1. INTRODUCTION

Optical microscopy provides us with rich physical and chemical information concerning living cells and tissues at sub-micrometer spatial resolutions. In particular, fluorescence microscopy has served as an invaluable tool in biomedical science due to its high detection sensitivity, high affinity, and specificity for molecular targets of interest. Despite these advantages, the use of fluorescent labels for targeting small-mass molecules (less than 300 Da) is often problematic. This is because most fluorescent labels are bulky, and the labels may alter the biological activity of the targeted small molecules [1]. Another approach is to use a label-free vibrational contrast, such as Raman scattering [2] or infrared absorption [3], which allows us to record molecular-specific spectral signatures. For observing intact living organisms, Raman scattering is preferred because it is hardly affected by water absorption and provides sub-cellular spatial resolution. A key challenge to standard Raman imaging is how to increase the speed, that is, how to obtain more signal photons than background photons, because spontaneous Raman scattering is generally much weaker than fluorescence.

Coherent Raman scattering microscopy [4–6], an emerging imaging technology using nonlinear optical effects, such as coherent anti-Stokes Raman scattering (CARS) [7,8] or stimulated Raman scattering (SRS) [9–11], has increasingly gained attention due to its enhanced sensitivity. By enhancing the Raman signal via coherent amplification with ultrafast laser pulses, the sensitivity can be significantly improved by up to several orders of magnitude. CARS and SRS imaging have been successfully applied to various studies, such as lipid biology [12], transdermal pharmacokinetics [13,14], and non-labeled histopathology [15,16].

One practical issue for coherent Raman microscopy is related to its complicated laser system. The coherent Raman process occurs through optical excitation via the beating of two incident pulses at a specific Raman-resonant frequency ${\mathrm{\Omega }}_R={\omega }_{\text{pump}}-{\omega }_{\text{Stokes}}$, where ${\omega }_{\text{pump}}$ and ${\omega }_{\text{Stokes}}$ are the angular frequencies of the pump and Stokes pulses, respectively. To implement this system, therefore, one has to prepare a perfectly synchronized, two- or multi-wavelength, widely tunable pulsed laser source, such as an optical parametric oscillator [17], or an additional frequency broadening via an optical fiber [18,19]. This complexity has made it difficult for non-physics researchers to take advantage of coherent Raman technology.

An alternative, simpler approach is single-beam multiplexed CARS microscopy [20–25]. Instead of aiming at a specific Raman frequency with two-color narrowband pulses, one can excite and detect multiple Raman modes simultaneously using a single broadband laser source. In addition to improved simplicity and robustness, impulsive excitation has proven particularly efficient in the low-wavenumber spectral region due to pump–Stokes degeneracy, where the Raman modes exist within the broadband laser bandwidth. With this approach, we have developed a single-beam phase-modulated CARS microscope [20] and have successfully demonstrated a direct label-free detection of small molecules (the Raman peak of taurine at approximately $1033{\mathrm{cm}}^{-1}$) inside a mouse cornea tissue using time-resolved heterodyne detection [21]. However, the detection sensitivity of previous single-beam CARS microscopy has been limited compared to that of multi-beam CARS or SRS systems.

Theoretically, the signal-to-noise ratio (SNR) of coherent Raman microscopy in the shot-noise-limited regime is proportional to the pump power times the root square of the probe power ($I_{\text{pump}}{I}_{\text{probe}}^{0.5}$) [6,11], and it reaches its highest value when the pump-to-probe power ratio is set to 2:1. In most single-beam CARS setups, however, the power of the probe beam is much smaller than desired. This is because there is a trade-off between the spectral resolution and the sensitivity. The spectral resolution of single-beam CARS is limited by the effective bandwidth of the probe beam, which is determined by the bandwidth of the filter element used for pump–probe separation, such as a bandpass filter [20,21], a spectral phase modulation gate [22,23], or a notch filter [24]. However, given a broadband mode-locked oscillator with a smoothed spectral power-density profile used as a single-beam source, directly reducing the probe bandwidth to obtain a high spectral resolution results in the reduced power of the probe. Consequently, the SNR available in a conventional single-beam CARS setup has been restricted by unbalanced pump-to-probe power ratios.

In this paper, we propose a single-beam phase-modulated stimulated Raman scattering (PM-SRS) microscopy with improved sensitivity. We overcame the above mentioned trade-off using a novel pulse-shaping technique, which we refer to as spectrally focused detection. Spectral focusing is known to be a method for generating a narrowband pulse from broadband, frequency-locked pulses. This strategy has been widely used in a variety of nonlinear optics applications, such as terahertz pulse generation [26], sum frequency generation [27], and coherent Raman scattering measurements [28,29]. Here, our basic idea is to use spectral focusing for selective spectroscopic detection rather than for narrowband nonlinear excitation. We prepare a pair of frequency bands for probe pulses: one is phase modulated, and the other is used as a strong local oscillator (LO) for optical heterodyne detection. While using efficient impulsive excitation and allocating a relatively large bandwidth to the probe pulses to improve the sensitivity, we can still obtain a spectral resolution smaller than the probe bandwidth with the help of spectral focusing via frequency-locked probe pulses.

Here, we present the system design and characterization of our first prototype of a single-beam PM-SRS microscope with spectral-focusing detection. We also demonstrate a non-labeled spectroscopic imaging of a lightweight anesthetic drug. The new single-beam scheme presented here is a potentially powerful and robust method for detecting the Raman signals of small drug molecules in living cells and tissues.

2. METHODS

A. Phase-Modulated Stimulated Raman Scattering

Figure 1 shows the schematics of amplitude-modulated SRS (AM-SRS) and PM-SRS. An SRS signal is observed via constructive or destructive spectral interference between a coherent Raman field and an LO field, namely, stimulated Raman gain (SRG) and stimulated Raman loss (SRL) [Fig. 1(a)]. In commonly used two-color AM-SRS, the intensity of either the pump or Stokes beams is modulated [Fig. 1(b)]. The intensity-modulated and non-modulated beams are combined such that the two-color pulses are spatially and temporally overlapped, generating an interference fringe in the ultrafast time domain [Fig. 1(c)]. When the beating frequency between the two-color pulses, ${\omega }_{\text{pump}}-{\omega }_{\text{Stokes}}$, matches the Raman resonant frequency ${\mathrm{\Omega }}_R$ of a sample, the incident pulses actively drive the molecular vibration. Here, the two pulses are used not only for excitation, but also for probing the vibration via self-heterodyne detection. Owing to this excitation-detection degeneracy, the relative phase of the pump and Stokes pulses is always cancelled out, and eventually, a fixed phase lag ($\mathrm{\Delta }\varphi =0$ or $\mathrm{\Delta }\varphi =-\pi$ on Raman resonance) is left between the induced coherent Raman field and the LO field. This explains why an AM-SRS output signal is synchronized with the AM input regardless of the relative phase between the pump and Stokes pulses.

