1. INTRODUCTION

Coherent anti-Stokes Raman scattering (CARS) microscopy [1] has become a widely used technique in the last 15 years. In the CARS process, usually two narrowband lasers are tuned in frequency to obtain a spectrum or set to a specific Raman transition for microscopy applications. Interaction of the probe with the induced coherence generates a signal at ${\omega }_{\mathrm{CARS}}=2{\omega }_P-{\omega }_{\mathrm{St}}$ that is resonantly enhanced whenever the difference frequency of pump and Stokes matches the vibrational frequency of a molecule. As a third-order process, CARS shows intrinsic three-dimensional sectioning capability while the superposition of coherently generated signal assures high sensitivity. CARS spectroscopy was originally invented and explored for the investigation of flames and combustion processes [2,3]. It has evolved into a powerful technique with application in many fields and has been developed in particular for microscopy. Signal levels orders of magnitude higher than in spontaneous Raman spectroscopy enable video-rate detection, which can even be applied for live cell imaging circumventing the need for staining [4]. These advantages led to many applications, especially in life sciences for biomedical imaging [5–8] but also for monitoring artificially engineered materials [9–11].

Sophisticated methods based on the CARS process have been developed. In multiplex CARS (M-CARS), entire vibrational spectra are obtained without the need for tuning by applying narrowband pump/probe in combination with broadband Stokes pulses [12]. In single-beam CARS (SB-CARS), the concept can be simplified even more. All frequencies are contained within one broadband spectrum that simultaneously excites all vibrations within the spectral range [13,14]. Probing with the same broadband spectrum leads to overlapping signals from different modes. By controlling the phase with a pulse shaper, the molecular information can still be retrieved [14–18].

However, one common drawback inherent to all CARS methods is the nonresonant background due to instantaneous electronic four-wave mixing responses. Interference with the resonant CARS signal often limits image contrast and spectral resolution. Several methods have been developed to minimize these effects with sophisticated excitation and detection schemes. The different polarization dependences of resonant and nonresonant responses [19,20], epi-detection [21], and time-delayed probing [22–24] allow for getting rid of the fast-decaying instantaneous response. Additionally, heterodyne detection, where the phase difference between a local oscillator and the excitation spectrum is utilized, can be applied [25]. Exploiting the flexibility of the pulse shaper, all the mentioned methods and even combinations thereof can be implemented in SB-CARS, making it a versatile approach for spectroscopy and imaging [15,17,26–28].

An important experimental aspect in the detection of CARS signals is the spectral resolution. While picosecond CARS assures the best spectral resolution, the optimal ratio of image contrast and signal intensity is actually achieved when the laser bandwidths are in the range of the Raman linewidths ($5–100{\mathrm{cm}}^{-1}$) [29]. Because excitation with picosecond pulses can only match the linewidths in the fingerprint region ($5–20{\mathrm{cm}}^{-1}$), it is advantageous to use shorter pulses for, e.g., optimal excitation of CH stretching vibrations (lipid linewidth $\sim 100{\mathrm{cm}}^{-1}$). By equally chirping pump and Stokes beams, it is possible to adjust the instantaneous bandwidth to certain Raman linewidths and in the limiting case even mimic the picosecond CARS scheme [Fig. 1(a)]. In this approach, referred to as spectral focusing [30–33], usually static dispersive elements like glass rods are introduced into the beam path to stretch the pump/Stokes frequencies in time and generate a constant instantaneous frequency difference (IFD) [29,34]. The Raman line can be chosen by the relative temporal delay of pump and Stokes while the signal is necessarily generated by the pump acting as probe [Fig. 1(b)]. The spectral focusing approach has been combined with several CARS variations and is particularly useful for the identification of structures based on the vibrational information of a certain Raman level, as we have shown recently for SB-CARS microscopy [35,36].

 

Fig. 1. General overview of the flexibility and the main modalities of tailored spectral focusing. (a) Equally chirped pump and Stokes frequencies lead to a constant instantaneous frequency difference (IFD) that drives a certain Raman mode at a frequency $\mathrm{\Omega }$. The spectral resolution can be controlled by the chirp of pump and Stokes and is represented by the bandwidth of the excitation ${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$. (b) The IFD and therefore the addressed Raman mode can be chosen by changing the time delay of pump and Stokes. Pump/Stokes frequencies outside the overlapping region do not take part in the excitation process (gray box) and can be cut off with the pulse shaper by amplitude shaping. Continually scanning the time delay allows for recording CARS spectra. (c) By identifying frequencies acting solely as probe, independent control thereof enables line scans with temporal resolution as well as increased signal levels. (d) Because of the narrow excitation, signal generated by the probe (green), which lies in the region between pump and Stokes, or by the pump acting as probe (blue) can be spectrally separated. Thereby, a large part of the background is suppressed. Merging the information of (a)–(d) into a single picture provides a compact and comprehensive description of tailored spectral focusing (e.g., Figs. 4 and 9).

