ωpωs) and a coherent Stokes Raman scattering (CSRS, ωCSRS = 2ωsωp) signal via a parametric process mediated by the Raman material [15]. In this case, there is no energy exchange between the material and the combined light fields, which is by definition a parametric process. Although the SRS and CARS processes are associated with different types of energy redistributions, a competitive loss of pump energy by those processes arises as they use energy of the common pump beam. As a result, the CARS signal, which is in proportion to the square of pump intensity, can significantly be modulated by the other coupled SRS processes and vice versa.

In the early 2000s, super-resolution fluorescence microscopies, such as photoactivated localization microscopy (PALM) [16], stochastic optical reconstruction microscopy (STORM) [17] and stimulated emission depletion (STED) [18–20] microscopy, have been successfully developed to break the diffraction limit to achieve a sub-100-nanometer resolution. Since then, many attempts have been made to develop a label-free version of super-resolution vibrational imaging. Several approaches based on the CRS process have been theoretically proposed, and some of them have been successfully demonstrated experimentally [21–32]. Recently, we have shown that a three-beam double SRS scheme, where the pump (p), Stokes (s), and depletion (d) beams in order of frequency are used, can make a significant suppression of a pump-Stokes (p-s) SRS or a pump-Stokes-pump (p-s-p) CARS signal by using a strong depletion beam. It was suggested that the three-beam double SRS scheme would be potentially useful for developing super-resolution SRS and CARS microscopy [33–37]. In the so-called parallel configuration, two SRS processes competitively occur between the pump and Stokes beams (p-s SRS) and between the pump and depletion beams (p-d SRS) for two different vibrational modes of the molecule. Since the depletion beam is much stronger than the Stokes beam, an intensity loss of the pump beam by the latter (p-d SRS) is overwhelmingly dominant. As a consequence, the p-s SRS and p-s-p CARS signals, which are proportional to the pump intensity and its square, respectively, are significantly suppressed by the presence of the strong depletion beam. For the ring-breathing and C-H stretching vibrational modes of benzene that are involved in the p-s and p-d SRS processes, we have achieved 60% and >95% suppression efficiencies for the p-s SRS and p-s-p CARS at the same depletion peak intensity (about 2.1 TW/cm2) [34,36], respectively. Therefore, we concluded that the CARS suppression method is more efficient and thus would be potentially useful for developing a STED-like super-resolution CARS microscopy. However, still the depletion beam intensity previously used for obtaining a >95% of CARS suppression efficiency would be too strong to be used for practical bio-imaging applications, where a sample damage easily occurs by an intense laser beam. A further improvement in suppression efficiency has thus been required to make a sufficient CARS suppression at a depletion beam intensity as low as possible.

In this report, we introduce a new double SRS-based CARS technique that can provide a more efficient way to suppress the non-resonant CARS signal. Unlike all the previous SRS and CARS spectroscopy and microscopy, we here demonstrate that vibrationally non-resonant CARS measurement can be used for vibrational spectroscopy and imaging studies. In contrast to our previously investigated parallel scheme using both the p-s and p-d SRS processes, two SRS processes occur between the pump and depletion beams (p-d SRS) and between the Stokes and depletion beams (s-d SRS) while there is no SRS between the pump and Stokes beams. Thus, the p-s-p CARS signal is generated by the vibrationally non-resonant CARS process. This optical geometry can be referred to as a converging configuration because both the pump and Stokes photons are converted to those of depletion beam via the two SRS processes. We compare the two approaches based on the parallel and converging configurations under the same experimental conditions and demonstrate that a higher CARS suppression efficiency can be achieved with the CARS imaging setup employing the converging configuration. We then propose two potential applications using the present three-beam CRS technique: (1) non-resonant background-free CARS imaging and (2) label-free super-resolution CRS imaging. We perform a simple numerical simulation to show how such vibrational imaging can be achieved by combing spatially-tailored multiple laser beams.

2. Basic concept of double SRS-CARS suppression

Figure 1 shows the basic concept of double SRS-based CARS suppression techniques in two different, parallel and converging, types of optical configurations. In contrast to conventional two-beam p-s-p CARS, three laser beams, i.e., pump, Stokes, and depletion, are used to simultaneously induce two different SRS processes (SRS1 and SRS2) for two Raman-active vibrational modes (ωv1, ωv2) of a given molecule. In the parallel configuration shown in Fig. 1(b), the frequency differences between the pump and Stokes beams and between the pump and depletion beams, denoted as Δωp-s and Δωp-d, respectively, match ωv1 and ωv2, i.e., Δωp-s = ωv1 and Δωp-d = ωv2 to produce a p-s SRS (SRS1) and a p-d SRS (SRS2) process, respectively. In the p-s SRS process, the pump and Stokes beams are combined to yield a weak stimulated Raman loss (SRL) in the pump beam (ωp) and a weak stimulated Raman gain (SRG) in the Stokes beam (ωs). Furthermore, a vibrationally resonant p-s-p CARS signal is generated at ωCARS = 2ωpωs by the same pump-Stokes beam pair via the parametric process, which is the same as the conventional two-beam CARS. However, in the presence of a strong depletion beam, which acts like the second Stokes beam for SRS2, the intensity of the pump beam is strongly attenuated by the p-d SRS process in addition to the p-s SRS process. Since the depletion beam is much stronger than the Stokes beam, most of the pump photons are converted to depletion beam photons via the p-d SRS process. Consequently, the p-s-p CARS signal that is proportional to the square of the pump intensity is significantly reduced upon the addition of the intense depletion beam.

 figure: Fig. 1

Fig. 1 Schematic diagrams of two different CARS suppression processes. (a) Spontaneous Raman spectrum of liquid benzene. Three-beam (pump-Stokes-depletion) double SRS-CARS suppression processes in the (b) parallel and (c) converging configurations. Two vibrational modes of benzene (ring breathing mode; ωv1 = 992 cm−1 and C-H stretching mode; ωv2 = 3062 cm−1) can be used for generating SRS1 (ωv1 = 992 cm−1) and SRS2 (ωv2 = 3062 cm−1) processes simultaneously (see the main text for more details).

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As in the parallel configuration, two SRS processes induced by two different pairs of the three incident laser beams are involved in the CARS suppression scheme based on the converging configuration (Fig. 1(c)). However, the frequencies of the pump (ωp), Stokes (ωs), and depletion (ωd) beams are set in such a way that the SRS1 process for ωv1 occurs by a pair of the Stokes and depletion beams (s-d SRS: Δωs-d = ωsωd = ωv1), not by the pump-Stokes pair, while the SRS2 process for ωv2 occurs by the pump-depletion pair (p-d SRS: Δωp−d = ωpωd = ωv2). In the absence of a depletion beam, the p-s-p four-wave mixing (FWM) signal generated at ωFWM = 2ωpωs is vibrationally non-resonant because the energy difference between the pump and Stokes beams (Δωp-s = ωpωs) is not in resonance with any vibrational mode of the molecule (Δωp-sωv). In this case, the pump-Stokes beam pair creates no vibrational coherence, which is why we will hereafter use the term, non-resonant p-s-p CARS, instead of p-s-p FWM as a counterpart of resonant p-s-p CARS in the parallel configuration. It should be emphasized that the addition of a strong depletion beam gives rise to large intensity losses in both the pump and Stokes beams via the SRS1 and SRS2 processes, which in turn significantly decrease the non-resonant p-s-p CARS field intensity. This loss of the non-resonant p-s-p CARS, which is obtained by taking the difference between the non-resonant p-s-p CARS signals with and without the depletion beam, is thus sensitive to both the two vibrational resonances (ωv1 and ωv2). There are two notable features in the present converging scheme. First, a non-resonant CARS signal that originally contains no vibrational information can be used to obtain vibrationally resonant SRS signals by modulating the depletion beam intensity. This can be a very useful way to remove a non-resonant CARS background contribution to the CARS imaging signal. Second, a more efficient suppression of the non-resonant CARS signal can be achieved by a double SRL effect in the pump and Stokes beams, which would be of use for super-resolution CRS imaging when combining an extra doughnut-shaped depletion beam with Gaussian-shaped pump and Stokes beams. Details of related applications will be further discussed in Sec. 6.

