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Coherent anti-Stokes Raman scattering (CARS) with femtosecond interaction pulses has become a popular and powerful spectroscopic method. Non-resonant background is one of the most limiting factors for implementing this method more widely. We propose a new approach that suppresses the non-resonant background contribution to the measured signal in CARS spectroscopy while simultaneously yielding high spectral resolution. The method is based on femtosecond pulse shaping of probe, Stokes and pump beams. Destructive interference suppresses the non-resonant background, resulting only in the resonant contribution being detected.
©2011 Optical Society of America
1. Introduction
Coherent anti-Stokes Raman scattering (CARS) is a four-wave mixing process whereby two electromagnetic frequencies excite coherent molecular vibrations in a molecule or group of molecules of interest. A resonance condition results when the frequency difference between the two beams matches a natural vibrational mode of the molecule(s). The beam with higher frequency is normally called the pump, and the beam with lower frequency is called the Stokes beam. A third beam, called the probe, scatters off the coherently excited vibrations and a fourth coherent beam is generated, called the anti-Stokes beam, with a frequency equal to the frequency of the probe wave plus the frequency of the excited molecular vibration [1]. Femtosecond (fs) pulses allow the attainment very high intensities within the volume where the pump, Stokes and probe beams interact (i.e., are appropriately phase-matched) while simultaneously keeping the average power at a relatively low level. CARS has been successfully implemented for time-resolved chemical analysis [2–4], remote sensing of complex molecules [5, 6], and non-invasive imaging of biological specimens [7–10]. However, one of the main limitations for applications of CARS spectroscopy is the presence of a strong non-resonant background component in the measured signal. This non-resonant background is due to interactions involving the highly detuned electronic energy levels. In the vast majority of applications, the non-resonant background has a constant amplitude across the spectral range which is limited by the bandwidth of the typical femtosecond pulses due to the high detuning of all four waves from electronic levels.
There are several methods available to reduce this non-resonant background. One of the most common techniques is to exploit the inherently different polarizations of the resonant and non-resonant contributions [11, 12]. However, this difference is typically small (less than 10 degrees) [11] which makes it difficult to apply in some applications. Another approach is the use of ultrashort laser pulses for the pump, Stokes and probe beams and to introduce a time delay between the pump/Stokes pair of pulses and the probe pulse [13, 14]. Due to the fact that non-resonant background is generated only when all three pulses overlap in time, it is possible to use this method for non-resonant background rejection if the excited vibrational states being probed persist longer (more than couple hundreds femtoseconds) than the delayed probe pulse. This approach, however, gives low spectral resolution that can limit its applicability.
There has been significant progress in spectroscopic methods, including CARS, based on femtosecond pulse shaping within the last five years [15–18]. Different amplitude and phase pulse shaping approaches can give high spectral resolution and, simultaneously, suppressed non-resonant background. Some of these methods, however, do not achieve good background suppression without significant non-linear signal reduction, or do not yield spectra readily comparable with normal Raman spectra. In [18], it was demonstrated that Lorentzian amplitude/phase pulse shaping could offer good comparability with Raman spectra and simultaneously good background suppression. The main disadvantage was that imperfections in the pulse shaping apparatus did not allow achieving an accurate Lorentzian pulse shape and hence some non-resonant background remained. Another disadvantage was that the spectral resolution was limited by the optical shaper resolution.
Another interesting approach to suppress non-resonant background was proposed in [19]. This method is based on destructive interference between the CARS signal generated in the sample and a phase-locked second harmonic generated in a non-linear crystal. Experimental confirmation was not shown, but this method suffers from the fact that the CARS and second harmonic signals are generated in different media, and full destructive interference can be achieved only when both signals are equal. Thus, it would need to be adjusted for each measurement and it would be difficult to implement efficiently in CARS microscopy due to high non-resonant as well as resonant signal variation across the sample. A similar approach was experimentally demonstrated in [20] where an external light source was used to achieve destructive interference with the non-resonant background. The resonant CARS signal was amplified by exploiting a heterodyne effect. This method requires interferometric stabilization to achieve stable phase matching between the CARS and additional external light source at the same optical frequency. Another noteworthy approach was proposed in [21] where a maximum entropy method was used to reconstruct the resonant CARS spectrum from the measured signal. However, this is a post-processing data analysis method and does not actually suppress the non-resonant background in the experiment. Further, this method works well only in the case of low non-resonant background or high dynamic range of the detector.