 

Fig. 1. Schematics of the SRS processes: (a)–(c) amplitude-modulated SRS (AM-SRS) and (d)–(f) phase-modulated SRS (PM-SRS). (a), (d) Frequency allocation and output intensity modulation, (b), (e) pulse train and radio-frequency modulation diagram, and (c), (f) temporal pulse intensity and effective refractive index change in the ultrafast regime. The non-resonant background contribution is not illustrated here for brevity.

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In the single-beam PM-SRS scheme, however, we divide a broadband laser spectrum into three frequency bands for the pump, PM probe, and LO probe pulses [Fig. 1(d)]. Instead of modulating the intensity, we apply a periodic saw-wave PM input from $-\pi$ to $\pi$ and, therefore, a virtually linear phase to the PM probe pulses [Fig. 1(e)]. Our single-beam PM-SRS is based on a pump–probe configuration [Fig. 1(f)]. The pump frequency band shown in Fig. 1(d) is used to generate a femtosecond pulse for impulsive excitation, exciting multiple molecular vibration modes simultaneously. From a classical perspective, each vibrational response to the impulsive excitation field $E_{\text{pump}}$ can be expressed as the temporal modulation of the effective refractive index. When the pulse width ${\tau }_{\text{pump}}$ is much shorter than the lifetime of the vibrational relaxation ${\tau }_R({\tau }_{\text{pump}}\ll {\tau }_R)$, the vibrational response $\mathrm{\Delta }n(t)$ is approximately given as

The coherent excitation is then followed by the PM probe ($E_{\mathrm{PM}}$) and the LO probe ($E_{\mathrm{LO}}$), as illustrated in Fig. 1(f). From multiply excited Raman modes, a targeted Raman frequency of ${\mathrm{\Omega }}_R$ is selectively probed by a phase-to-intensity conversion process using two-beam coupling via Raman-induced refractive index modulation in the temporal domain. When the probe frequencies ${\omega }_{\mathrm{PM}}$ and ${\omega }_{\mathrm{LO}}$ are tuned such that ${\mathrm{\Omega }}_R={\omega }_{\mathrm{PM}}-{\omega }_{\mathrm{LO}}$, and the probe pulse width $\mathrm{\Delta }{\tau }_{\mathrm{pr}}$ satisfies $\mathrm{\Delta }{\tau }_{\mathrm{pr}}/2{\tau }_R<1$, the PM-SRS signal $\mathrm{\Delta }{I}_{\mathrm{SRS}}$ detected at the LO probe band is derived to be

The signal detection mechanism represented by Eq. (2) can be regarded as heterodyne coherent Stokes Raman scattering (CSRS). In fact, the PM-SRS presented here is described as a special case of the dissipative coherent Raman process where heterodyne CARS and CSRS occur simultaneously. The resultant energy exchange between the two probe pulses is essentially equivalent to SRG and SRL. A clear difference from conventional AM-SRS is that the relative phase between the coherent Raman and LO fields ($\mathrm{\Delta }\varphi =2\pi f_{\mathrm{PM}}{t}_{\mathrm{PM}}+\mathrm{\Delta }{\varphi }_{\text{offset}}$) is not cancelled out in the pump–probe configuration. The Raman gain and loss is therefore alternately observed depending on the relative phase [Fig. 1(d)]. As a result, the PM-SRS output signal is synchronized with a $2\pi$ saw-wave PM input [Fig. 1(e)]. More detailed quantum descriptions of this heterodyne detection scheme have been discussed in Refs. [4,30,31].

The AC intensity signal modulated at the PM frequency $f_{\mathrm{PM}}$ can be extracted as an output via lock-in detection (or demodulation). This modulation transfer scheme significantly reduces low frequency noise and improves the detection sensitivity performance. Moreover, the PM-SRS system is robust against phase fluctuations from thermal drift or the vibrations of the optics because the AC modulus output (the R-output of a lock-in amplifier) is insensitive to the phase offset, $\mathrm{\Delta }{\varphi }_{\text{offset}}$. This is achieved only when we apply a $2\pi$ saw-wave or a linear phase modulation; any nonlinear PM input (e.g., sinusoidal modulation with resonant drive electronics) would generate spurious harmonic components that would severely impair the signal stability.

B. Spectrally Focused Detection

In a previous single-beam heterodyne CARS spectroscopy, a portion of a Fourier-transform-limited pulse (the non-resonant emission or excitation field itself) has been used as an LO, and a narrowband probe has been used to resolve the multiply excited Raman modes [20–25]. Our alternative strategy is to recover the unbalanced pump–probe power ratio due to the use of a narrowband probe by allocating a wide bandwidth to the PM and LO probe bands and by manipulating the spectral phase. Here, we show that spectrally focused detection with shaped probe pulses provides highly sensitive Raman signal detection with an improved spectral resolution.

Suppose we measure a specimen with Raman spectrum ${\chi }^{(3)}(\mathrm{\Omega })$, and the targeted molecule is excited by the pump field $E_{\text{pump}}(\mathrm{\Omega })$. The refractive index modulation induced by the excited molecular vibration can be described as

This trade-off can be circumvented by shaping the spectral phase of the two probes. As indicated in Eq. (5), the key requirement is that the frequency width of the probe cross correlation be smaller than that of the bandwidth-limited resolution. To obtain a sharp cross correlation of the probe pulses, we take the spectral focusing approach sketched in Fig. 2. Here, we assume the simplest spectral focusing scheme, where the same amount of linear chirp and group delay are applied to both probe bands. When the probe beat frequency matches the Raman resonant frequency ($\mathrm{\Delta }{\mathrm{\Omega }}_R={\omega }_{\mathrm{PM}}-{\omega }_{\mathrm{LO}}-{\mathrm{\Omega }}_R=0$), the induced coherent Raman field $E_{\mathrm{SRS}}(\omega )$ is perfectly phase matched with the LO field $E_{\mathrm{LO}}(\omega )$ [Fig. 2(a)]. Therefore, the spectral interference $\mathrm{\Delta }{I}_{\mathrm{SRS}}(\omega )$ becomes in-phase over the entire LO band, and the probe cross correlation $R_{\mathrm{CC}}(\mathrm{\Omega })$ reaches its maximum [Fig. 2(b)]. When the probe beat frequency is detuned ($\mathrm{\Delta }{\mathrm{\Omega }}_R\ne 0$), the frequency of the induced field $E_{\mathrm{SRS}}(\omega )$ is de-centered by $\mathrm{\Delta }{\mathrm{\Omega }}_R$, and a relative delay is generated between $E_{\mathrm{LO}}(\omega )$ and $E_{\mathrm{SRS}}(\omega )$ [Fig. 2(c)]. This delay, $\mathrm{\Delta }{\tau }_{\mathrm{SI}}$, leads to a spectral interference fringe [Fig. 2(d)]. The net integrated SRS signal described in Eq. (5) then sharply decreases with the frequency mismatch. The frequency pitch of the spectral interference is given as

