## Single-shot interferometric approach to background free broadband coherent anti-Stokes Raman scattering spectroscopy*

Optics Express, Vol. 17, Issue 1, pp. 123-135 (2009)

http://dx.doi.org/10.1364/OE.17.000123

Acrobat PDF (259 KB)

### Abstract

We introduce a single-shot interferometric approach to suppress the nonresonant background (NRB) contribution to a broadband coherent anti-Stokes Raman scattering (CARS) spectrum; this single-shot approach is conducive to rapid imaging. A pulse shaper prepares a narrowband pulse with two spectral components of differing phase. When the CARS fields generated by these two out-of-phase components are optically mixed, NRB signal is greatly reduced while a resonant CARS signal remains with minimal attenuation. We discuss and demonstrate two model schemes for the interfering pulse components: (1) two pulses with different bandwidths and the same center frequency (*ps-fs* scheme) and (2) two pulses with the same bandwidth and shifted center frequencies (*ps-ps* scheme). In both schemes, only the resonant signal from the “3-color” CARS mechanism survives. The resonant signal from “2-color” CARS mechanism vanishes along with the NRB. We discuss optimization conditions for signal intensity and shape of resonant CARS peaks. Experimental CARS spectra of c-hexane and benzonitrile demonstrate feasibility of these approaches.

© 2009 Optical Society of America

## 1. Introduction

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

2. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA **102**, 16807–16812 (2005). [CrossRef] [PubMed]

3. J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B **106**, 8493–8498 (2002). [CrossRef]

^{-1}) [6

6. H. A. Rinia, M. Bonn, and M. Muller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B **110**, 4472–4479 (2006). [CrossRef] [PubMed]

7. Y. J. Lee, Y Liu, and M. T. Cicerone, “Characterization of 3-color CARS in a 2-pulse broadband CARS spectrum,” Opt. Lett. **32**, 3370–3372 (2007). [CrossRef] [PubMed]

8. F. Ganikhanov, C. L. Evans, B. G. Saar, and X. S. Xie, “High-sensitivity vibrational imaging with frequency modulation coherent anti-Stokes Raman scattering (FM CARS) microscopy,” Opt. Lett. **31**, 1872–1874 (2006). [CrossRef] [PubMed]

9. J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-stokes raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B **105**, 1277–1280 (2001). [CrossRef]

10. J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. **26**, 1341–1343 (2001). [CrossRef]

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

12. C. L. Evans, E. O. Potma, and X. S. N. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ^{(3)} for vibrational microscopy,” Opt. Lett. **29**, 2923–2925 (2004). [CrossRef]

13. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. **31**, 241–243 (2006). [CrossRef] [PubMed]

14. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. **90**, 213902 (2003). [CrossRef] [PubMed]

15. B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B **112**, 3653–3661 (2008). [CrossRef] [PubMed]

16. T. W. Kee, H. X. Zhao, and M. T. Cicerone, “One-laser interferometric broadband coherent anti-Stokes Raman scattering,” Opt. Express **14**, 3631–3640 (2006). [CrossRef] [PubMed]

17. J. P. Ogilvie, E. Beaurepaire, A. Alexandrou, and M. Joffre, “Fourier-transform coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. **31**, 480–482 (2006). [CrossRef] [PubMed]

## 2. Theory

**P**

^{(3)}, which is expressed as

**χ**

^{(3)}is the third-order nonlinear susceptibility,

**E**(

*ω*) are the electric field vectors, and the subscripts

*p*,

*S*,

*pr*, and

*aS*indicate pump, Stokes, probe, and anti-Stokes transitions, respectively. Recent studies [7

7. Y. J. Lee, Y Liu, and M. T. Cicerone, “Characterization of 3-color CARS in a 2-pulse broadband CARS spectrum,” Opt. Lett. **32**, 3370–3372 (2007). [CrossRef] [PubMed]