In this paper, we demonstrate a new approach that effectively suppresses non-resonant background in CARS spectroscopy and, additionally, provides high spectral resolution. The method is based on the destructive interference between two phase-locked coherent CARS signals originating from non-resonant contributions generated in the same sample. It therefore does not require energy adjustment between the contributing components for full non-resonant background destructive interference nor does it require interferometric stability between beams along different optical paths. The measured signal comprises only the resonant part and does not require time consuming and potentially distorting post-acquisition signal processing.
2. Method description
Non-resonant background is generated from highly detuned electronic excited states (Fig. 1 ). Figure 1(a) shows two levels excited by one narrow-band pump, two narrow-band Stokes pulses of different frequencies, and two narrow-band probe pulses that differ in frequency by the same amount as the frequency difference between the Stokes pulses. The resulting CARS signal is generated at three different frequencies (Fig. 1(a), right). The CARS signal at the central frequency consists of two signals originating from two different paths. Those two signals can interfere constructively or destructively depending on the relative phase between both paths. This relative phase is dictated by the phase difference between the two Stokes frequencies and the phase difference between the two probe frequencies. The CARS signal is equal to zero at the central frequency if the phase is adjusted so that the two CARS signals are out of phase and both paths give the same efficiency. There will be non-zero CARS signal at the central frequency only if there is one real Raman line in the investigated system (Fig. 1 (b)). The CARS signal at the lower frequency is comprised of a non-resonant contribution only. The CARS signal at higher frequency has both non-resonant and resonant contributions if a real Raman line is excited by the lower frequency Stokes wave. Non-resonant contributions can also appear at the higher frequency if a real Raman line is excited by the higher frequency Stokes wave.
Fig. 1 Experimental scheme. One narrow-band pump and two narrow-band Stokes beams excite two non-resonant only contributing states (a) and one Raman active state (b). Two narrow-band probe beams with frequencies that differ by the same amount as the two Stokes beams are scattered from two levels generating CARS signals at three possible frequencies. The CARS signal at the central frequency is comprised of contributions from two different paths. In the case of a non-resonant contribution only, this central signal can be suppressed if there is destructive interference between both paths (a, lower spectrum) or can be enhanced if there is constructive interference (a, upper spectrum). Destructive interference with one Raman level (b) results in the Resonance contribution only in the signal at the central frequency (b, spectrum).
Raman spectra can be obtained by measuring the CARS signal at the central frequency while simultaneously varying the frequency of the narrow-band pump beam (Fig. 1). This method assumes some initial knowledge about the Raman spectra of the investigated sample because it is necessary to have only virtual levels (non-resonant contribution only) in one of the CARS signal paths. Otherwise, the measured signals will show combinations of several overlapping Raman lines shifted relative to each other by the frequency difference between the narrow-band Stokes and probe beams. Importantly, the destructive interference does not depend on the sample density because the non-resonant contributions from both paths are generated within the same sample and the same volume.
3. Numerical simulation
In CARS, the two laser pulses, Ep (pump) and Es (Stokes), induce the vibrational coherence A at frequency Ω according to [11]:
where Ωn, Γn are the frequency and relaxation rate, respectively, of vibrational level n; Cn, CNR are the amplitudes of the resonant (n-th level) and non-resonant non-linear susceptibilities, respectively. The probe pulse Epr scatters off the induced coherence producing the anti-Stokes polarization with the frequency response given byIn our numerical simulations, we took one Raman line with Γ=4cm−1 (Fig. 2 , red line) and the same line on top of the non-resonant background (Fig. 2, blue line). We took the spectral bandwidth for the pump, Stokes and probe pulses to be the same at 20cm−1. The spectral separation between the two narrow spectral components in the Stokes and probe beams was chosen to be 420cm−1 (Fig. 2, black line); both probe and pump beams have flat spectra phases. The Stokes beam has a π-step spectral phase between spectral components.
Fig. 2 Simulated Raman spectrum with a single resonant peak only (red, Γ=4cm−1) and the same spectrum with non-resonant background (blue). Spectra of the Stokes and Probe pulses (black).