3. Theory

Detailed theories of the double SRS-based CARS suppression techniques in the parallel and converging configurations was already described in our previous papers [33–36]. Therefore, we here give a brief summary of the essential theoretical results of those methods.

3.1 Parallel configuration

When the three laser beams (depletion>pump>Stokes in order of intensity) propagating along the z-axis in the laboratory frame interact with the sample in the parallel double SRS configuration shown in Fig. 1(b), it is assumed that the intensity variations of the Stokes and depletion beams by the SRS1 and SRS2 processes are negligibly small compared to their initial intensities. The pump intensity at z, Ip(z), which is dependent on both the Stokes and depletion beam intensities, is then given as [33–36]

Ip(z)=Ip(0)exp((gsωpωsIs(0)+gdωpωdId(0)+g¯Ip(0))z),
where Ip(0), Is(0) and Id(0) are the initial pump, Stokes and depletion beam intensities at z = 0. The constants, gs and gd, are related to the Raman gain coefficients for the SRS1 and SRS2 processes with the two Raman-active modes, respectively, and g¯ is the mean gain coefficient, which is defined as
g¯=[gsωpωsIs(0)+gdωpωdId(0)]/[ωpωsIs(0)+ωpωdId(0)].
By combining the equation of motion for two vibrational modes of the molecule with the Maxwell equation for the propagation of interacting light fields and substituting Eq. (1) into the resulting rate equation for the CARS field, one can obtain the p-s-p CARS intensity at z, ICARSpsp(z), as [34,35]
ICARSpsp(z)=(ωCARSωsσCARSR)2Ip2(0)Is(0)4(gsωpωsIs(0)+gdωpωdId(0)+g¯Ip(0))2(e(gsωpωsIs(0)+gdωpωdId(0)+g¯Ip(0))z1)2,
where σCARSR is the resonant CARS cross-section of the corresponding Raman mode. Using Eq. (3), we can calculate the CARS suppression efficiency in the parallel configuration (ηparallel) as
ηparallel=(1(e(gsωpωsIs(0)+gdωpωdId(0)+g¯Ip(0))z1)2(e(gsωpωsIs(0)+g¯Ip(0))z1)2(gsωpωsIs(0)+g¯Ip(0))2(gsωpωsIs(0)+gdωpωdId(0)+g¯Ip(0))2).
From Eq. (4), it becomes clear that the p-s-p CARS signal can be intentionally suppressed by increasing the depletion beam intensity Id(0) for fixed pump and Stokes beam intensities.

3.2 Converging configuration

As shown in Fig. 1(c), the two independent double SRS processes (s-d SRS and p-d SRS) simultaneously occur in the converging double SRS configuration. The pump and Stokes intensities, which are not coupled to each other, are thus simply given as [36]

Ip(s)(z)=Ip(s)(0)exp(gp(s)d(Id(0)+ωdωp(s)Ip(s)(0))z),
where gsd and gpd are the constants related to the Raman gain coefficients for the s-d SRS (SRS1) and p-d SRS (SRS2), respectively, in Fig. 1(c). The rate equation for the non-resonant p-s-p CARS signal in this converging configuration can be expressed as
zICARSNRpsp(z)=(ωCARSNRpspωp)σCARSNRIp(0)Is(z)ICARSNRpsp(z),
where ICARSNRpsp(z) and ωCARSNRpsp are the intensity at z and optical frequency of the non-resonant p-s-p CARS signal, respectively, and σCARSNR is the non-resonant third-order susceptibility. By substituting Eq. (5) into Eq. (6), one can obtain the non-resonant p-s-p CARS intensity at z as [36]
ICARSNRpsp(z)=(ωCARSNRpspωpσCARSNR)2Ip2(0)Is(0)4(gpd(Id(0)+ωdωpIp(0))+gsd2(Id(0)+ωdωsIs(0)))2×(e(gpd(Id(0)+ωdωpIp(0))+gsd2(Id(0)+ωdωsIs(0)))z1)2,
From Eq. (7), we can calculate the non-resonant CARS suppression efficiency in the converging configuration (ηconverging) as [36]
ηconverging=1(gpdωdωpIp(0)+gsd2ωdωsIs(0))2(gpd(Id(0)+ωdωpIp(0))+gsd2(Id(0)+ωdωsIs(0)))2×(exp[(gpd(Id(0)+ωdωpIp(0))+gsd2(Id(0)+ωdωsIs(0)))z]1)2(exp[(gpdωdωpIp(0)+gsd2ωdωsIs(0))z]1)2.
Although the formal expression for the non-resonant p-s-p CARS suppression efficiency in Eq. (8) appears to be complicated, one can easily find that the suppression efficiency increases with increasing depletion beam intensity Id(0) for fixed pump and Stokes beam intensities.

4. Experimental methods

4.1 Sample

For the double SRS-CARS suppression measurement, we use two vibrational modes of liquid benzene, the ring breathing mode at ωv1 = 992 cm−1 and the C-H stretching mode at ωv2 = 3062 cm−1 (Fig. 1(a)). The first vibrational mode (ωv1) is used for the p-s SRS in the parallel configuration or s-d SRS in the converging configuration while the second vibrational mode (ωv2) is used for p-d SRS in both configurations.

4.2 Three-beam double SRS-CARS suppression setup

The experimental setups for double SRS-based CARS suppression measurements in the parallel and converging configurations are the same except for using different sets of the pump, Stokes and depletion beam frequencies. The detailed experimental layout of a three-beam double SRS-CARS suppression setup was described elsewhere [34,37].

Briefly, the fundamental output (center wavelength: 1028 nm, bandwidth: ~8 nm, pulse duration: ~250 fs) of the femtosecond regenerative amplifier (PHAROS, Light Conversion) was split into three parts for generating the pump, Stokes, and depletion beams. One of them was spectrally narrowed by a narrow bandpass filter (NBF) and then used as a depletion beam, whose center wavelength (λd) and bandwidth (Δλd) were set to λd = 1026.5 nm and Δλd ~3.9 nm (Δωd ~37 cm−1), respectively. The other parts were used to pump a collinear and a noncollinear optical parametric amplifiers (COPA; ORPHEUS and NOPA: ORPHEUS-N, Light Conversion) to generate the pump and Stokes beams, respectively. In the converging configuration, the center wavelengths (bandwidths) of the pump (λp) and Stokes beams (λs) were set to λp = 781 nm (Δλp~1 nm; Δωp~16 cm−1) and λs = 931 nm (Δλs~9 nm; Δωs~104 cm−1) using a NBF and a pair of tilted NBFs, respectively. The three beams interact with the two Raman-active modes of benzene molecules via both the s-d SRS (Δωs-d = ωv1 = 992 cm−1) and p-d SRS (Δωp-d = ωv2 = 3062 cm−1) processes. In the parallel configuration, we tuned the wavelength of the Stokes beam to λs = 846 nm (Δλs~3 nm; Δωs~42 cm−1) so that the p-s SRS process instead of s-d SRS becomes effective because the beat frequency of the sum of pump and Stokes beams is close to the frequency of the ring breathing mode at ωv1 = 992 cm−1.