18. H. Kano and H. Hamaguchi, “Dispersion-compensated supercontinuum generation for ultrabroadband multiplex coherent anti-Stokes Raman scattering spectroscopy,” J. Raman Spectrosc. **37**, 411–415 (2006). [CrossRef]

*E*

_{n}(

*ω*) and

*E*

_{c}(

*ω*) are the electric fields of the narrowband and continuum pulses. The nonlinear polarizations and electric fields are treated as scalar values for simplicity. The third-order nonlinear susceptibility,

*χ*

^{(3)}, can be described as a function of (

*ω*-

_{p}*ω*) and can be expressed using parameters from a spontaneous Raman spectrum [19] as follows

_{S}*χ*

_{NR}^{(3)}and

*χ*

_{R}^{(3)}are the nonresonant and resonant contributions, respectively,

*Ω*is the frequency of the

_{R,i}*i*th Raman mode,

*A*is a constant representing the spontaneous Raman cross section, and

_{i}*Γ*is the Raman linewidth. From energy conservation considerations, (

_{i}*ω*-

_{p}*ω*) = (

_{S}*ω*-

_{aS}*ω*), and Eq. (4) can be expressed as a function of (

_{pr}*ω*-

_{aS}*ω*) as follows:

_{pr}*E*

_{c}(

*ω*) is generally much larger than that of

*E*

_{n}(

*ω*). Thus, the amplitude and the phase of

*E*

^{*}

_{c}(

*ω*+

_{p}*ω*-

_{pr}*ω*) is essentially constant within the integral over

_{aS}*dω*in Eqs. (2) and (3), when

_{pr}*E*

_{c}(

*ω*) is transform-limited and its spectral shape is smooth. Under these conditions the coupled double integrals in Eqs. (2) and (3) can be reasonably approximated as products of separate integrals. We make this assumption in the following (deviations from this approximation will be pointed out in the discussion of the

*ps-fs*scheme below).

*E*

_{n}(

*ω*) into a superposition of two pulse components whose amplitudes and phases are independently controlled. In case (1) “

*ps-fs*”, two narrowband Gaussian pulses have different bandwidths and are located at the same center frequency. In case (2) “

*ps-ps*”, two narrowband Gaussian pulses have the same bandwidths and the center frequencies are separated from each other. In both model cases, the resulting CARS spectra show a strong interferometric behavior with the relative phase between the two pulse components. Below we describe the “

*ps-fs*” and “

*ps-ps*” cases using both analytical expressions and simulations of spectra. In the spectral simulations we use a Raman spectrum with three peaks centered at

*Ω*

_{R,1}= 800 cm

^{-1},

*Ω*

_{R,2}= 1000 cm

^{-1}and

*Ω*

_{R,3}= 1200 cm

^{-1}, with amplitudes

*A*

_{1}=

*A*

_{3}= 0.5, and

*A*

_{2}= 1, and widths

*Γ*

_{1}=

*Γ*

_{2}= 10 cm

^{-1}and

*Γ*

_{3}= 5 cm

^{-1}, we also assume

*χ*

_{NR}^{(3)}= 0.2. In all simulations the full-width-half-maximum (FWHM) of the narrowband pulse is set to be 5 cm

^{-1}and the FWHM of the continuum pulse is set to be 2500 cm

^{-1}. Both the narrowband and continuum pulses are assumed to be transform-limited Gaussian functions. Figure 1 shows simulated 2- and 3-color CARS spectra generated with a single narrowband

*ps*probe pulse. This is given as reference for introduction to interferometric approaches using pairs of probe pulses.