The 2-dimensional spectrogram shown in Fig. 3 displays simulated CARS spectra at different pump beam frequencies which results in three distinct spectral lines (Fig. 3). The two intense lines on either side of the less intense central line correspond to the non-resonant background together with the resonant peak from the simulated Raman spectrum when the frequency difference between the pump and one of the Stokes spectral components matches the resonant Raman component. The central line on Fig. 3 corresponds to the situation when the non-resonant background is suppressed due to destructive interference between non-resonant signals from different paths. The sum of all CARS intensities across the low-frequency (left-most) line on Fig. 3 gives the CARS spectrum comprised of one Raman line on top of the non-resonant background (Fig. 4 , blue). This curve is almost identical to the CARS spectrum (Fig. 4, green) obtained from the same single Raman line on top of the non-resonant background (as shown in Fig. 2) using single Gaussian frequency pump, Stokes and probe pulses. The sum of all CARS intensities across the central line on Fig. 3 gives the single Raman line CARS spectrum with suppressed non-resonant background. Each of the two peaks corresponds to the frequency matching between the Raman line and frequency difference between the pump and one of the two Stokes spectral components. This curve is almost identical to the sum of the CARS spectra obtained from the same single Raman line but without non-resonant background and using single Gaussian frequency pump, Stokes and probe pulses (Fig. 4, red).
Fig. 4 Sum of CARS spectra obtained at different wavelengths of the pump beam. (Blue) corresponds to the sum of the low-frequency CARS components of Fig. 3. (Black) corresponds to the sum of the central-frequency CARS components of Fig. 3. (Green) corresponds to the CARS signal obtained with single frequency pump, Stokes and probe from the single Raman line on top of the non-resonant background (as in Fig. 2, blue). (Red) corresponds to the CARS signal obtained with single frequency pump, Stokes and probe from single Raman line without the non-resonant background (as in Fig. 2, red).
4. Experiment
The experiments employed a laser system based on a femtosecond Ti:Sapphire oscillator (Synergy, Femtolasers, Austria), amplifier (Spitfire Pro, Spectra Physics, USA) and optical parametric amplifier (OPA) (Topas, Light Conversion, Lithuania) (Fig. 5 ). The amplifier generated 3-mJ, 35-fs pulses with 800 nm central wavelength at a 1-kHz repetition rate. A portion (100 μJ) of the fundamental was coupled to a custom built spectral filter (Fig. 5, insert) based on a diffraction grating with 1200 gr/mm, lens with 30cm focal distance, silver mirror, two variable slits placed on translation stages perpendicular to the beam and two glass microscope cover slips (200 µm, borosilicate glass). The mirror and diffraction grating are placed in the focal plane of the lens. Two variable slits select two narrow spectral components separated by ~620 cm−1. One of the glass cover slips is placed on a rotational stage and is used to alter the phase between two narrow-band frequencies. Light reflected from the back mirror goes back through the lens and both frequencies are recombined on the same diffraction grating at a slightly lower position. This radiation serves as the probe beam with pulse energies of ~500 nJ.
An additional portion (1 mJ) of the fundamental radiation was used to pump the OPA. The signal and second harmonic of the idler radiation from the OPA were used as Stokes and pump beams, respectively. Both beams are coupled into similar spectral filters, but only one slit was used in the spectral filter for the pump beam. This slit is installed on a translation stage to allow scanning the central frequency of the pump beam within the spectral bandwidth of the signal radiation from the OPA. For these experiments, the slit was scanned in ~5-cm−1 increments. Variable neutral density filters were used in the spectral filter for the Stokes beam instead of transparent glass in order to balance the CARS signal generated by both paths (Fig. 1). The output pulse energies from both spectral filters was ~50 nJ. The spectral bandwidth of each narrow-band spectral component in the pump, Stokes and probe beams was ~10 cm−1.
In experiments reported here, we used glass and neat ethanol as model samples to generate a well characterized broadband CARS signal from a homogeneous sample. All three beams were focused in a standard BOXCARS geometry with a 25-cm focal length mirror into a 5-mm optical path cuvette containing neat ethanol. The CARS signal was filtered out using a spatial filter and directed to a 350-mm focal length spectrometer (Model 2035, McPherson, USA) with 0.3-nm spectral resolution equipped with a cooled CCD (iDus, Andor, Ireland). The signal beam from the OPA with a center wavelength λs=1260 nm was used as a Stokes beam. The second harmonic of the idler beam was used as a pump with a central wavelength λp = 1080 nm. The combination of pump/Stokes radiation excited Raman modes of ethanol in the range from 1200 to 1600 cm−1 with 1400 cm−1 central frequency; the exposure time was 0.1 seconds.