The pulse energies of the pump, Stokes and depletion beams were controlled by variable neutral density (ND) filters. In particular, the depletion pulse energy was varied from 0 to 100 nJ to measure the depletion beam intensity-dependent SRL and CARS suppression efficiencies. The pump and Stokes pulse energies were fixed at 6 nJ and 8 nJ, respectively, throughout the entire measurements. The three laser pulses were spatiotemporally overlapped using dichroic mirrors and two linear delay stages, and then focused on the liquid sample using an objective lens (NA = 0.3, 10x, focal length: 16 mm). Adjusting the depletion beam divergence allowed us to optimize the spatial overlap of the three laser beams at the position of the focal point to obtain the highest non-resonant p-s-p CARS suppression efficiency. Their focal spot sizes were estimated to be about 3.2 μm, 3.2 μm and 4.2 μm for the pump, Stokes, and depletion beams, respectively. The SRS and CARS signals from the sample were collected using a second objective lens (NA = 0.13, 4x) and detected with a spectrometer equipped with a CCD detector. Short pass filters (<1000 nm for SRS and <750 nm for CARS measurements) and a ND filter were placed in front of the spectrometer to remove strong noise contributions from the incident laser beams.

5. Results and discussion

5.1 Stimulated Raman loss by a depletion beam

Figure 2 displays the SRL signals of benzene measured with varying the depletion pulse energy (Ed) from 0 to 100 nJ. As shown in Fig. 1(b), two SRS processes, i.e., p-s SRS (SRS1) and p-d SRS (SRS2), arise while there is no s-d SRS in the parallel configuration (Fig. 2(a)) because Δωp-s = ωv1 = 992 cm−1 (ring-breathing mode) and Δωp-d = ωv2 = 3062 cm−1 (C-H stretching mode) but Δωs-d ( = 2078 cm−1) does not match any Raman-active mode frequency of benzene (non-resonant). Therefore, a significant SRL is observed only in the pump beam (at 781 nm), which is dominantly induced by the p-d SRS process (Δωp-d = ωv2 = 3062 cm−1) rather than the p-s SRS (Δωp-s = ωv1 = 992 cm−1), with a negligible change of the Stokes beam intensity (at 846 nm) as the depletion pulse energy increases. To quantify the extent of SRL, we define the SRL efficiency of the pump (Stokes) by the depletion beam as,

γp(s)=|ΔIp(s)|Ip(s)(Id(0)=0)=1exp[AId(0)],
where ΔIp(s) is the difference between the pump (Stokes) intensities with and without the depletion beam, and Ip(s)(Id(0) = 0) is the initial pump (Stokes) intensity in the absence of the depletion beam. The constant A is proportional to the Raman gain coefficient of the involved vibrational mode [33–37]. Although there is no SRL in the Stokes intensity by the depletion beam in the parallel configuration, we measured γs in Eq. (9) for the Stokes beam to compare its dependence on the depletion beam intensity. The plot of γp versus Ed in the parallel configuration (Fig. 2(b)) shows that the SRL efficiency at 781 nm (blue circle) gradually increases with Ed and reaches γp = 77% at Ed = 100 nJ but that at 846 nm (black square) is nearly constant regardless of Ed and close to zero (γs = 4%) even at Ed = 100 nJ. This indicates that the SRL of the pump is very large due to the strong p-d SRS process but the intensity change of the Stokes beam by the depletion beam is negligible because most of the pump photons are converted to those of the depletion beam via the p-d SRS.

 figure: Fig. 2

Fig. 2 SRL spectral changes (a, c) and SRL efficiencies (b, d) of liquid benzene as the increase of the depletion pulse energy (from 0 to 100 nJ) in the parallel and converging configurations.

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In the converging configuration (Fig. 2(c)), on the other hand, the Stokes beam intensity as well as the pump beam intensity are significantly reduced with increasing the depletion pulse energy because SRLs of the pump and Stokes beams concurrently arise by the s-d SRS (Δωs-d = ωv1 = 992 cm−1) and p-d SRS (Δωp-d = ωv2 = 3062 cm−1) processes that both involve Raman interactions with the depletion beam. Note that the Stokes and pump beams act as the first and second Raman pumps for the SRS1 and SRS2 processes, respectively. In contrast to the pump beam exhibiting a decrease of its whole spectrum (at 781 nm), however, a spectral dip by s-d SRL is observed on the relatively broad Stokes spectrum (at 931 nm). This is because the bandwidth of the Stokes beam used in our experiment is much broader (Δωs~104 cm−1) than that of the depletion beam (Δωd~37 cm−1), which determines the minimum bandwidth of the experimentally measured CRS peak. Unlike the parallel configuration, the SRL efficiencies of the pump and Stokes beams in the converging configuration increase with the depletion pulse energy (Ed) both at 781 nm (ωv2 = 3062 cm−1) and 931 nm (ωv1 = 992 cm−1) due to the two SRS processes (Fig. 2(d)). This double loss effect in the pump and Stokes intensities can facilitate a more efficient suppression of the non-resonant p-s-p CARS signal, which will be shown in the following subsection. Another notable feature is that the s-d SRL efficiency (931.6 nm; red circle) is about 80% at Ed = 100 nJ, which is slightly higher than approximately 70% of the p-d SRL efficiency (781 nm; black square) at the same depletion pulse energy. According to Eq. (9), the larger the Raman gain coefficient (A value) is, the higher the SRL efficiency (γp(s)) is at the same depletion beam intensity (Id(0)). Since the Raman gain coefficient of the ring-breathing mode (ωv1 = 992 cm−1) of benzene is larger than that of the C-H stretching mode (ωv2 = 3062 cm−1) as shown in Fig. 1(a), our experimental observation in Fig. 2(d) that the s-d SRL efficiency is higher than the p-d SRL efficiency is fully consistent with the theoretical prediction with Eq. (9).

5.2 Non-resonant CARS suppression by double SRS processes

Figure 3 depicts various CARS signals of benzene obtained with varying depletion pulse energy (Ed) in the two different (parallel and converging) three-beam double SRS schemes. When all three incident laser beams (p-s-d) interact with the sample, several FWM processes occur simultaneously. Especially, a few different CARS signals induced by p-s-p, p-d-p, s-d-p, and p-d-s CARS processes can be observed as can be seen in Figs. 3(a) and 3(d). Among them, we focus on the behaviors of the resonant (Fig. 3(b)) and non-resonant (Fig. 3(e)) p-s-p CARS signals with respect to the depletion beam intensity in the present study.

 figure: Fig. 3

Fig. 3 CARS spectral changes of liquid benzene as the increase of depletion pulse energy (Ed) in the (a) parallel and (d) converging configurations. The resonant (992 cm−1) and non-resonant (2072 cm−1) p-s-p CARS spectra in the red boxes of (a) and (d) are shown in (b) and (e), respectively. (c, f) CARS losses (black circles) and suppression efficiencies (blue squares) as a function of Ed.

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The depletion beam intensity-dependence of the CARS signals in the parallel configuration (Figs. 3(a)-3(c)) was already investigated in our previous work, but here they are presented for the sake of direct comparisons. Briefly, the resonant p-s-p CARS signal at 725 nm (ωv1 = 992 cm−1) gradually decreases with increasing Ed due to a decrease in the pump intensity at 781 nm by the p-d SRL as shown in Fig. 2(a). Note that the p-s-p CARS signal is proportional to the square of the pump intensity. Figure 3(c) depicts the p-s-p CARS signal change at 725 nm (black circle) and p-s-p CARS suppression efficiency (γCARSpsp; blue square), which is defined as, in terms of the experimentally measured quantities,

γCARSpsp=|ΔICARSpsp|ICARSpsp(Id(0)=0).
Here, ΔICARSpsp is the difference between the p-s-p CARS intensities with and without the depletion beam, and ICARSpsp(Id(0)=0) is the initial p-s-p CARS intensity in the absence of the depletion beam. The CARS suppression efficiency reaches γCARSpsp = 92% at Ed = 100 nJ, which is 1.2 times higher than that obtained with the previous setup. This 20% improvement of the CARS suppression efficiency is due to a more perfect spatial overlap between the three laser beams at the focal point by optimizing the beam divergence, which further enhances an SRL effect.