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The flexibility of a SB-CARS setup containing a pulse shaper further offers several advantages over other established spectral focusing implementations [15,35,36]. In this work we show how controlling the phase of all frequency regions taking part in the signal generation process enables the development of modalities for tailored spectral focusing. Especially in combination with detailed simulations, the potential of independently shaping the probe is explored and allows for significant improvements [Figs. 1(c) and 1(d)]:

The paper is organized as follows. First, the experimental setup as well as the principles and ideas of controlling and simulating the SB-CARS signal are explained. After a detailed introduction of the concept of tailored spectral focusing, we present time-delay measurements as an arising modality. The relation of the phase function and the spectral resolution is described for the experiment and confirmed by simulations. Then, the applicability of the concept to the fingerprint region is presented. At last, simultaneous multimodal imaging due to increased signal levels is demonstrated on biological tissue.

2. EXPERIMENTAL SETUP

The optical setup presented in Fig. 2 consists of a femtosecond oscillator and a pulse shaper, which allows for phase and amplitude shaping. The light source is a high-power Ti:Sa oscillator (Femtolasers Fusion Pro 800; mean power: 800 mW; repetition rate: 76 MHz) delivering pulses with durations $<10\mathrm{fs}$ centered around 800 nm. A set of chirped mirrors precompensates a large part of the second-order dispersion mainly introduced by the microscope objective. Spectral phase functions are applied by a liquid crystal mask (Jenoptik SLM 640d) in a 4f setup (gratings: $600\mathrm{lines}/\mathrm{mm}$; cylindrical mirrors: 350 mm focal length). Shaped pulses pass a polarizer to enable amplitude shaping and are then sent into a microscope (Olympus BX 51) equipped with a 0.7 NA, $60\times$ microscope objective and a 0.6 NA, $40\times$ collimation objective. Samples are fixed on a XYZ piezo stage (PINano, range of 200 μm in x, y, and z). In the experiment it is crucial to start with a flat phase (i.e., a transform-limited pulse) at the sample position. To correct for phase distortions from the setup, the nonresonant CARS signal from a glass microscope slide was optimized for maximum intensity with an evolutionary algorithm. In this setup not only CARS but also nonlinearly generated signals can be detected simultaneously in a broad spectral region from 350 nm to 700 nm. Signal detection can be done either with an intensified CCD camera (Andor ICCD) or with photomultipliers. In both cases the excitation laser light is blocked using an interference filter (Semrock, shortpass $\lambda <650\mathrm{nm}$ or $\lambda <700\mathrm{nm}$). The CCD camera is combined with a monochromator (Acton Research, 300i) for spectrally resolved acquisition with typical pixel dwell times of 10 ms. It is well suited for comparing signal intensities and identifying overlapping spectral regions. For fast imaging the single-channel detection is used. The signals are separated with long-, short-, and bandpass filters, depending on the measured sample. Data acquisition 100 times faster than in the spectrally resolved case is achieved and is therefore better suited for imaging due to the increased speed and reduced photodamage. Typical images ($200\mathrm{\mu m}\times 200\mathrm{\mu m}$) are obtained in 60–120 s.

 

Fig. 2. Experimental single-beam CARS setup. ChM, chirped mirrors; G, gratings; CM, cylindrical mirrors; SLM, spatial light modulator; Pol., polarizer; MO, microscope objectives; IF, interference filter; FM, flip mirror; F, filters; CARS, SHG, and TPEF, photomultipliers with bandpass filters for multimodal imaging.

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3. SINGLE-BEAM CARS: THEORY AND SIMULATION

