1. INTRODUCTION

Recently, a great deal of attention has been drawn to open-loop and adaptive pulse shaping techniques [1, 2, 3, 4]. The inherently large spectral bandwidth of ultrashort laser pulses has been utilized for various coherent control schemes, where the process outcome is manipulated through constructive and destructive interferences of possible excitation paths. The cancellation of the two-photon absorption [2], control of chemical reaction branching ratios [1], or vibrational wave packet dynamics [3, 4] are well-established examples of coherent control. Another important application of pulse shaping, relevant to the subject of this work, is the restoration of the spectral selectivity.

In coherent anti-Stokes Raman scattering (CARS) spectroscopy [5], two laser pulses, at carrier frequencies ${\omega }_1$ and ${\omega }_2$, initiate coherent molecular vibrations, and the third pulse (at carrier frequency ${\omega }_3$) scatters inelastically off them [see Fig. 1a ]. For this four-wave mixing (FWM) process, the specificity can be gained through the mode-selective excitation of Raman transitions, i.e., at the preparation stage, as well as through the shaping of the probe pulse. In a series of experiments, Silberberg's group demonstrated the use of periodic modulation [6] and steplike jumps [7, 8, 9] of the pulse phase for this purpose. An attractive alternative is to use linearly chirped pulses [10, 11, 12, 13, 14]. This simplest pulse shape is easy to produce and control. It also offers a very intuitive picture of how pulse shaping works.

We utilize a pair of broadband but linearly chirped laser pulses for selective excitation of adjacent Raman modes in a powder of sodium dipicolinate (NaDPA). Pulse chirp leads to the effective reduction of its instantaneous bandwidth. Provided that the preparation pulses have the same amount of chirp, as in Fig. 1b, their instantaneous frequency difference can be kept constant over the whole region where the pump and Stokes pulses are overlapped. The excitation bandwidth is then determined by the effective (instantaneous) spectral widths of the pump and Stokes pulses. The frequency difference depends on the time delay between the two pulses and can be conveniently adjusted.

Our approach is analogous to those described in [12, 13], but the probing of the induced molecular vibrations differs. We use a third, time-delayed ultrashort pulse to generate the background-free CARS signal. By varying the probe pulse delay, we can observe the coherence relaxation dynamics or even quantum beats if several Raman transitions are excited [15]. We can also directly map out the CARS signal intensity versus the Raman shift by scanning the timing between the shaped pump and Stokes pulses.

Note that the pulse configuration used here is conceptually opposite to the one employed in the hybrid CARS scheme (see [16]; known also as fs/ps CARS [17]), where broadband excitation of multiple Raman transitions via a pair of ultrashort transform-limited pulses is combined with their time-delayed but frequency-resolved probing. At last, the choice of NaDPA powder as an analyte is not arbitrary. NaDPA is an easy-to-make substitute for calcium dipicolinate (CaDPA), which in turn is a marker molecule for bacterial spores [18, 19]. To this end, the goal of this work [16, 20, 21, 22] is to develop a technique that would facilitate the interrogation of powderlike opaque solids and detection of harmful agents, such as B. anthracis spores, by means of CARS spectroscopy.

2. MATERIALS AND METHODS

We use a commercially available regenerative Ti:sapphire-based amplifier system (Legend, Coherent, Inc.), evenly pumping two optical parametric amplifiers (OPAs), to produce three synchronized laser pulses of different colors: pump (${\lambda }_1=722.5\mathrm{nm}$, $\mathrm{\Delta }{\nu }_1\equiv \mathrm{\Delta }{\omega }_1∕\left(2\pi c\right)\approx 287{\mathrm{cm}}^{-1}$), Stokes (${\lambda }_2=804\mathrm{nm}$, $\mathrm{\Delta }{\nu }_2=464{\mathrm{cm}}^{-1}$), and probe (${\lambda }_3=579\mathrm{nm}$, $\mathrm{\Delta }{\nu }_3=210{\mathrm{cm}}^{-1}$). Pulse shaping is done by sending the initially transform-limited preparation pulses through a $4\mathrm{cm}$ slab of SF11 glass. Additionally, the Stokes pulse is guided through a commercially available pulse shaper (Silhouette, Coherent, Inc.). The pulse shaper is used for fine tuning of the Stokes pulse phase to match its chirp to the chirp of the pump pulse. After the computer-controlled delay stages, the three beams are focused onto a single spot on the surface of a sample, which is a rotated pellet of NaDPA powder.