In the converging configuration (Figs. 3(d)-3(f)), the non-resonant p-s-p CARS signal (Δωp−s = 2072 cm−1) observed at 670-675 nm decreases as Ed increases due to simultaneous SRLs of the pump and Stokes beams in their SRS processes with the intense depletion beam (see Fig. 2(c)). In Fig. 3(e), the band at 675-685 nm is not the p-s-p CARS signal but the s-d-s-d-p six-wave-mixing signal that grows with Ed. Thus, the changes in the lineshape and intensity of the band at 670-675 nm have to be carefully examined. A stark contrast to the parallel configuration is that the loss of the non-resonant p-s-p CARS signal depends on the pump and Stokes intensities, as both are considerably modulated or attenuated by the introduction of the strong depletion beam via the s-d and p-d SRS processes as shown in Fig. 2(c).

Experimentally, we observe two interesting and characteristic features. First, a significant spectral change (spectral dip) of the non-resonant p-s-p CARS signal is accompanied by an overall decrease of the whole CARS band intensity as Ed increases. Without the depletion beam (Ed = 0 nJ), the initial non-resonant p-s-p CARS spectrum resembles the broad Gaussian-like Stokes spectral shape. As Ed increases, however, the following two effects start to contribute to the non-resonant p-s-p CARS signal: (1) a monotonic decrease of the narrowband pump intensity by the p-d SRL and (2) an increase of a dip signal on the Stokes spectrum by the s-d SRL (see Fig. 2(c)). As a consequence, the spectral dip on the non-resonant p-s-p CARS spectrum at 670-675 nm becomes pronounced as can be seen in Fig. 3(e), and at the same time its whole spectral intensity is significantly decreased as Ed increases.

Second, the non-resonant CARS suppression can be further enhanced by a double loss effect on the pump and Stokes intensities. Figure 3(f) shows that the CARS suppression efficiency at 672.5 nm reaches its maximum value (approximately 94%) at Ed = 50 nJ, which is just half of what (Ed = 100 nJ) is needed to make γCARSpsp reach its maximum value in the parallel geometry. Comparing the CARS suppression efficiencies (γCARSpsp) at the same Ed = 50 nJ in the parallel and converging configurations, γCARSpsp = 94% (converging) is 1.5 times higher than γCARSpsp = 60% (parallel). Figure 4 depicts the calculated CARS suppression efficiencies (η in Eqs. (4) and (8)) with respect to the depletion intensity (Id(0)) in the parallel and converging configurations. At Id(0)/Ip(0) = 20 and z = 0.05, the CARS suppression efficiency in the converging case, ηconverging, is 81%, which is 20% higher than ηparallel = 68% in the parallel case. These experimental and theoretical results show that the non-resonant CARS suppression using the converging scheme is much more efficient compared to the resonant CARS suppression using the parallel scheme and thus would be potentially useful for super-resolution vibrational imaging applications in the future.

 figure: Fig. 4

Fig. 4 Calculated CARS suppression efficiencies (η) from Eqs. (4) and (8) in the parallel (black for z = 0.05, blue for z = 0.5) and converging (red for z = 0.05, green for z = 0.5) configurations; gd = 1, gs = 2 and Ip(0) = Is(0).

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6. Applications

So far, we have mainly discussed the non-resonant p-s-p CARS suppression and the double SRS-based CARS spectroscopy. In the following subsections, we propose two potentially useful vibrational imaging applications and explain how the present converging geometry-based CARS technique can be used for those applications.

6.1 Non-resonant background-free CARS imaging

In a typical two-beam CARS technique, a non-resonant CARS signal has been regarded useless for obtaining chemical information of the molecule of interest because it is sensitive not to the molecular vibration but just to nonlinear electronic responses. However, the present three-beam CARS technique based on the converging geometry does provide vibration-specific information from the non-resonant CARS signal measurements because the non-resonant p-s-p CARS signal is modulated by the SRS processes induced by the depletion beam. Furthermore, it can be judiciously used to remove a non-resonant CARS background signal from chemical species, such as solvent molecules, other than the target molecules, which has long been one of the main drawbacks in CARS imaging in comparison to SRS imaging.

Figure 5 shows how the non-resonant CARS background from the solvent or any other uninteresting molecules in sample can be removed to ultimately obtain the vibrationally resonant CARS imaging signal of the target system using our converging configuration. As an illustrative example, let us consider a cylindrical polystyrene (PS) film in water under CARS imaging study (Fig. 5(b)). As described in the converging configuration of Fig. 1(c), three Gaussian-shaped pump, Stokes, and depletion beams are used (Fig. 5(a)). The frequency difference of the p-s pair is not in resonance with any vibrational mode of PS while those of the s-d (Δωs-d) and p-d (Δωp-d) pairs match the frequencies of two vibrational modes of PS, which are distinctively different from any vibrational modes of solvent water. Note that both Δωs-d and Δωp-d do not have to match two vibrational mode frequencies of PS and either of them can be resonant with just one of the Raman-active modes of PS in this case. For non-resonant background-free CARS imaging, one should take the difference between two imaging signals obtained using two (pump and Stokes) beams and three (pump, Stokes, and depletion) beams (see Fig. 5(a)). Without the depletion beam, a non-resonant p-s-p CARS background signal (CARS1) with the pump and Stokes beams is generated, but it does not provide any vibrational information. In the presence of the depletion beam in addition to the pump and Stokes beams, the SRLs of the pump and Stokes beams give rise to a decrease of the non-resonant p-s-p CARS signal (CARS2) only at the PS film, where the s-d SRS and p-d SRS processes occur. That is to say, the loss of the non-resonant p-s-p CARS signal strongly depends on the vibrationally resonant SRS processes of PS. On the other hand, the non-resonant p-s-p CARS signal remains constant at the water region without PS because neither s-d SRS nor p-d SRS process occurs with water molecules, which results in no change in the pump and Stoke beam intensities. By subtracting the CARS2 from the CARS1, therefore, one can completely remove the non-resonant CARS background of water without any loss of the resonant CARS signal and obtain a water background-free CARS image of the PS film. Here, it should be emphasized again that the label-free coherent Raman imaging of PS is achievable by measuring the vibrationally non-resonant CARS signal in the present three-beam converging scheme.

 figure: Fig. 5

Fig. 5 Simulation on non-resonant background-free CARS imaging using the converging geometry-based CARS technique. (a) Differential measurement between CARS1 obtained by using the two (pump and Stokes) beams (upper) and CARS2 obtained by using the three (pump, Stokes, and depletion) beams (lower). All the three beams have Gaussian-shaped intensity profiles. The difference signal (ΔCARS = CARS1 −CARS2) contains vibrationally resonant SRS information of the target molecule. (b) A PS film (width = 2 μm) in water used for CARS imaging. (c) Calculated cross-sections of the CARS images for a PS film in water in (b): CARS1 without depletion (black), CARS2 with depletion (red), ΔCARS (blue) and p-d-p resonant CARS (green).