In single-beam CARS spectroscopy, the signal field can be calculated using Eq. (1), where $E(\omega )=|E(\omega )|e^{i\varphi (\omega )}$ is the spectral complex amplitude [37]. The third-order susceptibility ${\chi }^{(3)}(\mathrm{\Omega })$ contains the molecular information and consists of a frequency-independent nonresonant part and the actual molecular vibrations. An exemplary susceptibility with three resonances ${\mathrm{\Omega }}_{\mathrm{res}}$, linewidths $\mathrm{\Gamma }$, and amplitudes $A_{\text{Raman}}$ is calculated from Eq. (3) and illustrated in Fig. 3(a). The Raman excitation probability $A(\mathrm{\Omega })$ [Eq. (2)] is the integral of all possible pump–Stokes frequency pairs with a certain frequency difference Ω. It can be interpreted as the ability of the laser field to excite a Raman level at $\mathrm{\Omega }$. It is maximized when the phase difference of pump and Stokes frequencies $\mathrm{\Delta }\varphi$ is zero, as it is fulfilled throughout the whole spectrum in the case of transform-limited (TL) pulses. Thus by controlling the phase difference of pump and Stokes frequencies, the excitation probability and therefore the subsequently generated CARS signal field can be controlled [13]. Figure 3(b) illustrates the excitation probabilities for a TL pulse (black) and for spectral focusing (red) at $2000{\mathrm{cm}}^{-1}$. Only with spectral focusing, a narrow excitation region can be chosen at a specific resonance, preventing signal generation from outside this region due to resonances or nonresonant contributions. $A(\mathrm{\Omega })$ is continuously decreasing because the number of pump–Stokes frequency pairs is reduced with increasing energy spacing, i.e., approaching the wings of the spectrum. The molecular response $R(\mathrm{\Omega })$ [Eq. (1), Fig. 3(c)] is obtained by weighting the excitation probability with the properties of the molecule, contained in its susceptibility. In single-beam CARS, the probe usually consists of many frequencies. Probing the molecular response can therefore lead to overlapping resonant signals from different vibrations when using TL pulses. The nonresonant contributions additionally lead to a huge background and therefore a nonspecific, washed-out signal. Spectral focusing, however, successfully suppresses most of the nonresonant contributions by directing the excitation to a narrow spectral region. All signals generated by a spectrally broad probe are now originating from the same resonant level. A strong and specific signal can thus be obtained by integrating the data in the detection window.

 

Fig. 3. (a) The third-order susceptibility contains a nonresonant electronic contribution (offset) and the vibrational resonances of the molecule. It is calculated from Eq. (3) with linewidths $\mathrm{\Gamma }$ of $15{\mathrm{cm}}^{-1}$ at $1000{\mathrm{cm}}^{-1}$, $2000{\mathrm{cm}}^{-1}$, and $2500{\mathrm{cm}}^{-1}$. (b) The excitation probability for spectral focusing (red) is nonzero only at the chosen resonance $\mathrm{\Omega }$, while the transform-limited pulse (black) is nonspecific throughout the spectrum. The molecular response in (c) shows that only one specific molecular resonance is excited in spectral focusing. In the case of a transform-limited pulse, not only are all resonances excited simultaneously but so are all virtual levels within the width of the spectrum. This leads to an overwhelming nonresonant background.

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For simulations of SB-CARS data, the amplitude of the excitation field $E(\omega )$ is obtained by a measurement of the laser spectrum. Its phase is defined by the phase parameters applied with the pulse shaper. The molecular susceptibility ${\chi }^{(3)}(\mathrm{\Omega })$ can be obtained by measurement or fitting CARS data [38–40]. As shown before, formulating Eq. (1) using Fourier transformations [Eq. (4)] speeds up the calculation of the CARS signal field by orders of magnitude because the time-consuming evaluation of integrals is avoided and replaced by simple multiplications of Fourier transformations [41].

In order to implement and understand the effect of different phase functions, it is common and most comprehensible to expand the spectral phase in a Taylor series with the coefficients ${\varphi }_n={\partial }^n\varphi (\omega )/{\partial {\omega }^n|}_{{\omega }_0}$ around the center frequency ${\omega }_0$ of the laser [42]. As a phase offset, the first term has no effect on the temporal shape of the pulse while the second (linear) expansion coefficient ${\varphi }_1$ only leads to a delay in time. The third (quadratic) term ${\varphi }_2$ results in a linear sweep of the frequencies in time and is referred to as linear chirp. It describes the dispersion of the group delay [often termed group delay dispersion (GDD)] and can be understood as the arrival time of the different frequencies with a constant offset ${\varphi }_1$. Complex phase functions as used throughout this paper can then be created by linearly combining individual, much simpler phase functions for different spectral regions in relation to a common $t_0$. Hence, by using the pulse shaper in the single-beam CARS approach, it is straightforward to construct phase functions that lead to different chirp, delay, or combinations of both, e.g., for pump, Stokes, and probe.

4. SPECTRAL FOCUSING FOR SB-CARS MICROSCOPY

A. Fundamentals of Spectral Focusing Employing Pulse Shaping

In traditional spectral focusing, the pump and Stokes pulses are equally stretched in time using dispersive elements like glass or grating compressors to achieve a constant instantaneous frequency difference (IFD) that drives a single Raman coherence [30,31]. Thus the excitation process is usually explained in the time domain. Changing the beating frequency of the pump and Stokes electric fields that matches the Raman frequency is done by delaying one of the pulses. Since the pulse shaper can be intuitively understood in the frequency domain, it is instructive to additionally look at the signal generation process in this domain.