### 2.1 ps-fs interference scheme

*ps-fs*scheme,

*E*

_{n}(

*ω*) consists of two Gaussian pulses

*E*

_{ps}(

*ω*) and

*E*

_{fs}(

*ω*), where the bandwidths are significantly different but center frequencies are the same. The electric fields of the two Gaussian pulses are expressed as

*E*

_{ps}(

*ω*) =

*E*

^{0}

_{ps}exp[-(2ln 2)×(

*ω*)-

*ω*

_{c})

^{2}/Δ

*ω*

_{ps}

^{2}] and

*E*

_{fs}(

*ω*) =

*E*

^{0}

_{fs}exp[-(2ln 2)×(

*ω*)-

*ω*

_{c})

^{2}/Δ

*ω*

_{fs}

^{2}], where

*E*

^{0}

_{ps}and

*E*

^{0}

_{fs}are the peak field amplitudes,

*ω*

_{c}is the center frequency, and Δ

*ω*

_{ps}and Δ

*ω*

_{fs}are the FWHM of the intensity spectra. The overall electric field of the narrowband pulse can be written as

*ϕ*is the phase difference between the two pulses. (Note that the

*fs*pulse is considered as a component of the

*narrowband*pulse.) We obtain expressions for 2-color or 3-color CARS emission intensity,

*I*(

*ω*)∝|

_{aS}*P*

^{(3)}(

*ω*)|

_{aS}^{2}, by combining Eq. (7) with Eqs. (5) or (6), respectively:

*χ*

^{(3)}with

*χ*

_{NR}^{(3)}(a frequency-independent constant) in Eqs. (8) and (9). In 2-color and 3-color CARS, interference between the signals generated from

*E*

_{ps}(

*ω*) and

*E*

_{fs}(

*ω*) results in strong dependence of NRB intensity on both Δ

*ϕ*and

*E*

^{0}

_{fs}/

*E*

^{0}

_{ps}as displayed in Fig. 2.

*E*

_{n}(

*ω*) composed of

*E*

_{ps}(

*ω*) and

*E*

_{fs}(

*ω*) with Δ

*ω*

_{ps}= 5 cm

^{-1}, Δ

*ω*

_{fs}= 50 cm

^{-1}and

*E*

^{0}

_{fs}/

*E*

^{0}

_{ps}= 0.1 Figures 2(b) and 2(c) show NRB intensity as a function of Δ

*ϕ*and

*E*

^{0}

_{fs}/

*E*

^{0}

_{ps}respectively. For any given value of

*E*

^{0}

_{fs}/

*E*

^{0}

_{ps}, the NRB contribution is minimized any time Δ

*ϕ*= π, when the two pulses are out of phase. It is maximally suppressed only when Δ

*ϕ*= π and ∫

^{∞}

_{-∞}

*E*

_{ps}(

*ω*)

*dω*= ∫

^{∞}

_{-∞}

*E*

_{fs}(

*ω*)

*dω*. In the case shown in Fig. 2, Δ

*ω*

_{fs}/Δ

*ω*

_{ps}=10, so the NRB signal vanishes at

*E*

^{0}

_{fs}/

*E*

^{0}

_{ps}= 0.1. Inspection of Eq. (8) immediately shows that both resonant and nonresonant signals arising from the 2-color mechanism are eliminated under the conditions of NRB suppression since the first integral term in Eq. (8) becomes zero under these conditions independent of the value of

*χ*

^{(3)}(

*ω*,

_{aS}*ω*). For 3-color CARS signal, described by Eq. (9), the integral involving

_{pr}*E*

_{ps}(

*ω*) and

*E*

_{fs}(

*ω*) can have a non-zero value under the conditions of NRB suppression due to the presence of the term

*χ*

^{(3)}(

*ω*,

_{aS}*ω*).