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Figure 5(c) shows the numerical simulation results on the non-resonant background-free CARS imaging of a cylindrical PS film (width = 2 μm) in water (Fig. 5(b)). For these numerical simulations, three Gaussian-shaped laser beams, i.e., pump (λp = 781 nm), Stokes (λs = 930 nm), depletion (λd = 1025.4 nm), were used, which all have the same ideally narrow bandwidth. The frequency differences of the s-d and p-d beam pairs match two vibrational modes of PS, which are the C-H stretching mode at 3052 cm−1 and ring-breathing mode at 1000 cm−1. Their focused beam profiles, Ij(x,r), where j = p, s and d, at the position x are given as

Ij(x,r)=Ij,0exp(2(rx)2(λj/2)2).
Here, Ij,0 is the intensity of each incident beam at r = x. It is assumed that the initial pump, Stokes and depletion beam intensities, Ij(x,r)dr, at z = 0 are the same, and that we have gpd = 1 and gsd = 2 for PS. Substituting Eq. (11), gpd = 1 and gsd = 2 into Eq. (7), one can obtain the intensity of the non-resonant p-s-p CARS signal, denoted as CARS2, at the position x in the presence of the depletion beam as
ICARSNRpsp(x,z)dr(σCARSNR(x))2Ip2(x,r)Is(x,r)(ωdωpIp(x,r)+ωdωsIs(x,r)+2Id(x,r))2×(e(ωdωpIp(x,r)+ωdωsIs(x,r)+2Id(x,r))z1)2.
When Id(x,r) = 0 in Eq. (12), we have the non-resonant p-s-p CARS intensity at x without the depletion beam (CARS1). For comparison, we also calculated the resonant p-d-p CARS intensity (rCARS) along the x-axis, which is given as
ICARSpdp(x,z)(σCARSR+σCARSNR)Ip2(x,r)Id(x,r)z2dr.
From Eqs. (12) and (13), one can obtain the calculated cross-sections of the CARS1 (black), CARS2 (red), ΔCARS = CARS1−CARS2 (blue), and rCARS (green) images with respect to x, which are depicted in Fig. 5(c). The non-resonant CARS background signals originating from water in the CARS1 (without depletion) and CARS2 (with depletion) images cancel out, whereas the SRS-induced signal at the PS film only survives in the ΔCARS (difference) image. Furthermore, a strong dip signal at the boundary of the PS film observed in the rCARS image, which originates from the interference of the resonant and non-resonant CARS signals in the present numerical simulation or possibly from the refractive index mismatch in a real experiment, is completely removed in the ΔCARS image.

6.2 Super-resolution CARS imaging

As a second application, we propose a super-resolution CRS microscopy to break the diffraction limit using the three-beam double SRS-CARS suppression scheme in the converging configuration. For super-resolution CARS imaging, two different sets of beams need to be used, which are two Gaussian-shaped pump and Stokes beams combined with (1) a doughnut-shaped ((d)-[p-s-d]) or (2) a Gaussian-shaped ((g)-[p-s-d]) depletion beam (Fig. 6(a)). They are to be spatially well overlapped at the focal point in the sample. Then, the difference (ΔCARS) between non-resonant p-s-p CARS signals (dCARS and gCARS) obtained by using the (d)-[p-s-d] and (g)-[p-s-d] beam configurations provides high resolution CARS images beyond the diffraction limit. In the first (d)-[p-s-d] configuration, the non-resonant p-s-p CARS signal is significantly suppressed at the rim of the doughnut-shaped depletion beam, where the SRLs of the pump and Stokes beams occur by the double (s-d and p-d) SRS processes. However, the CARS signal around the central node of the doughnut-shaped depletion beam survives. If the intense Gaussian-shaped depletion beam in the second (g)-[p-s-d] configuration depletes the p-s-p CARS almost completely, the differential CARS (ΔCARS = dCARS−gCARS) yields an SRS-induced vibationally resonant signal only at a limited region of the center of the doughnut-shaped depletion beam.

 figure: Fig. 6

Fig. 6 Simulation on super-resolution CARS imaging using the three-beam (pump-Stokes-depletion) double SRS-CARS suppression technique. (a) Differential measurement between dCARS (upper) and gCARS (lower). For the generations of the dCARS and gCARS signals, two Gaussian-shaped pump and Stokes beams combined with a doughnut-shaped (dCARS) and a Gaussian-shaped (gCARS) depletion beam are used. The difference CARS signal (ΔCARS = dCARS1−gCARS) yields an SRS-induced vibrationally resonant signal only at a limited region of the central node of the doughnut-shaped depletion beam. (b, c) Normalized dCARS signals, which is approximately equivalent to ΔCARS, at variable depletion intensities (a = 0, 1, 10, 20, 50) for (b) z = 0.05 and (c) z = 0.5. (d) Comparison between the spatial resolutions of dCARS at a = 50 in the parallel and converging configurations. The dashed lines represent the CARS intensity corresponding to 1/e2 of its maximum value.

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To show the enhanced spatial resolution in the converging geometry-based CARS imaging, we calculated the intensity profile of dCARS, which is approximately equivalent to that of the ΔCARS because gCARS≈0, at different depletion intensities (Figs. 6(b) and (c)). It is assumed that the pump, Stokes, and depletion beams have λp = 781 nm, λs = 931.6 nm and λd = 1026.5 nm, respectively, for generating the double SRS processes with the two vibrational modes of benzene used in the present experiment, and that they have spectrally narrow bandwidths (<1 nm). The radial intensity profiles of the pump (Ip(0,r)), Stokes (Is(0,r)) and depletion (Id(0,r)) beams at x = 0 are

Ip(0,r)=Ip,0exp(2r2(λs/2)2),
Is(0,r)=Is,0exp(2r2(λs/2)2),
Id(0,r)=Id,0(rλd/2)2exp(2r2(λd/2)2),
respectively, and hereafter the integrated intensity Ij(0) is defined as, for the sake of comparison of the relative initial intensities right before the sample at the focus (z = 0),
Ij(0)=Ij(0,r)dr,
where j = p, s and d. Substituting Eqs. (14)-(16) into Eq. (7), one can obtain the intensity profile of the non-resonant p-s-p CARS signal, ICARSNRpsp(r,z), along the radial direction (r) as
ICARSNRpsp(r,z)Ip2(0,r)Is(0,r)(gpd(Id(0,r)+ωdωpIp(0,r))+gsd2(Id(0,r)+ωdωsIs(0,r)))2×(e(gpd(Id(0,r)+ωdωpIp(0,r))+gsd2(Id(0,r)+ωdωsIs(0,r)))z1)2.
Assuming that the initial pump and Stokes beam intensities are the same, i.e.,, Ip(0) = Is(0) and that gpd = 1 and gsd = 2 for benzene, we calculated the radial distributions of the normalized CARS signals, ICARSNRpsp(r,z), at variable depletion beam intensities with respect to the pump intensity (a = Id(0)/Ip(0) = 0−50), which are shown in Figs. 6(b) and 6(c). As z (interaction length) or a (depletion intensity) increases, the vibrationally resonant CARS signal is generated at a narrower region. Without the depletion beam (a = 0), the spatial resolution, which is defined as the full width at the intensity where the CARS signal decreases to 1/e2, is 480 nm. For z = 0.5, the spatial resolution is about 127 nm at a = 50 (Id = 50Ip), which is 3.8 times higher than that in conventional two-beam CARS case without the depletion beam. By comparing the resolution enhancements in the parallel and converging configurations (Fig. 6(d)) at the same depletion intensity (a = 50), we found that the spatial resolution (127 nm) of the CARS signal in the converging configuration is 28% better than that (176 nm) in the parallel configuration. Therefore, the double SRS-CARS technique based on the converging scheme would be desirable for realizing super-resolution vibrational imaging at a lower depletion intensity.

7. Conclusions

We presented a description of a new double SRS-based CARS suppression technique in the converging configuration and demonstrated that a non-resonant CARS suppression of liquid benzene can be made by using three-colored laser beams (pump-Stokes-depletion). In contrast to the parallel configuration suppressing a resonant p-s-p CARS signal, the s-d (ring breathing mode; ωv1 = 992 cm−1) and p-d (C-H stretching mode; ωv2 = 3062 cm−1) SRS processes are used to suppress a non-resonant p-s-p CARS in the converging configuration. Thanks to the separate double SRL effect in the converging configuration, we could obtain a 1.5 times higher CARS suppression efficiency (94%) than that (60%) in the parallel configuration at the same depletion pulse energy (Ed = 50 nJ). With the enhanced CARS suppression efficiency, it would be possible to use a further reduced depletion intensity to obtain a desired CARS suppression efficiency for super-resolution CRS imaging without sample damage, which is a common but important issue for practical bio-imaging applications.