As presented above, the group delay dispersion, or in other words, the time-dependent instantaneous frequency, is directly controlled by the amount of chirp ${\varphi }_2$. Thus applying two equal quadratic phase functions to pump and Stokes with an energy spacing matching the Raman line creates a constant IFD that spectrally focuses the excitation energy into a single resonance. The dashed arrows in Fig. 4(c) show that only frequency pairs of pump and Stokes with an energy separation of $\mathrm{\Omega }$ are in phase and therefore maximizing the Raman excitation probability $A(\mathrm{\Omega })$ [Eq. (2)]. The excitation is thus restricted to a region around the resonance, resulting in an efficient suppression of nonresonant contributions due to other frequency pairs that are out of phase. The IFD can be easily adjusted with the shaper by shifting one of the parabolas, which is equivalent to adding a linear term (${\varphi }_1$). Again, the shift of the parabola in the frequency picture corresponds to a delay in the time picture and thus connects the usual explanations with the one presented. Furthermore, the instantaneous bandwidth can be independently tailored to match the Raman linewidth by varying the steepness of the parabolas. The build-up of the coherence, the role of the frequencies, and the effect of the phase functions are most intuitively understood in a time-frequency map by combining the time and frequency pictures.

 

Fig. 4. (a) and (b) show the blue-shifted spectral focusing CH stretching signal of acetonitrile as measured in the experiment. (c) depicts the laser spectrum with the applied phase functions for pump, Stokes, and probe regions as indicated at the right side of the figure. The distance of the parabolas determines the IFD, indicated as Ω. The time distribution of the frequencies is presented in (d). From the induced coherence, the shifted signal in (b) is constantly generated by the pump acting as a probe (blue) and the time-delayed probe frequencies (red). The integrated detector signal measured is shown by the corresponding signals in (a). The steep linear probe phase is cut off to better show the parabolic phase of pump and Stokes needed for spectral focusing.

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Figure 4(c) shows the laser spectrum and the applied phase function. The integrated signal and the generated CARS fields are depicted in Figs. 4(a) and 4(b), respectively. The illustrated regions acting as pump, Stokes, and probe can be directly transferred to the time-frequency map showing the resulting instantaneous frequencies in Fig. 4(d) due to the applied positive chirp [29,36]. The spacing of the centers of the parabolas determines time zero for the two ellipses. It defines the IFD that matches the Raman resonance ${\mathrm{\Omega }}_{\mathrm{res}}$ in the depicted case. The frequencies indicated as probe are delayed in time and arrive after the build-up of the coherence. Thereby, interactions of the probe with the pump or Stokes frequencies are prevented (see also Sections 4.B and 4.C) and signal due to fast-decaying nonresonant contributions is suppressed. Furthermore, the signal intensity of the generated CARS signal is significantly enhanced [36].

Because of the constant IFD, a coherence is continually built up and probed to generate signal. It has to be noted that the role of the different frequencies is naturally not predefined, since they all can act as pump, Stokes, or probe. However, if the amount of chirp is appropriately chosen, the excitation is limited to a narrow window around the Raman mode ${\mathrm{\Omega }}_{\mathrm{res}}$. This allows for identifying the probing frequencies that generate signal at different spectral positions (${\omega }_{Pr}={\omega }_{\mathrm{CARS}}-\mathrm{\Omega }$). Besides the region indicated as a probe, the pump frequencies can act as probes, too. Because of the specific excitation, the signal generated by the time-delayed probe [Fig. 4(b), red and blue] can be spectrally separated [see also Fig. 1(d)]. On the other hand, if the applied chirp is too low, the generated signals will be smeared out, overlap, and not distinguished clearly.

B. Signal Normalization and Space–Time Coupling

Space–time coupling is an intrinsic effect when pulses are shaped using a spatial light modulator (SLM) in the symmetry plane of a 4f setup [43–45]. The shaping of pulses results in a modulation of both the temporal shape of an ultrashort pulse and its transverse spatial energy distribution. The effect becomes apparent when imprinting a time delay (linear phase change) that leads to a linear shift in space. Consequently, with increasing delay, an increasing number of the time-delayed frequencies will be blocked by the edges of the microscope objective, resulting in reduced intensity in the focus. This might be insignificant when applying only small delays but becomes more important with steeper linear phases. Especially when comparing signal intensities in a time-delay scan, signal normalization might be required.

As a third-order process, the CARS signal shows a cubic dependence on the total laser intensity [Eqs. (1) and (2)]. By time delaying the probe frequencies, the excitation process is detached from the probing. The signal is therefore expected to change linearly with the intensity of the probe. As shown in Fig. 5(a), this can be verified by changing the probe intensity in the focus via amplitude shaping while measuring the resulting signal originating from the time-delayed probe [red part in Figs. 4(a) and 4(b)]. The effect of space–time coupling is presented in Fig. 5(b). A linear relation of the probe delay and the probe power in the focus is obtained. The probe delay is defined as the arrival time of the probe in relation to the end of the excitation [Fig. 1(c)]. For high chirp rates, the excitation is stretched in time and steeper phases have to be applied in order to achieve the same relative delay. This results in increased space–time coupling as confirmed by the vertical shift of the measured lines in Fig. 5(b). The advantages of decoupling the probe from the excitation become particularly important when comparing absolute signal intensities in time-delay scans (Section 4.C). Because of the linear relation of CARS signal and probe intensity in the presented scheme, signal normalization becomes straightforward.