The schematic layout of the setup and the pulse timing is given in Fig. 1c. The scattered CARS signal is collected in the backward direction by a $2\mathrm{in.}$ $(1\mathrm{in.}=2.54\mathrm{cm})$ concave mirror, slightly offset from the main axis. The light is filtered from the dominant pump, Stokes, and probe photons and refocused on the entrance slit of an imaging spectrometer (Chromex-250is) with a liquid-nitrogen-cooled charge-coupled device (LN2-cooled CCD; Spec-10, Princeton Instruments). CARS spectrum is recorded as a function of the probe or pump pulse delay, depending on the experiment.

3. SHAPING OF THE PREPARATION PULSES

As was mentioned above, we shape the initially transform-limited pump and Stokes pulses by sending them through a slab of SF-11 glass. To the first approximation, the dispersion of the medium produces a linear chirp of the pulses. Note that since the beams are not focused inside the glass, pulse propagation is well described within the linear model, i.e., without taking into account possible pulse reshaping due to the field-induced nonlinearities.

For the sake of simplicity, we assume the input pulses to have a Gaussian temporal profile, i.e., $E\left(t\right)=E_0\exp (-{\Gamma }_0{t}^2+i{\omega }_{0}t)$, where $E_0$ is the complex amplitude of the electric field, ${\omega }_0$ is the laser pulse carrier frequency, and ${\Gamma }_0\equiv a_0-i{b}_0$ is a complex coefficient related to the full-width-at-half-maximum (FWHM) duration of the pulse and its FWHM spectral width. Explicitly,

From the measured spectrum of the pump pulse and the known dispersion properties of the glass, we estimate the input pulse duration, ${\tau }_1^{\mathrm{in}}$, to be $51\mathrm{fs}$, and the output, after $4\mathrm{cm}$ of SF11 glass, ${\tau }_1^{\mathrm{out}}=0.48\mathrm{ps}$. The last number agrees well with the measured FWHM of the cross-correlation profile between the stretched pump and ultrashort transform-limited probe pulses [$2{\omega }_3-{\omega }_1$ process, see Fig. 2a ], which is $0.47\mathrm{ps}$. The calculated linear chirp, $2b$, is equal to $0.11\mathrm{mrad}{\mathrm{fs}}^{-2}$ $\left(0.58{\mathrm{cm}}^{-1}{\mathrm{fs}}^{-1}\right)$. This corresponds to $d{\lambda }_1∕dt\approx -31\mathrm{nm}∕\mathrm{ps}$ and results in $15\pm 2\mathrm{nm}∕\mathrm{ps}$ slope for the recorded cross-correlation spectrogram, since $d{\lambda }_{\mathrm{FWM}}∕dt\approx -({\lambda }_{\mathrm{FWM}}∕{\lambda }_1{)}^{2}d{\lambda }_1∕dt\approx 14\mathrm{nm}∕\mathrm{ps}$. The effective bandwidth of the pump pulse, $\mathrm{\Delta }{\nu }_1^{\mathrm{eff}}=({\tau }_1^{\mathrm{in}}∕{\tau }_1^{\mathrm{out}})\mathrm{\Delta }{\nu }_1\approx 30{\mathrm{cm}}^{-1}$, is reduced by almost an order of magnitude.