 

Fig. 2. Spectrally focused detection scheme: (a) group delay diagram of a perfectly frequency-matched detection where $\mathrm{\Delta }{\mathrm{\Omega }}_R=0$, (b) spectral interference corresponding to case (a) providing maximal SRS output, (c) group delay diagram of a detuned case where $\mathrm{\Delta }{\mathrm{\Omega }}_R\ne 0$, and (d) spectral interference corresponding to case (c), where the net SRS signal integrated over the LO band is cancelled out.

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From this expression, we find that the spectral resolution can be improved by providing a sufficiently large GDD to the probe pulses. For example, if a probe centered at 780 nm with a bandwidth of 10 nm (corresponding to $\mathrm{\Delta }{\mathrm{\Omega }}_{\mathrm{pr}}=164{\mathrm{cm}}^{-1}$) is linearly chirped by a GDD of $\beta =50000{\mathrm{fs}}^2$, we can obtain a fine spectral resolution of $\mathrm{\Delta }{\mathrm{\Omega }}_R=21.5{\mathrm{cm}}^{-1}$. This indicates that we can allocate a larger bandwidth without losing spectral resolution by using spectrally focused detection, enabling the efficient use of the energy budget of the single-beam setup.

C. Single-Beam PM-SRS Microscope

The single-beam PM-SRS microscope system consists of a single broadband Ti:sapphire laser (Vitara, Coherent: 80-MHz repetition rate, 15-fs pulse width, centered at 790 nm), a newly developed phase control unit and microscope, and monochromator optics for signal detection (Fig. 3).

 

Fig. 3. Single-beam PM-SRS microscope (CM: chirp mirrors, VHG: volume holographic grating, SLM: spatial light modulator, OI: optical isolator, PBS: polarizing beam splitter, BPF: bandpass filter, EOM: electro-optic phase modulator, $\lambda /4$: quarter-wave plate, HM: half mirror, OL1 and OL2: objective lenses, S: sample, C: camera, SL: variable slit on a translational stage, and PD: photodetector).

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The former part of the phase control unit is standard dispersion compensation optics that contain chirped mirrors for GDD compensation and a 4f pulse shaper with an SLM (LCOS-SLM, X10468-02, Hamamatsu: 800 pixel) for higher-order dispersion compensation (see Appendix A for details). Another important role of the SLM pulse shaper is arbitrary frequency allocation and pulse shaping of the LO band. The LO probe band (centered at between 790 nm and 860 nm, 10 nm bandwidth) is defined as the frequency region in which the spectral phases (delay, linear, and nonlinear chirp) are manipulated to perform the spectrally focused detection.

The latter part of the phase control unit is for high-speed phase modulation of the PM probe. The pulses in the PM probe band, which is defined as the passband of a bandpass filter [FBH780-10, Thorlabs: centered at 780 nm with a 10-nm bandwidth ($164{\mathrm{cm}}^{-1}$)], are phase modulated by an electro-optic modulator (EOM) (EO-PM-NR-C1, Thorlabs). The EOM is driven by a high-voltage saw-wave input modulated at 35 kHz with a rise–fall duty of 95%, generating a virtually linear $2\pi$-phase modulation. The temporal delay of the PM probe is adjusted by moving the end mirror of the PM probe, whereas that of LO probe is adjusted by giving the equivalent first-order spectral phase on the SLM. The same delay value ${\tau }_{\mathrm{pr}}$ is provided to both the PM and LO probe pulses. The PM probe and the reflected pump pulses (including the LO probe) are re-combined at the same bandpass filter and focused onto a sample via a microscope objective lens (M Plan Apo NIR $100\times$ NA 0.50, Mitsutoyo).

After the transmitted pulses are collimated by a second identical objective lens, the LO frequency band for the SRS output is selectively extracted via 4f monochromator optics to increase the SNR. The detection bandwidth and the center frequency are tuned with a variable slit on a translational stage at the intermediate Fourier plane. The filtered pulses are detected using a silicon PD (Newfocus 2031, Newport). The PD output is demodulated by a lock-in amplifier (LIA) (LI 5640, NF Corporation), followed by simultaneous recording of the DC and the LIA outputs with a digitizer (USB-6009, National Instruments) that provides the transmission and the PM-SRS images, respectively. Laser scanning is performed by driving an XYZ-positioning sample stage. The stage scanning, signal acquisition, and SLM phase manipulation are controlled using the Labview platform (National Instruments).

3. RESULTS

A. Selective Spectroscopic Detection

First, we evaluated the spectral resolution of the PM-SRS microscopy with the spectrally focused detection. Pure dimethyl sulfoxide (DMSO) enclosed in a quartz cuvette was used as a test sample. The SRS spectrum was acquired by scanning the center frequency of the LO band ${\omega }_{\mathrm{LO}}$, which was done by simply changing the SLM phase pattern. The detection bandwidth of the monochromator optics was set equal to the probe bandwidth ($164{\mathrm{cm}}^{-1}$), and the center frequency was synchronously tuned with the SLM frequency scan to increase the SNR.

To achieve a high spectral resolution, we designed and manipulated the spectral phase of the PM and LO probe pulses. In the PM probe band, a temporal delay was added by directly changing the optical path length, and linear and nonlinear chirps were passively provided by the band-pass filter. Therefore, no SLM-based manipulation was added to the PM probe (see Appendix A). In the LO probe band, the delay, linear, and nonlinear chirps were fully controlled by the SLM pulse shaper. To reproduce the measured phase profile of the PM probe shown in Fig. 8(a), a GDD of $+45000{\mathrm{fs}}^2$ and a third-order dispersion (TOD) of $+3.6\times {10}^6{\mathrm{fs}}^3$, which was derived by a polynomial fitting of the PM probe phase, were added to the LO probe. The delay of both the probes was set to ${\tau }_{\mathrm{pr}}=730\mathrm{fs}$.