 

Fig. 5. (a) The spectral focusing signal generated by the time-delayed probe is linearly dependent on the probe intensity measured in the focus and confirms that it is detached from the excitation process. (b) Because of space–time coupling, the probe intensity in the focus depends on the slope of the linear phase and therefore on the time delay. The probe delay is defined as the delay of the probe in relation to the end of the excitation.

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C. Time-Delay Scan

Another advantage that comes with the implementation of spectral focusing exploiting the flexibility offered by pulse shaping is the possibility of scanning the time delay of the independently controlled probe frequencies. By detecting the spectrally separated signal generated by the delayed probe, it is possible to follow the build-up and decoherence of a Raman mode, and it allows for the minimization of the nonresonant background even at the resonance position. Furthermore, monitoring the decoherence of different vibrational states can be used for spectroscopy or imaging purposes.

Figure 6(a) shows time-delay scans when focusing on the resonance of acetonitrile at $2942{\mathrm{cm}}^{-1}$ for different chirp rates. The probe delay denotes the time after the end of the excitation as calculated from the group delay of pump and Stokes [Fig. 1(c) and Section 3]. With increasing chirp, the frequencies are dispersed over a longer period of time, which is reflected in the longer build-up of the coherence. While for low chirp ($<500{\mathrm{fs}}^2$, not shown) nonresonant contributions are still present around time zero, higher chirp already reduces its generation to a very high extent even without additional delay of the probe. It has to be noted that care must be taken when interpreting the data at negative time delays. There, due to the simultaneous arrival, the probe can in principle also act as a pump or Stokes, generating a signal in the detection window. However, at high chirp rates, the influence of the generated signal due to the probe acting as pump or Stokes becomes insignificant.

 

Fig. 6. (a) Probe delay scan for different amounts of chirp measuring the CH stretching vibration of acetonitrile at $2942{\mathrm{cm}}^{-1}$. The data is corrected for space–time coupling and normalized to the data at $1000{\mathrm{fs}}^2$. (b) Spectra of sunflower oil measured at different probe delays at a constant chirp of $5000{\mathrm{fs}}^2$. For better comparison, the spectra are normalized to the CH stretching vibration at $2850{\mathrm{cm}}^{-1}$. At later time delays, the asymmetric olefinic =CH signal at $3015{\mathrm{cm}}^{-1}$ can be easily differentiated from the neighboring modes.

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For time-delay scans, the signal is expected to decrease starting at the end of the excitation, i.e., at zero probe delay. At a chirp of $1000{\mathrm{fs}}^2$, the data agrees well with the expectations, while for increasing chirp rates the reversal point is shifted to negative delays. Because the delay is calculated based on the extent of the dispersion of pump/Stokes, it highly depends on the definition of the pump/Stokes spectral regions. At higher chirp, the end of the excitation occurs earlier than in the calculated case because the low-intensity frequencies from the wings only have little contribution to the CARS signal. The axis, however, can be easily adjusted relative to the reversal point without losing information (not shown).

In Fig. 6(b) the concept is extended to follow the evolution of the CH vibrations of sunflower oil [46]. Measuring the spectra as a function of the probe delay reveals differences in the decoherence times, which can be exploited for imaging and spectroscopy. While the asymmetric olefinic =CH-signal at $3015{\mathrm{cm}}^{-1}$ increases with the probe delay, the signal at $2940{\mathrm{cm}}^{-1}$ decreases in relation to the symmetric CH stretch at $2850{\mathrm{cm}}^{-1}$. Only two peaks are distinguishable at early probe delay and are partly overlapping the weak signal at $3015{\mathrm{cm}}^{-1}$. Delaying the probe, however, allows for distinguishing the Raman modes even at low chirp rates solely based on the fast decay of the signal at $2940{\mathrm{cm}}^{-1}$. In Fig. 6(b) the olefinic CH vibration is clearly resolved at a delay of 200 fs.