We proposed two potentially useful applications for the converging geometry-based SRS-CARS suppression technique: (1) non-resonant background-free CARS imaging and (2) super-resolution vibrational imaging. The numerical simulation on differential CARS imaging of a PS film in water showed that the non-resonant CARS background signal from water can effectively be removed by taking the difference between the p-s-p CARS signals with and without the Gaussian-shaped depletion beam. Furthermore, we found that one can achieve an enhanced spatial resolution beyond the diffraction limit by performing the differential measurement with a doughnut- and a Gaussian-shaped depletion beam combined with two Gaussian-shaped pump and Stokes beams. Our simulation showed that the spatial resolution (127 nm) in the converging geometry-based CARS imaging is 3.8 times higher than that (480 nm) in the conventional two-beam CARS at a = Id(0)/Is(0) = 50 and z = 0.5. We anticipate that the present double SRS-based CARS suppression technique will be of practical use for developing label-free super-resolution CRS microscopy.

Funding

Institute for Basic Science (IBS-R023-D1), the Korea Basic Science Institute (D39617).

Acknowledgments

All the SRS and CARS measurements were performed using the femtosecond Multi-dimensional Laser Spectroscopic System (FMLS) at the Korea Basic Science Institute.

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6. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005). [CrossRef]   [PubMed]  

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8. D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J. X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013). [CrossRef]   [PubMed]  

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10. D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese Jr., T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014). [CrossRef]   [PubMed]  

11. B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011). [CrossRef]   [PubMed]  

12. C. Zhang, D. Zhang, and J. X. Cheng, “Coherent Raman scattering microscopy in biology and medicine,” Annu. Rev. Biomed. Eng. 17(1), 415–445 (2015). [CrossRef]   [PubMed]  

13. L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013). [CrossRef]   [PubMed]  

14. D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018). [CrossRef]  

15. K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013). [CrossRef]  

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References

  • View by:

  1. J. X. Cheng and X. S. Xie, Coherent Raman scattering microscopy, (CRC Press, 2013).
  2. C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
    [Crossref] [PubMed]
  3. B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
    [Crossref] [PubMed]
  4. A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999).
    [Crossref]
  5. J. X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19(6), 1363–1375 (2002).
    [Crossref]
  6. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
    [Crossref] [PubMed]
  7. X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
    [Crossref] [PubMed]
  8. D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J. X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
    [Crossref] [PubMed]
  9. A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
    [Crossref]
  10. D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
    [Crossref] [PubMed]
  11. B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
    [Crossref] [PubMed]
  12. C. Zhang, D. Zhang, and J. X. Cheng, “Coherent Raman scattering microscopy in biology and medicine,” Annu. Rev. Biomed. Eng. 17(1), 415–445 (2015).
    [Crossref] [PubMed]
  13. L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
    [Crossref] [PubMed]
  14. D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
    [Crossref]
  15. K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
    [Crossref]
  16. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
    [Crossref] [PubMed]
  17. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
    [Crossref] [PubMed]
  18. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
    [Crossref] [PubMed]
  19. S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
    [Crossref] [PubMed]
  20. V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
    [Crossref] [PubMed]
  21. C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
    [Crossref]
  22. C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
    [Crossref]
  23. L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: a theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
    [Crossref]
  24. W. R. Silva, C. T. Graefe, and R. R. Frontiera, “Toward label-free super-resolution microscopy,” ACS Photonics 3(1), 79–86 (2016).
    [Crossref]
  25. A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013).
    [Crossref] [PubMed]
  26. H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20(6), 6042–6051 (2012).
    [Crossref] [PubMed]
  27. A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
    [Crossref] [PubMed]
  28. D. Wang, S. Liu, Y. Chen, J. Song, W. Liu, M. Xiong, G. Wang, X. Peng, and J. Qu, “Breaking the diffraction barrier using coherent anti-Stokes Raman scattering difference microscopy,” Opt. Express 25(9), 10276–10286 (2017).
    [Crossref] [PubMed]
  29. W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
    [Crossref] [PubMed]
  30. W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
    [Crossref]
  31. W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
    [Crossref]
  32. W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
    [Crossref]
  33. M. Cho, “Three-beam double stimulated Raman scatterings,” J. Chem. Phys. 148(1), 014201 (2018).
    [Crossref] [PubMed]
  34. D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
    [Crossref] [PubMed]
  35. B. J. Rao and M. Cho, “Three-beam double stimulated Raman scatterings: Cascading configuration,” J. Chem. Phys. 148(11), 114201 (2018).
    [Crossref] [PubMed]
  36. B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
    [Crossref] [PubMed]
  37. D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
    [Crossref] [PubMed]

2018 (5)

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

M. Cho, “Three-beam double stimulated Raman scatterings,” J. Chem. Phys. 148(1), 014201 (2018).
[Crossref] [PubMed]

B. J. Rao and M. Cho, “Three-beam double stimulated Raman scatterings: Cascading configuration,” J. Chem. Phys. 148(11), 114201 (2018).
[Crossref] [PubMed]

B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
[Crossref] [PubMed]

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

2017 (2)

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

D. Wang, S. Liu, Y. Chen, J. Song, W. Liu, M. Xiong, G. Wang, X. Peng, and J. Qu, “Breaking the diffraction barrier using coherent anti-Stokes Raman scattering difference microscopy,” Opt. Express 25(9), 10276–10286 (2017).
[Crossref] [PubMed]

2016 (1)

W. R. Silva, C. T. Graefe, and R. R. Frontiera, “Toward label-free super-resolution microscopy,” ACS Photonics 3(1), 79–86 (2016).
[Crossref]

2015 (1)

C. Zhang, D. Zhang, and J. X. Cheng, “Coherent Raman scattering microscopy in biology and medicine,” Annu. Rev. Biomed. Eng. 17(1), 415–445 (2015).
[Crossref] [PubMed]

2014 (3)

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
[Crossref]

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: a theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
[Crossref]

2013 (5)

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013).
[Crossref] [PubMed]

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
[Crossref] [PubMed]

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J. X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
[Crossref]

2012 (3)

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20(6), 6042–6051 (2012).
[Crossref] [PubMed]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

2011 (3)

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
[Crossref]

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
[Crossref] [PubMed]

2010 (2)

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

2009 (2)

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
[Crossref] [PubMed]

2008 (2)

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

2007 (1)

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

2006 (2)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

2005 (1)

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

2002 (1)

1999 (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999).
[Crossref]

1994 (1)

Alfonso-García, A.

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
[Crossref]

Basu, S.

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Beeker, W. P.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bito, K.

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
[Crossref]

Boller, K. J.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

Boller, K.-J.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bryant, G. W.

Cerullo, G.

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

Chen, Y.

Cheng, J. X.

Cho, M.

M. Cho, “Three-beam double stimulated Raman scatterings,” J. Chem. Phys. 148(1), 014201 (2018).
[Crossref] [PubMed]

B. J. Rao and M. Cho, “Three-beam double stimulated Raman scatterings: Cascading configuration,” J. Chem. Phys. 148(11), 114201 (2018).
[Crossref] [PubMed]

B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
[Crossref] [PubMed]

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

Choi, D. S.

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
[Crossref] [PubMed]

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

Cleff, C.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Contreras-Rojas, L. R.

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
[Crossref] [PubMed]

Côté, D.

A. Gasecka, A. Daradich, H. Dehez, M. Piché, and D. Côté, “Resolution and contrast enhancement in coherent anti-Stokes Raman-scattering microscopy,” Opt. Lett. 38(21), 4510–4513 (2013).
[Crossref] [PubMed]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

Couderc, V.

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
[Crossref]

Currie, E.

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

Daniele, J. R.

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

Daradich, A.

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Dehez, H.

Evans, C. L.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

Fallnich, C.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

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B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
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C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
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W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
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W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
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Gross, P.

Guy, R. H.

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
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K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
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C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
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V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
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W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
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W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
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V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
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Kamin, D.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
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C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
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K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
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D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
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D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
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Krishnamachari, V. V.

A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
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D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
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D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
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V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[Crossref] [PubMed]

Leaird, D. E.

Lee, C.

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

Lee, C. J.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
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C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Lee, E. S.

