1. Introduction

Parametric four-wave mixing (4WM) processes represent one of the more general families of ultrafast time-resolved nonlinear optical spectroscopies [1], which acquire their full capability when executed with three incident pulses in three colors that can be independently controlled [2]. Beyond flexibility, 4WM in three colors achieves ultimate sensitivity by allowing background free detection. In this limit, detectivity is determined by the noise equivalent count rate, $R,$ of signal photons, which, for spontaneous scattering on a single center, is given quite generally by the product,

Various approaches have been previously used for non-resonant, background-free CARS spectro-microscopy [5–30]. These include second harmonic based [7] or supercontinuum (SC) based techniques [8–21], or reliance on a single broadband pulse [22–28], along with approaches requiring kHz amplifiers [29,30]. In [29], a multiplexed three-color three-pulse tr-CARS scheme was developed to acquire non-resonant background-free spectra with high spectral resolution and relatively broad spectral range (~900 cm⁻¹). However, this approach requires high intensity laser systems, including a kHz amplifier and optical parametric amplifier. The more efficient approach to achieve a large Raman frequency range (> 2000 cm⁻¹) from an unamplified and high repetition-rate source (> 100 MHz) is to use SC generated in nonlinear fibers [8–21]. This has been implemented in frequency domain two-color CARS, with degenerate pump and probe excitations driven by the narrowband source and the Stokes induced by the continuum [8]. Microscopy with two-pulse three-color CARS, in which two different frequency components of the continuum act as pump and Stokes and the narrowband pulse acts as probe [9], has also been effectively implemented to obtain images tagged by vibrational dephasing times [10]. This approach takes advantage of the time-delayed probe to separate the resonant signal from the nonresonant background by virtue of the contrast in coherence times of the nonresonant background (< 10 fs) and vibrational resonances (0.5 ps-10 ps). Approaches based on amplified laser systems to pump multiple optical parametric amplifiers to generate multiple fs pulses are limited in repetition rate, typically to < 10 MHz. In contrast, oscillator pumped fiber-based setups have the advantage of higher repetition rate (> 100 MHz) at significantly reduced cost and complexity, signal-to-noise ratio improvement by higher data acquisition rates, and peak powers reduced by the fill factor to prevent sample damage. Despite these promising advantages, reports of $t-$domain 4WM via SC generation in fibers have been limited to impulsive application of the pump and dump (Stokes) pulses. Here, we demonstrate three-color, three-pulse, tr-CARS based on SC generation in a commercially available PCF and subsequent slicing of the spectrum with filters to generate the desired pump, Stokes, and probe pulses with independently controllable time-frequency profiles. The demonstration suggests that the approach is well suited to address the challenges of single-molecule ultrafast coherent spectroscopy [31–33].