5. SPECTRAL RESOLUTION

A. Influence of the Phase Function

The influence of the applied phase functions on the spectral resolution and on background suppression is presented in Fig. 7. For clarity and simplification, the interference with nonresonant contributions is initially omitted and only purely resonant signals considered. This is justified because it closely resembles the experiment. In tailored spectral focusing, nonresonant parts are drastically reduced when detecting only the spectrally separated signal generated by the time-delayed probe [red signal in Figs. 4(a) and 4(b)]. As explained in the previous section, the steepness (${\varphi }_2$: quadratic phase function) of the parabolas controls the amount of chirp and therefore the instantaneous bandwidth $\mathrm{\Delta }\omega$ of pump and Stokes. Its influence on the pulse is displayed in the time-frequency map of Fig. 7(a). The higher the chirp, the narrower the instantaneous bandwidth becomes and the longer the frequencies are stretched in time. The equal amount of chirp applied ensures a constant IFD and hence also leads to equal bandwidths $\mathrm{\Delta }\omega$ of pump and Stokes. In addition, the linear phase function of the probe solely leads to a delay in time, which is used here to suppress the generation of nonresonant background.

 

Fig. 7. Influence of the chirp rate on the measured linewidth. (a) Phase, time-frequency plot, and resulting instantaneous bandwidth for low ($\mathrm{\Delta }{\omega }_1$, red) and significantly higher chirp ($\mathrm{\Delta }{\omega }_2$, green). (b) Excitation process following from the phases in (a). The combination of the instantaneous bandwidths of pump and Stokes can lead to excitation within a range ${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$ [see Fig. 1(a)] around a selectable center frequency. In case No. 2 the IFD coincides with the resonance while in Nos. 1 and 3 the IFD is detuned away from the resonance by $\mathrm{\Delta }\mathrm{\Omega }$. (c) Spectral resolution increases with the chirp rate and approaches the natural linewidth depicted as a gray area.

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Figures 7(b) and 7(c) show how the amount of chirp affects the measured linewidth of a Raman level ${\mathrm{\Omega }}_{\mathrm{res}}$ (green rectangle) when the IFD is detuned by a frequency $\mathrm{\Delta }\omega$. At a given point in time, the pump frequencies create virtual levels with a range of approximately $\mathrm{\Delta }\omega$ and interact with the simultaneously arriving Stokes frequencies, which cover a range of $\mathrm{\Delta }\omega$ [compare to Fig. 7(a)]. The possible pump–Stokes frequency pairs at each point in time will therefore cover a range ${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$ as defined by the convolution of pump and Stokes frequencies [Eq. (2), Fig. 1(a)]. In this simplified picture, it is obvious that the measured linewidth, as shown in Fig. 7(c), is highly dependent on the range of pump–Stokes frequency pairs at one point in time, even when only considering resonant contributions.

The maximum signal is generated when the instantaneous frequency difference coincides with the Raman line (case No. 2, Fig. 7). If the applied chirp is too small, as depicted by the red phase in Fig. 7(a) and left scheme in Fig. 7(b), the bandwidth of the excitation ${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$ becomes broader. When detuning the IFD, the Raman level is still covered to some extent. Thus a resonant signal is created although the center of excitation is already outside the linewidth. This results in a broadened measured linewidth as depicted in Fig. 7(c) (cases No. 1 and 3). By applying steeper parabolas and thus a higher chirp, as shown in the right scheme of Fig. 7(b), the improved accuracy of the IFD ($\sim 2\mathrm{\Delta }\omega$) leads to a more focused excitation when detuned by the same frequency $\mathrm{\Delta }\mathrm{\Omega }$. The frequency pairs do not coincide with the Raman level anymore and lead to a narrower measured linewidth. The limiting width is given by the natural linewidth of the Raman resonance and cannot be improved by increasing the chirp. Additional chirp only stretches the pulses in time and leads to decreased signal levels while maintaining the linewidth.

Furthermore, the flexible adjustment of the instantaneous bandwidth to varying Raman linewidths allows for the suppression of the otherwise overwhelming nonresonant background of broadband pulses. The excitation is focused to a small region around the resonance and the excitation of any virtual levels nearby [dashed lines in Fig. 7(b)] is minimized. Also, since a higher chirp results in stretched pulses, the nonresonant contributions are decreasing, while resonant coherence is continuously built up until the interaction with the probe frequencies generates signal in the detection window. The possibility to flexibly adjust the chirp to match the bandwidth ${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$ with the linewidth of a Raman level demonstrates one of the main advantages of implementing spectral focusing with a pulse shaper.

B. Linewidth: Measurement versus Simulation

Figure 8 shows spectral focusing measurements and simulations of the CH resonance of acetonitrile at $2942{\mathrm{cm}}^{-1}$ for different amounts of chirp. The inset displays the extracted full width at half-maximum (FWHM) value and therefore the dependence of the obtained spectral resolution on the applied chirp. The simulation was carried out using the definitions and equations presented. The generation of nonresonant background was minimized by delaying the probe to arrive 300 fs after the end of the excitation. The very good agreement of simulation and experiment confirms the justification of the employed simulation and that all phase functions have been applied correctly in the experiment. As expected from the explanations above, the linewidth strongly depends on the applied chirp and can be used to control the spectral resolution within the limits of applicable phase functions. The implementation of spectral focusing in a single-beam CARS experiment containing a pulse shaper therefore allows for fast and flexible adjustment and optimization of resonant signal levels and good spectral resolution while suppressing most of the nonresonant background.