_{pr}*E*

_{fs}(

*ω*) and

*E*

_{ps}(

*ω*) depicted in Fig. 2(a), will be of equal amplitude and will cancel because the two contributions are phase shifted by π with respect to each other. In such a spectrum, the 3-color resonant Raman features generated by

*E*

_{fs}(

*ω*) are smeared out, yielding a more-or-less spectrally flat signal, while the resonant Raman features generated by

*E*

_{ps}(

*ω*) are sharp and dispersive, characteristic of high-resolution CARS spectra. As with the NRB, the resonant components are π out of phase, but the resonant signal from

*E*

_{fs}(

*ω*) only slightly attenuates the resonant signal from

*E*

_{ps}(

*ω*) due to the flat line shape of the

*E*

_{fs}(

*ω*)-derived signal, and the fact that the latter is spread out over a wider frequency range. Thus, the surviving signal is composed primarily of contributions from the resonant CARS signal due to the

*ps*pulse.

*ω*

_{ps}= 5 cm

^{-1}, and with Δ

*ω*

_{fs}= 50 cm

^{-1}or 500 cm

^{-1}. The peak shapes are not significantly impacted by the relative widths the

*ps*and

*fs*probe components, but the larger value of Δ

*ω*

_{fs}yields an increased recovery of resonant Raman signal. This increased recovery with broad

*fs*probe pulse can be seen more clearly in Fig. 3(b), where the peak intensity of the Raman mode at 1000 cm

^{-1}is plotted as a function of increasing Δ

*ω*

_{fs}/Δ

*ω*

_{ps}, Δ

*ω*

_{ps}being fixed at 5 cm

^{-1}. The peak intensity asymptotically increases towards 100% recovery of the pure resonant signal, which is shown as the dotted line in Fig. 3(a). The dotted line, as a reference, is calculated with

*χ*

_{NR}^{(3)}= 0 and

*E*

_{n}(

*ω*) composed only of

*E*

_{ps}(

*ω*), with

*E*

_{ps}(

*ω*) having an integrated intensity equal to that of

*E*

_{ps}(

*ω*)+

*E*

_{fs}(

*ω*) in the corresponding solid line. Figure 3 shows that with Δ

*ω*

_{fs}= 50 cm

^{-1}and 500 cm

^{-1}, the peak intensity of the Raman mode at 1000 cm-1 reach 59% and 90% intensities of the pure resonant CARS amplitude, respectively. However, we note that it may not be possible to completely suppress the NRB for a large Δ

*ω*

_{fs}(e.g. Δ

*ω*

_{fs}= 500 cm

^{-1}). In cases where there is non-negligible variation in amplitude and phase of the continuum pulse within frequency intervals equal to the broad

*fs*pulse bandwidth, the two integrals in Eqs. (5) and (6) cannot be separated to good approximation, and the simplified analysis presented here does not necessarily hold. However, depending on the details of the shape of the continuum pulse, we may still expect a significant decrease in NRB contribution for much of the CARS signal bandwidth by adjusting the relative intensity and phase of the two narrowband pulse components.

### 2.2 ps-ps interference scheme

*ps-ps*scheme,

*E*

_{n}(

*ω*) consists of two narrowband Gaussian pulses whose bandwidths are the same but whose center frequencies are shifted, as shown in Fig. 4(a). The electric fields of the

*ps*pulses can be expressed as

*E*

_{ps1}(

*ω*) =

*E*

^{0}

_{ps}exp[-(2ln2)×(

*ω*-

*ω*

_{c}+ Δ

*ω*

_{c}/2)

^{2}/Δ

*ω*

_{ps}

^{2}] and

*E*

_{ps2}(

*ω*) =

*E*

^{0}

_{ps}exp[-(2ln2)×(

*ω*-

*ω*

_{c}-Δ

*ω*

_{c}/2)

^{2}/Δ

*ω*

_{ps}

^{2}], where Δ

*ω*

_{c}is the frequency separation between the two pulses. The overall electric field of the narrowband pulse is thus written as:

*ps-ps*scheme when we combine Eq. (10) with Eqs. (5) or (6), respectively:

^{∞}

_{-∞}[

*E*

_{ps1}(

*ω*)e

_{p}^{iΔϕ}+

*E*

_{ps2}(

*ω*)]

_{p}*dω*= 0, is satisfied, the entire resonant 2-color CARS spectrum, as well as NRB contributions from both 2-color and 3-color mechanisms vanish, as with the

_{p}*ps-fs*scheme. In the

*ps-ps*scheme, the NRB suppression condition is fulfilled when Δ

*ϕ*= π and |

*E*

_{ps1}| = |

*E*

_{ps2}| irrespective of the value of Δ

*ω*

_{c}, provided the amplitude of the NRB does not change significantly over the interval Δ

*ω*

_{c}.