Because of slightly different dispersion of SF-11 glass at the Stokes wavelength and the different initial bandwidth of the Stokes pulse, its propagation through the same glass thickness does not result in the same chirp. Indeed, direct calculations give the linear chirp $0.13\mathrm{mrad}{\mathrm{fs}}^{-2}$ $\left(0.70{\mathrm{cm}}^{-1}{\mathrm{fs}}^{-1}\right)$. To match the chirp of the two preparation pulses, we utilize the pulse shaper Silhouette, mentioned above. We use the multiphoton intrapulse interference phase scan (MIIPS) method [24, 25] to compensate for the phase distortions due to optical elements other than SF-11 glass (with the slab removed from the beam path), and then put the glass bar back and impose a parabolic phase on top of the found spectral compensation mask. This is equivalent to merely changing the length of the glass slab.

With a thin microscope cover slide placed in the focus of the overlapped beams, we monitor the spectrum of the FWM due to the pump, Stokes, and probe pulses (${\omega }_1-{\omega }_2+{\omega }_3$ process) as a function of the probe pulse delay to check for the center frequency variation in the FWM signal [see Fig. 2b]. Obviously, the absence of such variation is a direct indication that the two pulses have the same chirp. Note that the spectral bandwidth of the recorded signal is determined by the bandwidth of the probe pulse rather than of the preparation pulses. Assuming a perfect match of the pump and Stokes linear chirps, we estimate the output Stokes pulse duration as $0.79\mathrm{ps}$ and the effective bandwidth $\mathrm{\Delta }{\nu }_2^{\mathrm{eff}}\approx 18.5{\mathrm{cm}}^{-1}$. The resulting spectral bandwidth of the pump-Stokes convolution, responsible for Raman excitation, is therefore $\mathrm{\Delta }{\nu }_{12}^{\mathrm{eff}}=\left[\right(\mathrm{\Delta }{\nu }_1^{\mathrm{eff}}{)}^2+(\mathrm{\Delta }{\nu }_2^{\mathrm{eff}}{)}^2{]}^{1∕2}\approx 35{\mathrm{cm}}^{-1}$, i.e., less than the frequency difference between the two Raman modes of NaDPA powder, 1395 and $1442{\mathrm{cm}}^{-1}$, shown in the inset of Fig. 1a.

4. SELECTIVE EXCITATION AND TIME-DELAYED PROBING

According to the spontaneous Raman spectrum of NaDPA [see the inset in Fig. 1a], the vibrational transitions of interest have a wavenumber difference of $47{\mathrm{cm}}^{-1}$, i.e., they are well within the bandwidth of the probe pulse. This makes it difficult to resolve the two Raman transitions by means of a straightforward CARS spectrum acquisition. Fortunately, one can still gain the required resolution through the time-resolved measurements, and there are two complementary ways to do it.

The first one is demonstrated in Fig. 3 . CARS spectra are recorded for fixed pump-Stokes timing as a function of the probe pulse delay, as it is typically done in femtosecond CARS measurements [26]. For such spectrograms, the response at zero probe delay is usually overwhelmed by the nonresonant (NR) contribution due to the instantaneous electronic response and off-resonant Raman modes. The Raman-resonant contribution results in a long-living but exponentially decaying signal at the positive probe delays. The excitation of multiple Raman modes, with frequency differences within the probe pulse spectral bandwidth, manifests itself through the observation of quantum beats [15], which are amplitude modulations of the recorded time-resolved CARS signal at the beat frequencies of Raman-mode pairs.

The set of spectrograms in Fig. 3 shows a gradual change from a single-mode to double-mode excitation, and then back to the single-mode dynamics but for the other Raman transition. When the effective pump-Stokes frequency difference is far detuned from any particular Raman mode, as in Figs. 3a, 3h, the spectrograms exhibit an asymmetric FWM profile due to solely the NR contribution. The asymmetry along the probe pulse delay is introduced by the multiple scattering of incoming photons in the powder, which favors negative probe delays (when the probe pulse is ahead of the pump-Stokes pair) over positive ones for the FWM to occur. Tuning the pump-Stokes frequency difference closer to one of the Raman modes, as in Figs. 3b, 3g, results in the appearance of an exponentially decaying CARS signal at positive probe delays. Finally, the double-mode excitation [see Figs. 3c, 3d, 3e, 3f] leads to the signal modulation as a function of the probe pulse timing. The variation in the contrast of the beating pattern is an indication of the selective excitation of the two Raman modes. Indeed, the contrast is expected to be maximal when the mode contributions into the CARS signal are equal. It deteriorates otherwise, and one observes purely exponential decay (without oscillations) if only a single mode is excited.