 

Fig. 8. Comparison of the measured (red) and simulated (black) linewidths obtained for the CH stretching vibration of acetonitrile at $2942{\mathrm{cm}}^{-1}$ in dependence of the amount of chirp applied. The measured spectra for $3000{\mathrm{fs}}^2$ and $9000{\mathrm{fs}}^2$ are depicted in light and deep red, respectively. The inset shows the obtained FWHM of the lines in dependence of the chirp. The probe was delayed in all cases to 300 fs after the end of the excitation.

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6. SPECTRAL FOCUSING IN THE FINGERPRINT REGION

Exploiting the flexibility of the pulse shaper allows for extending the spectral range of the presented scheme to the fingerprint region. By appropriately choosing the frequency regions from the broadband laser spectrum, CH stretching vibrations of functional groups and the low-wavenumber region can be reached. The fingerprint region as a whole carries most of the molecule’s specific structural chemical information, making it the key part of a spectrum to even distinguish molecules with small differences.

While the pump and Stokes regions can be chosen arbitrarily from all over the spectrum to drive the coherence of a chosen resonance, the probe frequencies, however, are also determined by the position of the detection window (${\omega }_{\mathrm{CARS}}={\omega }_{\mathrm{Pr}}+\mathrm{\Omega }$). When applying spectral focusing in the fingerprint region, the order of the pump and probe regions has to be changed to still shift the signal to the detection window and pass the cutoff filter. Figure 9 shows the excitation and the signal generation along with the applied phase function for the measurement of the resonance of toluene at $1004{\mathrm{cm}}^{-1}$. In order to prevent destruction of the sample due to high laser power, the intensity of the laser was reduced to 30% and frequencies not taking part in the signal generation process cut out by amplitude shaping. Thereby, the intensity remains constant when performing a spectral scan. A low-pass filter at 700 nm was chosen and the blue wing of the spectrum blocked in the Fourier plane of the shaper. The scheme also allows for choosing the probe frequencies so that the generated signal overlaps with the blue wing of the spectrum. Because the blue wing is coherent in space and time with the generated spectral focusing signal, heterodyne measurements in the fingerprint region are feasible when omitting the filter (not shown) [26,47].

 

Fig. 9. (a) and (b) show the blue-shifted spectral focusing signal in the fingerprint region of toluene as measured in the experiment. (c) depicts the spectrum with the applied phase functions for pump, Stokes, and probe regions as indicated at the right side of the figure. Note that their order has changed compared to Fig. 4. The time distribution of the frequencies is depicted in (d). The signal generated by the pump acting as probe (blue) cannot pass the filter at 700 nm ($\mathrm{14,285}{\mathrm{cm}}^{-1}$). As shown in (a), the detector records only the signal generated by the time-delayed probe frequencies (red). (e) Influence of the amount of chirp on the measured linewidth of the band at $1004{\mathrm{cm}}^{-1}$. Applied chirps from top to bottom are $2000{\mathrm{fs}}^2$, $3000{\mathrm{fs}}^2$, $5000{\mathrm{fs}}^2$, $7000{\mathrm{fs}}^2$, $9000{\mathrm{fs}}^2$, $\mathrm{12,000}{\mathrm{fs}}^2$, and $\mathrm{15,000}{\mathrm{fs}}^2$. The delay of the probe was set to 200 fs after the end of the excitation.

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In Fig. 9(d), pump and Stokes drive the coherence at ${\mathrm{\Omega }}_{\mathrm{res}}$ and are probed by the time-delayed frequencies indicated to generate resonant signal [Figs. 9(a) and 9(b), red]. Because of the changed order of pump and probe, the signal generated by the pump acting as probe [Fig. 9(d), blue] will in this case not pass the filter. By scanning the steepness and the spacing of the parabolas, the spectra of toluene in dependence of the chirp are obtained. Figure 9(e) shows the measured Raman lines at $1004{\mathrm{cm}}^{-1}$ with increasing spectral resolution, corresponding to increased chirp. The slight shift to lower wavenumbers when applying low chirp can be explained by interference with nonresonant signal, resulting in dispersive lineshapes and therefore a shift in frequency. In this case, the bandwidth of the excitation [${\mathrm{\Delta }\mathrm{\Omega }}_{\mathrm{IFD}}$, Fig. 1(a)] is so high that the pump acting as probe is generating a broad nonresonant signal that leaks into the detection window and interferes with the resonant one originating from the actual time-delayed probe. Again, this shows the importance of choosing the right amount of chirp.