2. Experiment

2.1. Methods

A detailed schematic of the three-color, three-pulse tr-CARS setup is shown in Fig. 1. A mode-locked Ti:sapph laser (Coherent Mira Seed) operating at 798 nm (average power = 700 mW, $f=$76 MHz, $\delta t=$40 fs) is used to pump a 12 cm long, polarization maintaining PCF (NKT Photonics NL-PM-750). The fiber is mounted in a protective module (FemtoWHITE 800), and housed in a commercial intensity control/fiber-coupling unit (Newport Wavelength Extender (WE) SCG-02). The WE splits the pump beam using a polarizing cube (PCBS) into two, and provides variable attenuators consisting of half waveplates and Glan-laser polarizers to control the intensities in the two arms. The first arm passes through a Faraday isolator (FI) and is used to pump the PCF with 50% coupling efficiency. The second arm, which consists of the remaining Ti:sapph output, is utilized as either the reference pulse in cross-correlation measurements or as the Stokes pulse in the CARS measurements (see below). The spectrally broad output of the PCF (inset of Fig. 1) is further split into red and blue arms using a 660 nm long wave pass dichroic mirror (Semrock FF660-Di02), followed by bandpass filters in each arm to select the desired colors. In the present, 10 nm FWHM bandpass filters centered at 610 nm (Thorlabs FB610-10) and 710 nm (Thorlabs FB710-10) are used in the blue and red arms, respectively. The sliced pulses are then recombined along with the leftover fundamental in a collinear geometry using a 757 nm long wave pass dichroic mirror (Semrock FF757-Di01). Separate delay lines and attenuators are used to introduce relative delay between the pulses and for intensity control. The collinear CARS measurements are carried out on liquid trans-1,2-bis-(4-pyridyl) ethylene (BPE) dissolved in methanol, or in pure styrene, contained in 1 mm quartz cuvettes. A 0.25 NA objective lens is used to focus the three beams to a spot size of ~10 $\mu$m. In our tr-CARS configuration, the sliced pulses at 708 nm and 612 nm serve as pump (Pu) and probe (Pr), while the leftover fundamental at 798 nm serves as the Stokes (St), to generate the anti-Stokes signal ${\omega }_{Pu}-{\omega }_{St}+{\omega }_{\mathrm{Pr}}={\omega }_{AS}$ centered at 557 nm. The transmitted excitation pulses, along with the CARS signal, are collimated and spectrally filtered (Semrock FF01-554/23-25) to isolate the anti-Stokes signal. The signal is collected using an avalanche photodiode (APD Excelitas SPCM-AQRH-16-FC), and recorded using a dual-channel photon counter (Stanford Research Systems SR400). The pulses are characterized through sum-frequency generation (SFG) cross-correlation using a 1 mm BBO crystal placed in the sample position. The three-pulse instrument response is characterized through third-order cross-correlation frequency-resolved optical gating (XFROG) [34] by replacing the sample with pure carbon disulfide (CS₂) and using a spectrograph (Andor iDus 401/Shamrock 303i) in place of the APD. The pulses are not precompensated for group-delay dispersion (GDD) of the objective lens, which is estimated to be 2200 fs² at 612 nm (4 cm, fused silica).

 

Fig. 1 Experimental apparatus for three-color three-pulse CARS ($\lambda /$2 – half waveplate, PCBS – polarizing cube beamsplitter, FI – Faraday isolator, AT1, AT2 – attenuator assemblies consisting of half waveplates and Glan-laser polarizers, L1, L2 – aspheric lenses for focusing and collimation, PCF – photonic crystal fiber, WE – wavelength extender, DM1, DM2 – 660 nm and 757 nm long wave pass dichroic beamsplitters, BPF1, BPF2, BPF3, BPF4 – bandpass filters centered at 800 nm, 710 nm, 610 nm, and 554 nm respectively, SPF – 390 nm short wave pass filter, APD – avalanche photodiode, Spec – spectrograph, PMT – photomultiplier tube. Inset shows the SC spectrum on log scale.

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2.2. Characterization of the sliced PCF pulses

SC generation in the NL-PM-750 PCF, and applications therein, are available in prior reports [35–37]. The PCF displays anomalous dispersion with two zero crossings at 750 nm and 1260 nm. The output characteristics of the highly nonlinear fiber depend on the intensity, wavelength, and bandwidth of the pump beam. When directly pumped with the 40 fs (25 nm FWHM) Ti:sapph laser at 0.5 W average power, a fairly flat SC is generated across the wavelength range 400-900 nm, as illustrated in the inset of Fig. 1. Note that the red edge of the displayed spectrum is limited by the spectral response of our spectrometer, otherwise it stretches out to 1600 nm [35,36]. Under this pumping condition, the sliced pulses of average power ~5 mW stretch out to ~1 ps. It is in principle possible to compress these output pulses. Instead, we generate nearly transform-limited output pulses directly by limiting both bandwidth and intensity of the pump laser to counter-balance the interplay of self-phase modulation and dispersion. The generation of transform-limited SC components at these low intensities is thought to principally arise from soliton fission [13,38]. With the bandwidth of the pump laser limited to 10 nm using a bandpass filter (Fig. 1, BPF1), by adjusting the pump intensity, near transform-limited 100 fs pulses can be extracted from the PCF. Under these conditions, the SC is strongly colored, with spectral structure that tunes as a function of pump power [13,38]. This is illustrated in Fig. 2(a). For the set of spectral slices pre-specified by the bandpass filters to $\lambda (\delta \lambda )=$612(5) nm, 708(8) nm, and 798(10) nm, the shortest pulses are obtained when the PCF is pumped at 36 mW (total SC output of 18 mW). The strongly modulated SC spectrum obtained under this pumping condition is the green trace in Fig. 2(a), and the normalized spectra of the filtered slices are shown in Fig. 2(b). The filter functions inscribe the bands in the SC spectrum, to slice out sections of stationary phase, albeit with different intensities. The extracted powers at 612 nm and 708 nm are 110 $\mu$W and 25 $\mu$W, respectively. With RMS pulse-to-pulse intensity fluctuations of the pump laser of 1.4%, the RMS noise in the generated pulses at 612 nm and 708 nm is 23% and 10%, respectively.