Figure 4(a) plots the spectrum obtained with the spectrally focused detection. We can see a sharp Raman peak of DMSO at $665{\mathrm{cm}}^{-1}$. The full-width at half-maximum (FWHM) of the Raman peak is estimated to be $25{\mathrm{cm}}^{-1}$, which corresponds to a $6.6\times$ higher spectral resolution compared to the probe bandwidth. This result roughly agrees with the theoretical resolution expressed in Eq. (10) ($\mathrm{\Delta }{\mathrm{\Omega }}_R=23.9{\mathrm{cm}}^{-1}$ ($28.7{\mathrm{cm}}^{-1}$ in FWHM) for $\mathrm{\Delta }{\mathrm{\Omega }}_{\mathrm{pr}}=164{\mathrm{cm}}^{-1}$ and $\beta =+45000{\mathrm{fs}}^2$).

 

Fig. 4. PM-SRS spectrum of pure DMSO detected by the spectrally focused detection: (a) with the high-resolution setting derived by the polynomial fitting of the PM probe phase profile shown in Fig. 8(a) (delay: 730 fs, GDD: $+45000{\mathrm{fs}}^2$, TOD: $+3.6\times {10}^6{\mathrm{fs}}^3$, detection bandwidth: $164{\mathrm{cm}}^{-1}$) and (b) with the defocused setting (squares) (delay: 1530 fs, GDD: $+70000{\mathrm{fs}}^2$, TOD: $+5.0\times {10}^6{\mathrm{fs}}^3$, detection bandwidth: $125{\mathrm{cm}}^{-1}$). The spectrum measured with non-shaped LO pulses is also shown (triangles).

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Even though we successfully achieved an improved spectral resolution in terms of the FWHM, some residual non-resonant background (approximately 7% of the Raman peak intensity) was still visible in the off-resonant region. In addition, we observed an unwanted spectral sidelobe near the Raman peak. To reduce the background and the sidelobe, we provided a larger delay (1530 fs) to the probes and a larger GDD ($+70000{\mathrm{fs}}^2$) and TOD ($+5.0\times {10}^6{\mathrm{fs}}^3$) to the LO band to “defocus” the spectral selectivity. The detection bandwidth of the monochromator was reduced to $125{\mathrm{cm}}^{-1}$ because the frequency near the filter edges provided little contribution to the SRS signal in this case. Using this defocused setting, we obtained a smooth Raman spectrum profile with a spectral resolution of $60{\mathrm{cm}}^{-1}$ in FWHM [Fig. 4(b)]. We confirmed that using a non-shaped LO probe results in a reduced resolution close to bandwidth limited ($120{\mathrm{cm}}^{-1}$). The spectrally focused detection in this case still provided an improved resolution by a factor of 2 compared to non-shaped probing. We also confirmed that the non-resonant background was suppressed down to 1.5% in the off-resonant region due to the larger probe delay.

While giving a larger delay could further increase the signal-to-background ratio [32] and improve the detectability, it would also reduce the absolute signal level [Eq. (2)] and degrade the imaging speed. In practice, therefore, it is important to optimize the probe delay depending on the application.

In designing the spectrally focused probes, note that the achievable spectral resolution and delay time of the LO probe are limited by the finite spatial bandwidth of the 4f pulse shaper (Appendix B). The cutoff delay time, at which the space–time coupling loss (or the vignette at the objective lens) reaches 50%, is 2.2 ps in the current setup. Higher spectral resolutions will be available when using a high-resolution SLM and 4f optics with a sufficient spatial bandwidth.

B. PM-SRS Signal versus Chemical Concentration

To quantify the detection sensitivity of PM-SRS, we measured the SRS signal intensity for different concentrations of DMSO in water. The exposure powers of the pump (including the LO band) and the PM probe pulses on the sample were 26 and 3.0 mW, respectively. The measured SRS signal level was proportional to the square of the total incident power (Appendix C). The pulse-shaping parameters used in this experiment were the same as those used in Fig. 4(b).

Figures 5(a) and 5(b) depict the calibration curves derived from the recorded SRS signal intensities at $670{\mathrm{cm}}^{-1}$. An excellent linear dependence of the SRS signal on the concentration, which is the advantage of using a strong LO field, was successfully confirmed. Note that the error bars in Figs. 5(a) and 5(b) represent the residual non-resonant background intensity (measured between 500 and $540{\mathrm{cm}}^{-1}$) that causes stationary spectral interference with the resonant Raman signal. The temporal fluctuation (or RMS noise level) of the SRS output in this measurement was in the order of ${10}^{-7}$ (with a 1-s integration time), which hardly affects the total amount of error. At 1.0% DMSO (140 mM), we obtained a signal-to-background ratio of 2.0. The corresponding PM-SRS signal and background levels in the AC/DC intensity ratio ($\mathrm{\Delta }I/I_{\mathrm{LO}}$) were $2.4\times {10}^{-6}$ and $1.2\times {10}^{-6}$, respectively. From the result, the limit of the detectability at which the signal-to-background ratio reaches unity is estimated to be 0.5% (70 mM).

 

Fig. 5. SRS signal versus DMSO concentration in water: (a) all the measured data (dots) and the linear fit calibration curve (dotted line) and (b) an enlarged view of the low concentration region. The error bars represent the stationary interference background on off-resonant frequencies.

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C. Vibrational Imaging

To demonstrate the non-labeled imaging capability of the PM-SRS microscope, we imaged a transparent droplet of pure sevoflurane, an inhaled anesthetic drug, in water. In the vibrational imaging experiment, a small amount of liquid sevoflurane and water was injected and enclosed into a quartz cuvette, and the sample was placed on the laser focal plane. A two-dimensional near-infrared transmission image and an SRS image (image size: $200\mathrm{pixels}\times 200\mathrm{pixels}$, field of view: $100\mathrm{\mu m}\times 100\mathrm{\mu m}$) were simultaneously captured using XY-raster stage scanning with a linear velocity of $0.5\mathrm{mm}/\mathrm{s}$. A total of 2000 samples were sequentially acquired along the $X$-direction with a sampling rate of 10 kHz and then reduced to 200 pixels by $10\times$ binning (pixel integration time: $1\mathrm{ms}/\text{pixel}$), where the time constant of the LIA output was 0.1 ms. The number of lines along the $Y$-direction was 200 (0.5-μm steps).