7. SIMULTANEOUS MULTIMODAL IMAGING

Signals like second-harmonic generation (SHG) or two-photon excited fluorescence (TPEF) [48], which are often used in multimodal microscopy, benefit from short femtosecond pulses. The signal intensity of the nonlinear process of order $n$ scales with the duration $\tau$ of the pulse $S\propto 1/{\tau }^{(n-1)}$ [49]. In picosecond CARS experiments, however, two tunable picosecond lasers are used in order to improve contrast and spectral resolution and are therefore not well suited for multimodal imaging. As has already been discussed, spectral focusing is essentially able to achieve similar resolution by stretching initially very short fs pulses in time. Unfortunately, this also leads to significantly reduced SHG and TPEF signal levels. Multimodal imaging and resonant CARS imaging with optimal contrast and signal intensity in typical spectral focusing setups can thus only be achieved by switching between fs pulses and spectral focusing. One exception is the use of ultrabroadband 5 fs lasers in a specialized and complex setup [50]. However, in the framework of the broadband single-beam CARS setup presented, simultaneous measurements of spectrally separated SHG and TPEF, as well as the resonant spectral focusing CARS signal, are readily possible. Because of the transform-limited nature of the probe, the signal levels of SHG and TPEF are significantly increased (compared to usual spectral focusing where the probe is also highly chirped). In addition, it is possible to distinguish overlapping signals based on their different dependence on the phase of the incoming laser beam [51].

Figure 10 shows the obtained multimodal images of human skin tissue. When transform-limited pulses are applied, the CARS signal gives the structure [Fig. 10(a)] while spectral focusing at $2850{\mathrm{cm}}^{-1}$ allows for selectively imaging lipid cells due to their strong CH resonance [Fig. 10(b)]. Figure 10(c) highlights the achieved contrast along the blue lines in Figs. 10(a) (gray background) and 10(b) (black line). The simultaneously recorded SHG image in Fig. 10(d) illustrates the distribution of collagen and shows signal between lipid cells. The TPEF signal in Fig. 10(e) is also simultaneously recorded with the spectral focusing phase function from Figs. 10(b) and 10(d). The data is combined in an RGB image in Fig. 10(f) that shows the complementary information of the multimodal signals as well as distinct discrimination between cells and neighboring tissue.

 

Fig. 10. Multimodal imaging of $200\mathrm{\mu m}\times 200\mathrm{\mu m}$ human skin tissue with (a) a transform-limited pulse and (b), (d)–(f) spectral focusing. (c) illustrates the high contrast achieved with spectral focusing (black line) compared to TL pulses (gray background) along the blue lines in (a) and (b). The images show (a) and (b) CARS, (d) SHG, and (e) TPEF signal. (f) A multimodal RGB image is constructed by combining the simultaneously collected CARS (red), SHG (blue), and TPEF (green) data obtained with a spectral focusing phase function. The chirp was set to $3000{\mathrm{fs}}^2$, and the probe was delayed 100 fs after the end of the excitation (Fig. 4). Signals were collected using photomultipliers and bandpass filters (CARS: $640\pm 10\mathrm{nm}$, SHG: $400\pm 10\mathrm{nm}$, TPEF $500\pm 20\mathrm{nm}$).

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8. CONCLUSION

In conclusion, a scheme for spectral focusing CARS microspectroscopy based on flexible control of the spectral phase and amplitude by elaborated shaping of sub-10 fs pulses is presented. Exploiting the flexibility of a pulse shaper allows for independent control over the pump, Stokes, and probe frequencies in the focus of a microscope. Raman modes of complex samples from the fingerprint to the CH region around $3000{\mathrm{cm}}^{-1}$ are accessible just by switching the applied phase function. The instantaneous bandwidth of pump and Stokes can be variably adjusted to the linewidths of different Raman modes throughout the spectrum, optimizing spectral resolution and signal intensity. By identifying frequencies taking part in the signal generation process, the potential of independently shaping the probe can be explored. Simulations of the single-beam CARS signal for different phase functions are explained in detail and confirm the experimental results. Delaying the probe allows for a full build-up of the coherence, while the signal due to other parts of the spectrum acting as probe can be spectrally separated. Therefore, increased signal levels with minimized nonresonant backgrounds are obtained. Because of the transform-limited nature of the time-delayed probe, nonlinear signals like SHG or TPEF are significantly enhanced. Contrast obtained with spectral focusing and simultaneous multimodal imaging is demonstrated by measurements of human skin tissue. Furthermore, the possibility of creating contrast based on differences of the decoherence times of molecular vibrations is exemplarily shown on the CH-modes of sunflower oil.

Implementing spectral focusing into a SB-CARS setup by imprinting arbitrary phase functions on fs-pulses with a pulse shaper therefore offers advantages over alternative implementations and a wide range of possibilities for further development.