 

Fig. 2 (a) SC spectra with different output powers, (b) normalized spectra of the probe (612 nm), pump (708 nm), and Stokes (798 nm) pulses sliced from the SC spectrum given by the green trace in (a).

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To characterize the sliced pulses, we carry out cross-correlation and XFROG measurements, which are summarized in Figs. 3 and 4. Using the filtered 798 nm (94 fs) pulse as reference, the cross-correlations of the pump (708 nm) and probe (612 nm) pulses yield widths of FWHM = 150 fs and 153 fs, respectively (Fig. 3). Assuming Gaussian profiles, the cross-correlation widths $\delta t_{i,j}={[\delta t_i^2+\delta t_j^2]}^{1/2}$ imply pulse widths of FWHM = 120 fs for both pump and probe slices. This is to be compared with their respective bandwidth-equivalent transform limit of 92 fs and 110 fs. The residual pulse broadening can be entirely accounted by GDD in the objective lens. Thus, for a Gaussian pulse traveling a distance $z$ in a dispersive medium: $\tau /{\tau }_0={[1+{(z/L_D)}^2]}^{1/2},$ where $L_D={\tau }_0^2/{\beta }_2$ is the dispersive length and ${\beta }_2$ is the second-order dispersion coefficient [39]. The observed broadening suggests that the pulses are subject to $GDD\equiv {\beta }_{2}z={\tau }_0{({\tau }^2-{\tau }_0^2)}^{1/2}~$2400 fs² and ~2000 fs² at 612 nm and 708 nm, which is close to the value of $GDD=$2200 fs² and 1800 fs² that we estimate for the objective lens at the same wavelengths ($z=$4 cm, fused silica). In effect, the sliced pulses out of the PCF appear to be transform-limited, with pulse widths limited by the pump laser.

 

Fig. 3 Cross-correlations of pump (black dotted) and probe (open orange circles) pulses with the 798 nm reference pulse.

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Fig. 4 (a) Measured XFROG trace, (b) retrieved temporal (black solid) and phase profiles (open circles), together with a quadratic fit (green solid).

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The third-order XFROG measurement, which is shown in Fig. 4, captures the instrument response function for 4WM measurements and confirms that the residual chirp in the pulses due to GDD in the objective is linear (quadratic phase). The measurement carried out in liquid CS₂ consists of recording the anti-Stokes spectrum as a function of delay of the 610 nm probe pulse, and with coincident pump and Stokes pulses that are fixed in time. In effect, this is a spectrally-resolved tr-CARS measurement in the absence of vibrational resonances; therefore, it measures the instantaneous response of the system. The XFROG trace is shown in Fig. 4(a), and the retrieved temporal intensity (black solid) and phase (open circles) profiles using the Femtosoft XFROG software (version 3.2.4), are shown in Fig. 4(b). The temporal phase is predominantly quadratic, as shown by the fit (in green). The fit yields $GDD=$4300 fs², in excellent agreement with the additive $GDD$ values (2400 fs² + 2000 fs²) extracted above from the cross-correlation measurements. Thus, near transform-limited 100 fs pulses, in three colors, at an average power of ~100 $\mu$W in each sliced pulse, are obtained out of the PCF at 76 MHz repetition rate.