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
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Leproux, P.

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
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C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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Liu, W.

D. Wang, S. Liu, Y. Chen, J. Song, W. Liu, M. Xiong, G. Wang, X. Peng, and J. Qu, “Breaking the diffraction barrier using coherent anti-Stokes Raman scattering difference microscopy,” Opt. Express 25(9), 10276–10286 (2017).
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C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

Marangoni, M.

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

Min, W.

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

Mittal, R.

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
[Crossref]

Nikolaenko, A.

A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
[Crossref] [PubMed]

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W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
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Offerhaus, H. L.

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
[Crossref]

W. P. Beeker, P. Gross, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009).
[Crossref] [PubMed]

Okuno, M.

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
[Crossref]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Peng, X.

Piché, M.

Polli, D.

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

Potma, E. O.

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
[Crossref]

A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
[Crossref] [PubMed]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

Puoris’haag, M.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

Qu, J.

Rao, B. J.

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
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B. J. Rao and M. Cho, “Three-beam double stimulated Raman scatterings: Cascading configuration,” J. Chem. Phys. 148(11), 114201 (2018).
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B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
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Reichman, J.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

Rhee, H.

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

Rizzoli, S. O.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[Crossref] [PubMed]

Roeffaers, M. B. J.

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
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M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Saar, B. G.

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
[Crossref] [PubMed]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

Shen, Y.

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
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Shim, S.-H.

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

Silva, W. R.

W. R. Silva, C. T. Graefe, and R. R. Frontiera, “Toward label-free super-resolution microscopy,” ACS Photonics 3(1), 79–86 (2016).
[Crossref]

Slipchenko, M. N.

Song, J.

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Stanley, C. M.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

Stranick, S. J.

Tsai, J. C.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

Tsai, T. H.

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

Valensise, C. M.

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

Volkmer, A.

Wang, D.

Wang, G.

Wang, H.

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: a theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
[Crossref]

Wang, M. C.

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
[Crossref] [PubMed]

Wei, L.

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
[Crossref] [PubMed]

Weiner, A. M.

Westphal, V.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[Crossref] [PubMed]

Wichmann, J.

Xie, X. S.

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
[Crossref] [PubMed]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
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A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999).
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Yu, Y.

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
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C. Zhang, D. Zhang, and J. X. Cheng, “Coherent Raman scattering microscopy in biology and medicine,” Annu. Rev. Biomed. Eng. 17(1), 415–445 (2015).
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Zhang, X.

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

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A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999).
[Crossref]

ACS Photonics (1)

W. R. Silva, C. T. Graefe, and R. R. Frontiera, “Toward label-free super-resolution microscopy,” ACS Photonics 3(1), 79–86 (2016).
[Crossref]

Annu. Rev. Biomed. Eng. (1)

C. Zhang, D. Zhang, and J. X. Cheng, “Coherent Raman scattering microscopy in biology and medicine,” Annu. Rev. Biomed. Eng. 17(1), 415–445 (2015).
[Crossref] [PubMed]

Chem. Phys. (1)

K. Bito, M. Okuno, H. Kano, P. Leproux, V. Couderc, and H. Hamaguchi, “Three-pulse multiplex coherent anti-Stokes/Stokes Raman scattering (CARS/CSRS) microspectroscopy using a white-light laser source,” Chem. Phys. 419(20), 156–162 (2013).
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ChemPhysChem (1)

X. Zhang, M. B. J. Roeffaers, S. Basu, J. R. Daniele, D. Fu, C. W. Freudiger, G. R. Holtom, and X. S. Xie, “Label-free live-cell imaging of nucleic acids using stimulated Raman scattering microscopy,” ChemPhysChem 13(4), 1054–1059 (2012).
[Crossref] [PubMed]

J. Am. Chem. Soc. (1)

D. Fu, Y. Yu, A. Folick, E. Currie, R. V. Farese, T. H. Tsai, X. S. Xie, and M. C. Wang, “In vivo metabolic fingerprinting of neutral lipids with hyperspectral stimulated Raman scattering microscopy,” J. Am. Chem. Soc. 136(24), 8820–8828 (2014).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

A. Alfonso-García, R. Mittal, E. S. Lee, and E. O. Potma, “Biological imaging with coherent Raman scattering microscopy: a tutorial,” J. Biomed. Opt. 19(7), 071407 (2014).
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J. Chem. Phys. (3)

M. Cho, “Three-beam double stimulated Raman scatterings,” J. Chem. Phys. 148(1), 014201 (2018).
[Crossref] [PubMed]

B. J. Rao and M. Cho, “Three-beam double stimulated Raman scatterings: Cascading configuration,” J. Chem. Phys. 148(11), 114201 (2018).
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B. J. Rao, D. S. Choi, and M. Cho, “Selective suppression of CARS signal with two competing stimulated Raman scattering processes,” J. Chem. Phys. 149(23), 234202 (2018).
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J. Opt. Soc. Am. B (1)

J. Phys. Chem. Lett. (1)

D. Kim, D. S. Choi, J. Kwon, S.-H. Shim, H. Rhee, and M. Cho, “A selective suppression of stimulated Raman scattering with another competing stimulated Raman scattering,” J. Phys. Chem. Lett. 8(24), 6118–6123 (2017).
[Crossref] [PubMed]

J. Raman Spectrosc. (1)

W. P. Beeker, C. J. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “A theoretical investigation of super-resolution CARS imaging via coherent and incoherent saturation of transitions,” J. Raman Spectrosc. 42(10), 1854–1858 (2011).
[Crossref]

Laser Photonics Rev. (1)

D. Polli, V. Kumar, C. M. Valensise, M. Marangoni, and G. Cerullo, “Broadband coherent Raman scattering microscopy,” Laser Photonics Rev. 12(9), 1800020 (2018).
[Crossref]

Mol. Pharm. (1)

B. G. Saar, L. R. Contreras-Rojas, X. S. Xie, and R. H. Guy, “Imaging drug delivery to skin with stimulated Raman scattering microscopy,” Mol. Pharm. 8(3), 969–975 (2011).
[Crossref] [PubMed]

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Chem. Chem. Phys. (1)

D. S. Choi, B. J. Rao, D. Kim, S.-H. Shim, H. Rhee, and M. Cho, “Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes,” Phys. Chem. Chem. Phys. 20(25), 17156–17170 (2018).
[Crossref] [PubMed]

Phys. Rev. A (6)

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K. J. Boller, “Ground-state depletion for sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 86(2), 023825 (2012).
[Crossref]

C. Cleff, P. Groß, C. Fallnich, H. L. Offerhaus, J. L. Herek, K. Kruse, W. P. Beeker, C. J. Lee, and K.-J. Boller, “Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 87(3), 033830 (2013).
[Crossref]

L. Gong and H. Wang, “Breaking the diffraction limit by saturation in stimulated-Raman-scattering microscopy: a theoretical study,” Phys. Rev. A 90(1), 013818 (2014).
[Crossref]

W. P. Beeker, C. Lee, K.-J. Boller, P. Groß, C. Cleff, C. Fallnich, H. L. Offerhaus, and J. L. Herek, “Spatially dependent Rabi oscillations: An approach to sub-diffraction-limited coherent anti-Stokes Raman-scattering microscopy,” Phys. Rev. A 81(1), 012507 (2010).
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A. Nikolaenko, V. V. Krishnamachari, and E. O. Potma, “Interferometric switching of coherent anti-Stokes Raman scattering signals in microscopy,” Phys. Rev. A 79(1), 13823 (2009).
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W. Liu and H. Niu, “Diffraction barrier breakthrough in coherent anti-Stokes Raman scattering microscopy by additional probe-beam-induced phonon depletion,” Phys. Rev. A 83(2), 023830 (2011).
[Crossref]

Phys. Rev. Lett. (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (2)

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(46), 16807–16812 (2005).
[Crossref] [PubMed]