When the beating is observed, the difference frequency can be retrieved (see Fig. 4 ). In particular, we get $46\pm 3{\mathrm{cm}}^{-1}$ from the fast-Fourier transform (FFT) of the recorded signal, corrected for its exponential decay. The decay times for 1395 and $1442{\mathrm{cm}}^{-1}$ transitions are found to be $0.7\pm 0.1\mathrm{ps}$ $(\mathrm{\Delta }\nu =7.6\pm 1.1{\mathrm{cm}}^{-1})$ and $0.8\pm 0.2\mathrm{ps}$ $(\mathrm{\Delta }\nu =6.6\pm 1.6{\mathrm{cm}}^{-1})$, respectively. They are in agreement with the linewidths estimated from the spontaneous Raman spectrum of NaDPA powder, 6.7 and $7.5{\mathrm{cm}}^{-1}$.

The second approach is to fix the probe pulse timing and record the CARS signal as a function of the pump or Stokes pulse delay. Obviously, it is advantageous to have the probe pulse delayed with respect to the preparation pulses in order to suppress the NR contribution into the generated signal. The resulting profiles of the spectrally integrated CARS signal, when the probe pulse timing corresponds to the quantum-beat peaks, are shown in Fig. 5 . CARS spectrum (with the spectral resolution defined by the spectral width of the convoluted pump-Stokes pair) is mapped out along the pump pulse delay. From the known pulse chirp, one can determine the frequency difference between the two Raman transitions. We estimate it to be $62\pm 14{\mathrm{cm}}^{-1}$, which is somewhat higher than the value derived from spontaneous Raman measurements. The inset in the right top corner of Fig. 5 is an example of the original CARS spectrograms, before the integration over the spectrum. One can see a slight upward shift of the peak CARS wavelength when the $1442{\mathrm{cm}}^{-1}$ vibrational mode is superseded by the Raman transition at $1395{\mathrm{cm}}^{-1}$.

5. CONCLUSION

A combination of linearly chirped preparation pulses and time-delayed ultrafast probing conveniently brings together the excitation selectivity and background-free acquisition of the Raman-resonant CARS signal. The two time scales allow for the standard time-resolved measurements of the coherence decay as well as the frequency-resolved mapping of the CARS spectrum as a function of the relative pump-Stokes delay. The described approach is shown to work even for highly scattering solids, such as powders, when the input laser pulses and the generated CARS signal are subject to multiple scattering inside the sample. Finally, the linear chirp is the simplest pulse shape to produce and manipulate, which makes the technique attractive for practical applications. One possibility is to use broadband (chirped) laser pulses for adiabatic preparation of a highly coherent molecular supersposition state, which has previously been done with narrow-linewidth lasers slightly detuned from a Raman resonance [27, 28].

ACKNOWLEDGMENTS

We thank Marlan O. Scully, Yuri V. Rostovtsev, and George R. Welch for motivating our work, for stimulating discussions of the results, and for support of the project; we are grateful to Jaan Laane and his group for their help with spontaneous Raman measurements on NaDPA powder, and to Coherent Inc. for lending us commercially available pulse shaper Silhouette. The work is sponsored by the Defense Advanced Research Projects Agency, the National Science Foundation (grant PHY-0354897), an Award from Research Corporation, and the Robert A. Welch Foundation (grant A-1547).