3. CARS measurements and discussion

The time-frequency profiles of the filtered pulses were designed to interrogate quantum beats among ubiquitous, aromatic $C=C$ stretching modes of organic molecules, which occur near 1600 cm⁻¹. These are the prominent lines seen in the Raman spectra of BPE and styrene, which are shown in Fig. 5, along with the measured tr-CARS time traces. Note that both Raman and CARS are determined by the third order polarization, $P^{(3)}.$ The first measures the imaginary part, $\mathrm{Im}[P^{(3)}(\omega )],$ in the frequency domain, while the latter measures $|P^{(3)}(t){|}^2$ in the time domain [1]. As such, for an ensemble measurement with homogeneously broadened lines, the Raman spectrum contains all of the information necessary to predict the tr-CARS response. With the 708 nm pulse acting as pump and the 798 nm pulse acting as Stokes, the polarization that can be prepared is delimited by the Raman window given by the spectral convolution:

 

Fig. 5 Measured (black) and simulated (red) tr-CARS traces for (a) BPE and (b) styrene. The simulations are based on the windowed inverse Fourier transform of the Raman spectra (Eq. (3) of text). The Raman spectra and window function (blue) are shown in the insets.

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A principle advantage of the three-color 4WM was advanced as a background-free detection method, yet the time trace of the signal in Fig. 5(a) clearly rides over a background of 10⁴ counts, comparable to the signal. This we have verified to arise from a two-photon induced fluorescence in BPE, which coincides with the anti-Stokes window. The baseline of 400 counts in the case of styrene [Fig. 5(b)] is due to scattered stray light, which sets the noise equivalent count rate in the setup. Otherwise, the dynamic range of the signal, $S:N~$100, agrees with the shot noise, $N/N^{1/2},$ where $N~$10⁴ is the signal photon count rate. The effect of source noise, due to pulse-to-pulse fluctuations of the nonlinear SC generation in the PCF, is not apparent.

4. Conclusion

Based on fundamental considerations, namely Eq. (1), we have argued that ultimate limits in detectivity of ultrafast time-resolved processes in molecular matter is reached through three-color fs lasers operating near or above 100 MHz. We have shown that this can be accomplished in a compact setup, through the use of a PCF, and we have proven the concept by implementing it to carry out tr-CARS measurements. The key finding is that nearly transform-limited 100-fs coherent multicolor pulses can be extracted from a single PCF by controlling the bandwidth and intensity of the pump pulse. The approach is amenable to a variety of adaptations and improvements. The repetition rate is only limited by the pump source, and, given the low requirement on pump power, the repetition rate of the system can be readily increased to 10 GHz using demonstrated passively mode-locked Ti:sapph oscillator technology [41]. And while we demonstrated the operation with prescribed fixed colors and pulse widths, it should be clear that through the use of variable bandpass filters, the entire PCF spectrum (400-1600 nm) is accessible to generate multiple compressible pulses of different color. To this end, the combination of the PCF and a pulse shaper [42] would greatly add to flexibility and compactness.

The development we presented is part of a program aimed at preparing and manipulating quantum coherences on individual molecules. Through the use of Eq. (1), it is easy to show that such measurements are impractical on bare molecules: $R~$1 Hz, $ff=$10⁻⁵, for a molecule with a very large Raman cross-section of 3$\times$10⁻²⁵ cm². To reach single-molecule sensitivity, one takes advantage of the surface-enhanced Raman scattering (SERS) effect [32,33] through the use of plasmonic nano-antennas [43]. The standard SERS enhancement factor, $EF={\beta }^4,$ which results from the enhanced local field $\beta =E_L/E_0,$ modifies Eq. (1):