Figure 6(a) depicts the vibrational spectrum of sevoflurane measured by PM-SRS, where the pulse shaper settings were similar to those used in Fig. 4(b) (delay: 1120 fs, GDD: $+70000{\mathrm{fs}}^2$, TOD: $+5.0\times {10}^6{\mathrm{fs}}^3$, detection bandwidth: $110{\mathrm{cm}}^{-1}$). The Raman resonance peak of sevoflurane was observed at approximately $730–740{\mathrm{cm}}^{-1}$. The peak SRS signal level and water background level (primarily from modulated non-resonant background) were $\mathrm{\Delta }I/I=3.0\times {10}^{-5}$ and $\mathrm{\Delta }I/I=1.5\times {10}^{-6}$, respectively.

 

Fig. 6. PM-SRS imaging of a droplet of an anesthetic drug (sevoflurane) in water: (a) PM-SRS spectrum of sevoflurane (blue squares) and water (red circles), (b) near-infrared transmission image, (c) raw on-resonant SRS image at $730{\mathrm{cm}}^{-1}$, (d) normalized SRS image at $730{\mathrm{cm}}^{-1}$, and (e) normalized off-resonant SRS image at $620{\mathrm{cm}}^{-1}$. No spatial filtering was used in the images. The scale bar is 20 μm.

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Figure 6(b) shows a near-infrared transmission image (DC output). We observed a strong negative contrast around the droplet attributable to the difference in the refractive index between sevoflurane and water. Figure 6(c) shows a raw SRS output image captured at the resonant frequency ($730{\mathrm{cm}}^{-1}$). Even though a clear vibrational contrast was obtained at this point, the negative contrast was still reflected in the raw SRS image as shown in Fig. 6(c). Nevertheless, in a ratio SRS image normalized by the DC output shown in Fig. 6(d), such a negative-contrast artifact was successfully removed. The SNR of the normalized SRS image (defined as the ratio between the averaged SRS signal in the sevoflurane droplet region and the standard deviation in the water background region) was calculated to be 6.2. The vibrational contrast disappeared in the off-resonant image ($620{\mathrm{cm}}^{-1}$), as shown in Fig. 6(d), which clearly demonstrates the molecular-specific imaging capability of this modality.

4. DISCUSSION

Our PM-SRS setup has several advantages over previous single-beam CARS systems:

It is worth noting that recent investigations of a spectrally tailored single-beam CARS system (Brückner et al. [33,34]) have reported improved spectral resolution and sensitivity (i) and time-resolved detection (iv), although the quantification capability and detectability are still limited because it is based on homodyne CARS.

Another advantage of the PM-SRS imaging system is the compatibility with our previously reported single-beam CARS spectroscopy [20,21], which is also based on impulsive excitation and heterodyne detection. This compatibility is important because it allows us to work on imaging and spectroscopy studies on the same platform. In addition, the impulsive excitation setup can be upgraded to a multiplex SRS imaging system by simply replacing the monochromator with multiple bandpass filters.

Our single-beam PM-SRS microscope is aimed at detecting a small-molecule drug hidden behind the background noise in living cells or tissues. In a biological setup, the detectability of standard CARS and SRS is still limited to tens of mM or more [5]. Detecting sub-mM concentrations is strongly desired, yet currently only achieved by imaging coupled with small Raman tags that have a resonant peak in a cell-silent spectral region [35]. A time-resolved, pump–probe method seems to be the most promising strategy to suppress the Raman-background from macromolecules in a non-labeled manner.

The major limitation of the current prototype is the residual non-resonant background ($\mathrm{\Delta }I/I\sim {10}^{-6}$) whose amplitude is proportional to the temporal pump–probe overlap, $E_{\text{pump}}{E}_{\text{pump}}^{*}{E}_{\mathrm{PM}}$. In the present study, we focused on impulsive excitation to achieve the highest excitation efficiency for low-wavenumber Raman modes. The modulated non-resonant background could be further reduced by combining the spectrally focused detection with other efficient excitation methods, such as multi-pulsed excitation by sinusoidal spectral-phase modulation [36] or phase-coded excitation [37]. Targeting high-wavenumber modes ($>2500{\mathrm{cm}}^{-1}$) can also be achieved by using a sub-10-fs broadband laser [19,33,34]. Another technical task is to reduce the sidelobe level in the cross-correlation trace. One can find that the presented selective detection scheme based on cross correlation is a spectral analogue of the matched filtering technique, which has been used in a variety of fields, including radar systems [38] and optical image correlators [39]. Further suppression of the background and sidelobe could be achieved using a more sophisticated matched-filter design.

Time-resolved SRS spectroscopy has been used to probe vibrational modes in the excited electronic states of pigments or fluorescent molecules [40], where the first pulse is used for electronic excitation and the second and third pulses are used for SRS measurements. In PM-SRS, by contrast, only the Raman modes excited by the pump pulse are probed, whereas self-induced Raman modes excited by the PM and LO probe pulses are rejected. In fact, the latter self-heterodyned SRS effect does occur in our PM setup. However, it simply results in a DC intensity offset and provides no observable AC signal. Therefore, PM-SRS probes purely time-resolved Raman signals, which have never been achieved by conventional AM-SRS. Even though delaying the probes reduces the overall sensitivity to some extent, the detectability (or the signal-to-background ratio) of drug molecules with a long relaxation lifetime (a few ps or more) could be substantially improved.

Another background mechanism that may limit detectability in standard SRS microscopy includes AM-induced backgrounds, such as cross-phase modulation, photo-thermal lensing effects, and transient absorption [41]. In PM-SRS, however, such an AM-induced artifact is estimated to be negligibly small because the measured intensity modulation of the PM probe is in the order of ${10}^{-3}$.

5. CONCLUSIONS

In conclusion, we have developed a new single-beam coherent Raman microscope and characterized its performance, including its spectral selectivity, sensitivity, detectability, and vibrational imaging capability. The mechanism of the pump–probe SRS technique, which we refer to as PM-SRS, is understood to be a special case of the dissipative coherent Raman process, where non-self-heterodyned CARS and CSRS occur simultaneously.