 

Fig. 1 Technique and experiment schematics: (a) CARS energy level diagram. The two broadband but shaped preparation pulses, pump $\left({\omega }_1\right)$ and Stokes $\left({\omega }_2\right)$, excite Raman-active vibrational modes of the sampled molecules. The third pulse $\left({\omega }_3\right)$ probes the initiated coherent molecular vibrations. Inset: spontaneous Raman spectrum of NaDPA powder in the range of interest, acquired with a CW laser operating at $532\mathrm{nm}$. (b) Time-frequency diagram of the selective Raman excitation with linearly chirped laser pulses. The difference frequency $\mathrm{\Delta }\omega \equiv {\omega }_1-{\omega }_2$ depends on the relative timing ${\tau }_{12}$ between the preparation pulses. (c) Experimental setup layout. The pump and Stokes pulses are sent through $4\mathrm{cm}$ pieces of SF-11 glass. The Stokes pulse also passes through a commercially available pulse shaper (Silhouette, Coherent), where a parabolic phase mask is added to compensate for the difference in the chirp, produced by the glass slabs. The pump and probe time delays are adjusted relative to the Stokes pulse. The three beams are focused (with 40 to $50\mathrm{cm}$ focal length lenses) on the sample, a pellet of NaDPA powder. The generated and scattered CARS photons are collected with a $2\mathrm{in.}$ spherical mirror $(f=20\mathrm{cm})$ in the backward direction, at an angle of $30°$ to the main axis. The collected light is filtered and refocused on the entrance slit of an imaging spectrometer (Chromex-250is) with a LN2-cooled CCD; CCD - charge coupled device.

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Fig. 2 Pulse shaping characterization: (a) Cross-correlation spectrogram between the chirped pump and transform-limited probe pulses. The spectrum of FWM signal ($2{\omega }_3-{\omega }_1$ process), generated on a cover glass slide, is recorded as a function of the probe pulse delay; (b) Cross-correlation spectrogram between the linearly chirped pump, Stokes, and ultrashort probe pulses. Again, the spectrum of the FWM signal (${\omega }_1-{\omega }_2+{\omega }_3$ process) from a cover glass slide is acquired as a function of the probe pulse delay.

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Fig. 3 Selective excitation of Raman modes in NaDPA powder, $1442{\mathrm{cm}}^{-1}$ and $1395{\mathrm{cm}}^{-1}$. The relative timing ${\tau }_{12}\equiv t_1-t_2$ between the two linearly chirped preparation pulses, pump $({\lambda }_1=722.5\mathrm{nm})$ and $({\lambda }_2=804\mathrm{nm})$, is set as (a) $-333$, (b) $-133$, (c) $-100$, (d) $-67$, (e) 0, (f) $+67$, (g) $+100$, and (h) $+300\mathrm{fs}$. The induced molecular vibrations are probed with an ultrashort pulse at ${\lambda }_3=579\mathrm{nm}$. CARS spectrum as a function of the probe pulse delay is recorded. Timing of the pump-Stokes pulses leads to consecutive excitation of a single Raman mode at $1442{\mathrm{cm}}^{-1}$; both Raman modes, as it can be inferred from the beating; a single Raman mode at $1395{\mathrm{cm}}^{-1}$. The pump, Stokes, and probe pulse energies are 2.8, 1.1, and $0.39\mathrm{\mu }\mathrm{J}$, respectively. The integration time is $0.2\mathrm{s}$ per step.

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Fig. 4 Cross section of the spectrogram in Fig. 3e at $\lambda =535\mathrm{nm}$. The beat frequency at positive probe delays corresponds to the frequency difference between the two excited Raman modes, $47{\mathrm{cm}}^{-1}$. Inset: FFT of the recorded modulation, corrected for the exponential decay.

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Fig. 5 Spectrally-integrated CARS signal as a function of the pump pulse timing, ${\tau }_{12}$. The probe pulse delay is set as (a) 1.4, (b) 2.2, and (c) $2.9\mathrm{ps}$, i.e., close to the peaks of the quantum beat profile in Fig. 4, when the two Raman modes are excited. The pump, Stokes, and probe pulse energies are 3.3, 1.2, and $0.37\mathrm{\mu }\mathrm{J}$, respectively. The integration time is $0.2\mathrm{s}$ per step. Inset: CARS spectrogram recorded in case (b).

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