L. Wei, Y. Yu, Y. Shen, M. C. Wang, and W. Min, “Vibrational imaging of newly synthesized proteins in live cells by stimulated Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110(28), 11226–11231 (2013).
[Crossref] [PubMed]

Science (5)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322(5909), 1857–1861 (2008).
[Crossref] [PubMed]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330(6009), 1368–1370 (2010).
[Crossref] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[Crossref] [PubMed]

Other (1)

J. X. Cheng and X. S. Xie, Coherent Raman scattering microscopy, (CRC Press, 2013).

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Figures (6)

Fig. 1
Fig. 1 Schematic diagrams of two different CARS suppression processes. (a) Spontaneous Raman spectrum of liquid benzene. Three-beam (pump-Stokes-depletion) double SRS-CARS suppression processes in the (b) parallel and (c) converging configurations. Two vibrational modes of benzene (ring breathing mode; ωv1 = 992 cm−1 and C-H stretching mode; ωv2 = 3062 cm−1) can be used for generating SRS1 (ωv1 = 992 cm−1) and SRS2 (ωv2 = 3062 cm−1) processes simultaneously (see the main text for more details).
Fig. 2
Fig. 2 SRL spectral changes (a, c) and SRL efficiencies (b, d) of liquid benzene as the increase of the depletion pulse energy (from 0 to 100 nJ) in the parallel and converging configurations.
Fig. 3
Fig. 3 CARS spectral changes of liquid benzene as the increase of depletion pulse energy (Ed) in the (a) parallel and (d) converging configurations. The resonant (992 cm−1) and non-resonant (2072 cm−1) p-s-p CARS spectra in the red boxes of (a) and (d) are shown in (b) and (e), respectively. (c, f) CARS losses (black circles) and suppression efficiencies (blue squares) as a function of Ed.
Fig. 4
Fig. 4 Calculated CARS suppression efficiencies (η) from Eqs. (4) and (8) in the parallel (black for z = 0.05, blue for z = 0.5) and converging (red for z = 0.05, green for z = 0.5) configurations; gd = 1, gs = 2 and Ip(0) = Is(0).
Fig. 5
Fig. 5 Simulation on non-resonant background-free CARS imaging using the converging geometry-based CARS technique. (a) Differential measurement between CARS1 obtained by using the two (pump and Stokes) beams (upper) and CARS2 obtained by using the three (pump, Stokes, and depletion) beams (lower). All the three beams have Gaussian-shaped intensity profiles. The difference signal (ΔCARS = CARS1 −CARS2) contains vibrationally resonant SRS information of the target molecule. (b) A PS film (width = 2 μm) in water used for CARS imaging. (c) Calculated cross-sections of the CARS images for a PS film in water in (b): CARS1 without depletion (black), CARS2 with depletion (red), ΔCARS (blue) and p-d-p resonant CARS (green).
Fig. 6
Fig. 6 Simulation on super-resolution CARS imaging using the three-beam (pump-Stokes-depletion) double SRS-CARS suppression technique. (a) Differential measurement between dCARS (upper) and gCARS (lower). For the generations of the dCARS and gCARS signals, two Gaussian-shaped pump and Stokes beams combined with a doughnut-shaped (dCARS) and a Gaussian-shaped (gCARS) depletion beam are used. The difference CARS signal (ΔCARS = dCARS1−gCARS) yields an SRS-induced vibrationally resonant signal only at a limited region of the central node of the doughnut-shaped depletion beam. (b, c) Normalized dCARS signals, which is approximately equivalent to ΔCARS, at variable depletion intensities (a = 0, 1, 10, 20, 50) for (b) z = 0.05 and (c) z = 0.5. (d) Comparison between the spatial resolutions of dCARS at a = 50 in the parallel and converging configurations. The dashed lines represent the CARS intensity corresponding to 1/e2 of its maximum value.

Equations (18)

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I p (z)= I p (0)exp( ( g s ω p ω s I s (0)+ g d ω p ω d I d (0)+ g ¯ I p (0) )z ),
g ¯ = [ g s ω p ω s I s (0)+ g d ω p ω d I d (0) ]/ [ ω p ω s I s (0)+ ω p ω d I d (0) ] .
I CARS psp (z)= ( ω CARS ω s σ CARS R ) 2 I p 2 (0) I s (0) 4 ( g s ω p ω s I s (0)+ g d ω p ω d I d (0)+ g ¯ I p (0) ) 2 ( e ( g s ω p ω s I s (0)+ g d ω p ω d I d (0)+ g ¯ I p (0) )z 1 ) 2 ,
η parallel =( 1 ( e ( g s ω p ω s I s (0)+ g d ω p ω d I d (0)+ g ¯ I p (0) )z 1 ) 2 ( e ( g s ω p ω s I s (0)+ g ¯ I p (0) )z 1 ) 2 ( g s ω p ω s I s (0)+ g ¯ I p (0) ) 2 ( g s ω p ω s I s (0)+ g d ω p ω d I d (0)+ g ¯ I p (0) ) 2 ).
I p(s) (z)= I p(s) (0)exp( g p(s)d ( I d (0)+ ω d ω p(s) I p(s) (0) )z ),
z I CARS NRpsp (z)=( ω CARS NRpsp ω p ) σ CARS NR I p (0) I s (z) I CARS NRpsp (z) ,
I CARS NRpsp (z)= ( ω CARS NRpsp ω p σ CARS NR ) 2 I p 2 (0) I s (0) 4 ( g pd ( I d (0)+ ω d ω p I p (0) )+ g sd 2 ( I d (0)+ ω d ω s I s (0) ) ) 2 × ( e ( g pd ( I d (0)+ ω d ω p I p (0) )+ g sd 2 ( I d (0)+ ω d ω s I s (0) ) )z 1 ) 2 ,
η converging =1 ( g pd ω d ω p I p (0)+ g sd 2 ω d ω s I s (0) ) 2 ( g pd ( I d (0)+ ω d ω p I p (0) )+ g sd 2 ( I d (0)+ ω d ω s I s (0) ) ) 2 × ( exp[ ( g pd ( I d (0)+ ω d ω p I p (0) )+ g sd 2 ( I d (0)+ ω d ω s I s (0) ) )z ]1 ) 2 ( exp[ ( g pd ω d ω p I p (0)+ g sd 2 ω d ω s I s (0) )z ]1 ) 2 .
γ p(s) = | Δ I p(s) | I p(s) ( I d (0)=0) =1exp[ A I d (0) ],
γ CARS psp = | Δ I CARS psp | I CARS psp ( I d (0)=0) .
I j (x,r)= I j,0 exp( 2 ( rx ) 2 ( λ j /2 ) 2 ).
I CARS NRpsp (x,z) dr ( σ CARS NR (x) ) 2 I p 2 (x,r) I s (x,r) ( ω d ω p I p (x,r)+ ω d ω s I s (x,r)+2 I d (x,r) ) 2 × ( e ( ω d ω p I p (x,r)+ ω d ω s I s (x,r)+2 I d (x,r) )z 1 ) 2 .
I CARS pdp (x,z) ( σ CARS R + σ CARS NR ) I p 2 (x,r) I d (x,r) z 2 dr.
I p (0,r)= I p,0 exp( 2 r 2 ( λ s /2 ) 2 ),
I s (0,r)= I s,0 exp( 2 r 2 ( λ s /2 ) 2 ),
I d (0,r)= I d,0 ( r λ d /2 ) 2 exp( 2 r 2 ( λ d /2 ) 2 ),
I j (0)= I j (0,r)dr ,
I CARS NRpsp (r,z) I p 2 (0,r) I s (0,r) ( g pd ( I d (0,r)+ ω d ω p I p (0,r) )+ g sd 2 ( I d (0,r)+ ω d ω s I s (0,r) ) ) 2 × ( e ( g pd ( I d (0,r)+ ω d ω p I p (0,r) )+ g sd 2 ( I d (0,r)+ ω d ω s I s (0,r) ) )z 1 ) 2 .

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