The trade-off between sensitivity and spectral resolution, which has restricted the use of single-beam coherent Raman microscopy, has been overcome by spectrally focused detection with shaped probe pulses. We demonstrated that this new selective detection scheme provides a fine spectral resolution ($25{\mathrm{cm}}^{-1}$ in our current setup), even when combined with efficient impulsive excitation. Like AM-SRS, the modulation transfer scheme using high-speed phase modulation provides high SNR and the heterodyne SRS detection ensures an excellent linear relationship between the signal and the chemical concentration. In a proof-of-concept imaging experiment, the molecular-specific vibrational contrast of a transparent anesthetic drug was successfully visualized. These results are supported by precise on-sample pulse measurement and a flexible spectral phase control technique that can be implemented with a standard SLM-based pulse shaper. We anticipate that the presented time-resolved SRS scheme could potentially improve the detectability of non-labeled coherent Raman microscopy.

APPENDIX A: PULSE MEASUREMENTS

Because single-beam coherent Raman microscopy uses a broadband pulse, precise spectral phase measurement and control are essential. In our single-beam PM-SRS setup, the spectral phase of the pump pulse is measured and pre-compensated using multi-photon intra-pulse interference phase scanning (MIIPS), an SLM-based pulse measurement method [42]. The advantage of MIIPS over other measurement techniques is its on-sample measurement capability, which is particularly desirable in nonlinear microscopy applications.

In MIIPS measurements, a type-I BBO crystal is placed on the sample plate, and the sum-frequency generation (SFG) intensity is recorded with a spectrometer (USB2000, Ocean Optics). Careful calibrations of the SLM and the spectrometer were performed prior to the measurements. In addition, before a direct on-sample measurement, we confirmed that even a strong negative chirp was successfully compensated for by MIIPS [Fig. 7(a)]. The residual phase error after the MIIPS compensation relative to a commercial SPIDER system [43] (FC-SPIDER, APE) was 0.36 rad RMS between 750 and 840 nm [Fig. 7(b)], corresponding to a near-transform-limited pulse with a 19.5-fs pulse width. The relative phase error was presumably caused by imperfect $2\pi$ phase wrappings on the SLM due to the limited spatial bandwidth of the 4f optics. In the actual on-sample MIIPS, we can avoid most of the phase wrappings by presetting the chirped mirrors such that the positive GDD of the intermediate optics, and the objective lens is compensated for right at the sample. Therefore, the accuracy of the on-sample MIIPS measurement could be better than the test result shown here. Figure 7(c) plots the SLM input profile that was obtained from the on-sample MIIPS. We can see that no phase wrapping occurred in the scanning range of the LO probe band ($>790\mathrm{nm}$).

 

Fig. 7. Spectral phase compensation by MIIPS. (a) The spectral phase profiles before (dashed line) and after compensation (solid line) and the spectral intensity profile (dotted line) and (b) the phase profile after MIIPS compensation (solid line) compared to that measured with a commercial SPIDER system for reference (dashed line). The test pulses were sampled immediately after the 4f pulse shaper but before the bandpass filter (a silver mirror inserted prior to OI in Fig. 3). The strong negative chirp from the chirped mirrors was successfully compensated. (c) The SLM input level on an 8-bit grayscale after direct on-sample MIIPS compensation (solid line) and the $2\pi$-phase level (dashed line). The LO probe band is not yet allocated. All data here were recorded with the same SLM pattern after five MIIPS iterations.

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In fact, when we initially tried measuring the entire pump pulse using MIIPS, we observed a spurious multi-peaked SFG spectrum and could not obtain the converged output data even after several MIIPS iterations (not shown). From the data analysis, we found that this was caused by the bandpass filter for the pump–probe separation, which had steep phase jumps near the cutoff and cut-on wavelengths. To avoid this error, we separately measured the spectra of the longer wavelength above the cutoff and the shorter wavelength below the cut-on. After both MIIPS measurements (five iterations for each), we further adjusted the relative delay and the zeroth-order phase offset between the longer and shorter pump frequency bands so that the total SFG output reached the maximum. The SLM pulse shaping pattern in Fig. 7(c) was obtained as a result of these procedures.

The spectral phase of the PM probe was measured using a similar on-sample SFG setup; however, this time, we used an alternative algorithm (phase-resolved interferometric spectral modulation: PRISM [44]) that enables high-resolution spectral phase measurements. We confirmed that the PM probe indeed had a strong nonlinear chirp and a steep phase profile near the spectral edges at 775 and 785 nm [Fig. 8(a)], which can be explained by the dispersion characteristics of a Bragg reflector [45]. The temporal pulse shape of the PM probe was also double-checked via SFG cross-correlation measurements, where the relative delay of the near-transform-limited pump and the PM probe was scanned by moving the end mirror of the probe arm. As predicted by the PRISM data, the recorded PM probe pulse had an asymmetric temporal profile [Fig. 8(b)]. The asymmetric pulse had a sharp rise and a long tail toward the delayed time direction. Fortunately, such an asymmetric pulse shape is preferred when probing the Raman vibrational coherence close to the pump pulse while minimizing the non-resonant background. For this reason, we apply no additional phase compensation to the PM probe band, whereas the phase profile of the LO probe band is adjusted to reproduce that of the PM probe.

 

Fig. 8. Characterization of the PM probe pulse. (a) The spectral intensity profile measured by a spectrometer and the phase profile estimated by PRISM. The PRISM output is shown as a dotted line. The SLM (LCOS-SLM, X10468-02, Hamamatsu) had 256 gray levels and 800 pixels at $20\mathrm{\mu m}/\text{pixel}$. The spectral resolution of the SLM near 780 nm was $0.24\mathrm{nm}/\text{pixel}$. The PRISM measurement was performed with $800\text{samples}/\text{group}\times 4\text{groups}=3200\text{samples}$. Each group had randomly selected phase-modulated pixels (200 pixels) and non-modulated pixels (600 pixels). The phase advance per sample in the modulated pixels was uniformly distributed between $\pi /2$ and $\pi$. The PRISM output was obtained by smoothing the raw output data with a 7-pixel median filter and a 5-pixel moving-average filter. The phase profile was further fitted with a fifth-degree polynomial (solid line). (b) The temporal amplitude profile recorded from the SFG cross-correlation measurement (solid line) and the temporal profile calculated from the PRISM data (dashed line). The discrepancy between the two results is seemingly caused by the limited spectral resolution of the 4f pulse shaper optics.

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APPENDIX B: BANDWIDTH OF THE 4F PULSE SHAPER

The available amount of temporal delay and chirp and, in turn, the maximum frequency resolution in a SLM-based 4f pulse shaper is limited by the spatial bandwidth, which is determined by two limiting factors.