Initially, glass was used to calibrate the optical system and achieve full destructive interference between both paths generating CARS at the central frequency. This calibration was performed by adjusting the Stokes and probe beam slits to equalize spectral width. The separation between slits was also adjusted to yield identical frequency separation between the two spectrally narrow components in the Stokes and probe beams. The pump beam slit was set to cut ~10cm−1 in the middle of the pump spectra and was not changed during the calibration procedure. Two variable neutral density filters were used to equalize the non-resonant CARS signals from both paths contributing to the overall CARS signal. A glass cover slip placed on a rotational stage was used to alter the phase between the two narrow-band frequencies to achieve destructive interference between both paths in the CARS process. We achieved about 20 times suppression of the non-resonant background compared with the CARS signal from any of the paths separately. The glass was then removed and a cuvette containing a neat ethanol sample was placed in the focal point to generate CARS signal. Slits, neutral density filters and microscope cover slips in the Stokes and probe spectral filters were not changed during collection of the CARS signal from the investigated sample.
5. Results and discussion
Neat ethanol was subsequently used as a model sample to demonstrate the proposed method. The broadband Pump/Stokes beams excite Raman modes within a band centered at 1200 cm−1 and the narrow-band probe gives a high-resolution CARS spectrum with significant non-resonant background (Fig. 6 ).
Fig. 6 Spontaneous Raman spectrum of ethanol (red), and CARS spectrum (blue) recorded with broadband pump/Stokes and narrow-band probe.
CARS signals obtained by varying the position of the slit on the pump beam shows three lines (Fig. 7(a) ). The left line represents the non-resonant component only. The right line represents both resonant and non-resonant contributions. The central spectral component represents the resonant contribution only (non-resonant background is suppressed about 20 times).
Fig. 7 CARS spectra from neat ethanol at different values of the central wavelength of the narrow-band pump wave (a). Sum of all CARS spectra obtained at different wavelengths of the Pump beam (b, black). Part of spontaneous Raman spectra covered by pump-Stokes excitation (b, red). CARS spectra obtained at 1060nm probe beam wavelength. The shaded sliding rectangle represents the part of the spectrum used for integrating over the CARS signal with suppressed non-resonant background (c). Sum of all CARS spectra without non-resonant background obtained at different wavelengths of the pump beam (d).
The Raman spectrum of the ethanol can be obtained by summing all CARS spectra (Fig. 7(b)). The right broadband peak represents non-resonant contribution only. The left peak shows non-resonant and resonant contributions from ethanol. The asymmetric spike on top of this peak represents interference between the 1454-cm−1 Raman line and the non-resonant contribution. The central part of the spectrum comprises the two Raman lines at 1276cm−1 and 1454cm−1 with low (suppressed) background. Spectral resolution is dictated by the spectral bandwidth of all spectral components of pump, Stokes and probe used in CARS process. Some small background observed in the experiment is attributed to non-complete suppression of the non-resonant background mainly due to laser energy fluctuation. Those lines are well correlated with the spontaneous Raman spectrum (Fig. 6, red line) within the spectral range 1200 – 1600 cm−1. A single CARS spectrum shows three very distinct spectral lines (Fig. 7(c)). Obviously it is easy to filter-out central CARS spectral component with suppressed non-resonant contribution. Summing all CARS spectra without both side spectral components gives resonant CARS spectra only (Fig. 7(d)).
It is necessary to have only virtual levels (non-resonant contribution only) in one of the CARS signal paths in order to obtain non-resonant background suppression. CARS spectra obtained only from virtual levels should be smooth and should not contain any sharp elements characteristic of the real Raman levels. CARS spectra obtained only from the non-resonant contribution (high frequency CARS spectral component on Fig. 7(b)) can be used to verify this requirement.
6. Conclusion
We have demonstrated a new approach to obtain CARS spectra with suppressed non-resonant background and good spectral resolution. This approach is based on destructive interference between non-resonant contributions generated in the same volume of the investigated sample. Destructive interference happens between non-linear polarizability generated in the same sample volume and non-resonant background suppression does not depend on the sample concentration and CARS generation efficiency. Destructive interference of the non-resonance background does not require interferometric stability between beams travelling through the sample along different optical paths. One of the disadvantages of this method is the relative complexity of the experimental setup that requires three spectral shapers. Also, the spectra generated in the OPA are less stable which leads to relative amplitude fluctuation between two frequencies in the pump beam and reduces destructive interference efficiency between the non-resonant components. However, this method provides nearly complete non-resonant background suppression without resonant component distortion.
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