The first limitation is related to the spatial frequency bandwidth of the SLM device and is defined as

(B1)$$\mathrm{\Delta }{k}_{\mathrm{SLM}}=\frac{{\lambda }_0}{2d_{\mathrm{SLM}}}{k}_0,$$

where ${\lambda }_0$ is the designed center wavelength of the pulse shaper (${\lambda }_0=800\mathrm{nm}$), $k_0$ is the wavenumber, and $d_{\mathrm{SLM}}$ is the pixel pitch of the SLM ($d_{\mathrm{SLM}}=20\mathrm{\mu m}$). Note that this definition is based on the full pixel resolution (2 pixels per cycle). The corresponding spatial bandwidth is estimated to be $\mathrm{\Delta }{k}_{\mathrm{SLM}}=0.02k_0$.

The second limitation is the spatial bandwidth of the 4f optics, defined as

(B2)$$\mathrm{\Delta }{k}_{4f}=\frac{D_{\text{beam}}}{2f}{k}_0,$$

where $D_{\text{beam}}$ is the incident beam width at the diffraction grating (at VHG in Fig. 3), and $f$ is the focal length of the 4f optics. In our current setup ($d=2.5\mathrm{mm}$, $f=130\mathrm{mm}$), the spatial bandwidth is calculated to be $\mathrm{\Delta }{k}_{4f}=0.01k_0$.

The ratio of the bandwidths, $\mathrm{\Delta }{k}_{4f}/\mathrm{\Delta }{k}_{\mathrm{SLM}}$, gives the spatial beam overlap between the shaped and non-shaped pulses after the pulse shaper, where half of one beam overlaps the other beam when $\mathrm{\Delta }{k}_{4f}/\mathrm{\Delta }{k}_{\mathrm{SLM}}\approx 1.0$. In the current setting, $\mathrm{\Delta }{k}_{4f}/\mathrm{\Delta }{k}_{\mathrm{SLM}}\approx 0.5$, which means that the spatial bandwidth limit is dominated by the 4f optics. This 4f-optics-limited bandwidth of $\mathrm{\Delta }{k}_{4f}=0.01k_0$ corresponds to half of the full SLM resolution (4 pixels per cycle) and determines the spatial frequency cutoff, where the optical throughput decreases by half due to imperfect beam overlap (loss by vignette at the objective pupil). The cutoff spatial frequency is then converted to the cutoff delay time by the following time–space relationship:

(B3)$$\mathrm{\Delta }{\tau }_{\text{cutoff}}=\frac{2\pi f\mathrm{\Delta }{k}_{4f}}{c{k}_0^2}\frac{f_g}{\cos {\theta }_0},$$

where $c$ is the speed of light, $f_g$ is the spatial frequency of the grating ($f_g=600{\mathrm{mm}}^{-1}$), and ${\theta }_0$ is the diffraction angle for the designed center wavelength (${\theta }_0=13.9\mathrm{deg}$). From Eq. (B3), the cutoff delay time of our current setup is derived to be $\mathrm{\Delta }{\tau }_{\text{cutoff}}=2.1\mathrm{ps}$, which agrees well with the measured cutoff delay time (2.2 ps).

APPENDIX C: POWER SCALING AND SNR LIMIT

According to Eq. (2), the SRS output signal is theoretically proportional to $I_{\text{pump}}{I}_{\mathrm{PM}}^{0.5}{I}_{\mathrm{LO}}^{0.5}$ and therefore to the square of the total incident laser power. We validated the quadratic power scaling of the PM-SRS signal by changing the incident beam power with a neural density (ND) filter inserted prior to the microscope. We confirmed that the estimated scaling factor was nearly quadratic ($\mathrm{\Delta }{I}_{\mathrm{SRS}}\sim I_{\text{total}}^{1.98}$) [Fig. 9(a)]. We also verified the linear power scaling of the detection by changing the detected beam power with an ND filter inserted after the microscope, and the result showed a perfectly linear dependence [Fig. 9(b)]. This result confirms that the AC signal (the lock-in amplifier output) normalized by the DC level is proportional to the sample concentration, regardless of the amount of optical loss after the sample focal point.

 

Fig. 9. Power scaling of the PM-SRS signal: (a) lock-in amplifier output signal versus total input power plotted on a log–log scale, showing that the SRS signal is approximately scaled as a quadratic function ($\mathrm{\Delta }{I}_{\mathrm{SRS}}\sim I_{\text{total}}^{1.98}$), and (b) linear dependence of the SRS signal on the detected DC level.

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Note that the detection sensitivity of PM-SRS is ultimately limited by the shot noise of the LO field, which is proportional to $I_{\mathrm{LO}}^{0.5}$. Therefore, the theoretical SNR limit of PM-SRS in the shot-noise-limited regime scales as $\mathrm{SNR}=|\mathrm{\Delta }{I}_{\mathrm{SRS}}|/I_{\mathrm{LO}}^{0.5}\propto I_{\text{pump}}{I}_{\mathrm{PM}}^{0.5}$.

Funding

Japan Agency for Medical Research and Development (AMED).

Acknowledgment

This work was supported by the Japan Agency for Medical Research and Development. The authors thank T. Suzuki and M. Hayashi for the design and development of the instruments and H. Mogi for the helpful technical discussions. The authors are also grateful to M. Kawagishi and S. Terada for valuable suggestions for the experiment.

REFERENCES

1. B. R. Stockwell, “Exploring biology with small organic molecules,” Nature 432, 846–854 (2004). [CrossRef]  

2. G. J. Puppels, F. F. M. de Mul, C. Otto, J. Greve, M. Robert-Nicoud, D. J. Arndt-Jovin, and T. M. Jovin, “Studying single living cells and chromosomes by confocal Raman microspectroscopy,” Nature 347, 301–303 (1990). [CrossRef]  

3. D. Naumann, D. Helm, and H. Labischinski, “Microbiological characterizations by FT-IR spectroscopy,” Nature 351, 81–82 (1991). [CrossRef]  

4. J.-X. Cheng and X. S. Xie, eds., Coherent Raman Scattering Microscopy (Taylor and Francis, 2011).

5. J.-X. Cheng and X. S. Xie, “Vibrational spectroscopic imaging of living systems: An emerging platform for biology and medicine,” Science 350, aaa8870 (2015). [CrossRef]  

6. W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: Beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62, 507–530 (2011). [CrossRef]  

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

8. C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: Chemically selective imaging for biology and medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008). [CrossRef]  

9. 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, 1857–1861 (2008). [CrossRef]  

10. P. Nandakumar, A. Kovalev, and A. Volkmer, “Vibrational imaging based on stimulated Raman scattering microscopy,” New J. Phys. 11, 033026 (2009). [CrossRef]  

11. Y. Ozeki, F. Dake, S. Kajiyama, K. Fukui, and K. Itoh, “Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy,” Opt. Express 17, 3651–3658 (2009). [CrossRef]  

12. X. Nan, J.-X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cell with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44, 2202–2208 (2003). [CrossRef]  

13. 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. Pharmaceutics 8, 969–975 (2011). [CrossRef]  

14. N. A. Belsey, N. L. Garrett, L. R. Contreras-Rojas, A. J. Pickup-Gerlaugh, G. J. Price, J. Moger, and R. H. Guy, “Evaluation of drug delivery to intact and porated skin by coherent Raman scattering and fluorescence microscopies,” J. Control. Release 174, 37–42 (2014). [CrossRef]  

15. P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. 70, 9562–9569 (2010). [CrossRef]  

16. C. W. Freudiger, R. Pfannl, D. A. Orringer, B. G. Saar, M. Ji, Q. Zeng, L. Ottoboni, W. Ying, C. Waeber, J. R. Sims, P. L. De Jager, O. Sagher, M. A. Philbert, X. Xu, S. Kesari, X. S. Xie, and G. S. Young, “Multicolored stain-free histopathology with coherent Raman imaging,” Lab. Invest. 92, 1492–1502 (2012). [CrossRef]  

17. F. Ganikhanov, S. Carrasco, and X. S. Xie, “Broadly tunable dual-wavelength light source for coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 31, 1292–1294 (2006). [CrossRef]  

18. T. W. Kee and M. T. Cicerone, “Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 29, 2701–2703 (2004). [CrossRef]  

19. H. Kano and H. Hamaguchi, “Ultrabroadband (> 2500 cm^-1) multiplex coherent anti-Stokes Raman scattering microspectroscopy using a supercontinuum generated from a photonic crystal fiber,” Appl. Phys. Lett. 86, 121113 (2005). [CrossRef]  

20. T. Suzuki and K. Misawa, “Efficient heterodyne CARS measurement by combining spectral phase modulation with temporal delay technique,” Opt. Express 19, 11463–11470 (2011). [CrossRef]  

21. M. Kawagishi, Y. Obara, T. Suzuki, M. Hayashi, K. Misawa, and S. Terada, “Direct label-free measurement of the distribution of small molecular weight compound inside thick biological tissue using coherent Raman microspectroscopy,” Sci. Rep. 5, 13868 (2015). [CrossRef]  

22. D. Oron, N. Dudovich, and Y. Silberberg, “Single-pulse phase-contrast nonlinear Raman spectroscopy,” Phys. Rev. Lett. 89, 273001 (2002). [CrossRef]  

23. S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803 (2005). [CrossRef]  

24. O. Katz, J. M. Levitt, E. Grinvald, and Y. Silberberg, “Single-beam coherent Raman spectroscopy and microscopy via spectral notch shaping,” Opt. Express 18, 22693–22701 (2010). [CrossRef]  

25. C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40, 809–816 (2009). [CrossRef]  

26. A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137–139 (1994). [CrossRef]  

27. M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,” Appl. Phys. B 73, 273–277 (2001). [CrossRef]  

28. T. Hellerer, A. M. K. Enejder, and A. Zumbusch, “Spectral focusing: High spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. 85, 25–27 (2004). [CrossRef]  

29. D. Fu, G. Holtom, C. Freudiger, X. Zhang, and X. S. Xie, “Hyperspectral imaging with stimulated Raman scattering by chirped femtosecond lasers,” J. Phys. Chem. B 117, 4634–4640 (2013). [CrossRef]  

30. S. Mukamel and S. Rahav, “Ultrafast nonlinear optical signals viewed from the molecule’s perspective: Kramers–Heisenberg transition-amplitudes versus susceptibilities,” Adv. At. Mol. Opt. Phys. 59, 233–263 (2010).

31. S. Rahav and S. Mukamel, “Stimulated coherent anti-Stokes Raman spectroscopy (CARS) resonances originate from double-slit interference of two-photon Stokes pathways,” Proc. Natl. Acad. Sci. 107, 4825–4829 (2010). [CrossRef]  

32. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505–1507 (2002). [CrossRef]  

33. L. Brückner, T. Buckup, and M. Motzkus, “Enhancement of coherent anti-Stokes Raman signal via tailored probing in spectral focusing,” Opt. Lett. 40, 5204–5207 (2015). [CrossRef]  

34. L. Brückner, T. Buckup, and M. Motzkus, “Exploring the potential of tailored spectral focusing,” J. Opt. Soc. Am. B 33, 1482–1491 (2016). [CrossRef]  

35. L. Wei, F. Hu, Y. Shen, Z. Chen, Y. Yu, C. Lin, M. C. Wang, and W. Min, “Live-cell imaging with alkyne-tagged small biomolecules by stimulated Raman scattering,” Nat. Methods 11, 410–412 (2014). [CrossRef]  

36. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512–514 (2002). [CrossRef]  

37. H. Li, D. A. Harris, B. Xu, P. J. Wrzesinski, V. V. Lozovoy, and M. Dantus, “Coherent mode-selective Raman excitation towards standoff detection,” Opt. Express 16, 5499–5504 (2008). [CrossRef]  

38. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745–808 (1960). [CrossRef]  

39. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

40. M. Yoshizawa and M. Kurosawa, “Femtosecond time-resolved Raman spectroscopy using stimulated Raman scattering,” Phys. Rev. A 61, 013808 (1999). [CrossRef]  

41. D. Zhang, P. Wang, M. N. Slipchenko, and J.-X. Cheng, “Fast vibrational imaging of single cells and tissues by stimulated Raman scattering microscopy,” Acc. Chem. Res. 47, 2282–2290 (2014). [CrossRef]  

42. B. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B 23, 750–759 (2006). [CrossRef]  

43. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998). [CrossRef]  

44. T. Wu, J. Tang, B. Hajj, and M. Cui, “Phase resolved interferometric spectral modulation (PRISM) for ultrafast pulse measurement and compression,” Opt. Express 19, 12961–12968 (2011). [CrossRef]  

45. A. Yariv and P. Yeh, Photonics, Optical Electronics in Modern Communications, 6th ed. (Oxford University, 2006).