*ϕ*= π and various values of Δ

*ω*

_{c}. This NRB suppression condition for the

*ps-ps*scheme is similar in nature to the pulse shaping approach demonstrated by Silberberg et al. [20

20. D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, “Narrow-band coherent anti-stokes Raman signals from broad-band pulses,” Phys. Rev. Lett. **88**, 063004 (2002). [CrossRef] [PubMed]

14. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. **90**, 213902 (2003). [CrossRef] [PubMed]

15. B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B **112**, 3653–3661 (2008). [CrossRef] [PubMed]

*ps-ps*scheme discussed here, with Δ

*ω*

_{c}= Δ

*ω*

_{ps}, and can thus be considered a special case of that scheme. (See below.) Here we show that as Δ

*ω*

_{c}is increased, the signal intensity increases. However, when the spacing exceeds twice the FWHM of the non-interferometric spectral feature, i.e. Δω

_{c}>2[

*Γ*

^{2}+ (Δ

*ω*

_{ps})

^{2})]

^{1/2}, there is no further increase in signal amplitude, and a peak splitting artifact emerges, as clearly demonstrated by the Raman mode at 1200 cm

^{-1}. The maximum peak intensity in the

*ps-ps*scheme is close to 100% of the pure resonant [

*χ*

_{NR}^{(3)}= 0] CARS intensity calculated with one of two separate

*ps*pulses. If, for consistency with the

*ps-fs*scheme discussion, we compare calculated signal recovery against signal calculated with a single

*ps*pulse having the same pulse energy as the sum of the geminate

*E*

_{n}(

*ω*) pulses, we calculate a maximum signal recovery of 50%. The signal increase and peak splitting with increased Δ

*ω*

_{c}in the

*ps-ps*3-color CARS can be understood as a result of interactions between two out-of-phase resonant CARS polarizations. When Δω

_{c}is large and the two peaks are sufficiently separated, both peaks appear individually and the peak heights remain unaffected. For a small Δ

*ω*

_{c}, destructive interference in the overlap region of the two pulse spectra can reduce the total (time-averaged) light intensity. However, this destructive interference leads to a signal reduction of only a factor of two between Δ

*ω*

_{c}= 5 cm

^{-1}and 20 cm

^{-1}, while the CARS peak height ratio for the peaks resulting from these conditions is six. This additional increase is a result of a faster-rising electric field in the time domain for Δω

_{c}= 20 cm

^{-1}, and thus a more efficient sampling of the resonant Raman response at early times, before it decays. This is shown in Figure 5 (d) below. A time-domain trace of the probe pulse described in Ref. [14

14. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. **90**, 213902 (2003). [CrossRef] [PubMed]

*ω*

_{c}=Δ

*ω*

_{ps}case described here. From a practical perspective, it is more straightforward to make fine adjustments to the probe pulse parameters and thus achieve high spectral resolution in the

*ps-ps*scheme described above than it is to control a full ultrabroad pulse, as done in the single pulse CARS method [14

**90**, 213902 (2003). [CrossRef] [PubMed]

15. B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B **112**, 3653–3661 (2008). [CrossRef] [PubMed]

### 2.3 Time domain considerations

*ps-fs*and

*ps-ps*schemes described above. In both schemes, the probe field amplitude is zero at t=0. With probe pulses such as these, the single-shot interference CARS schemes for NRB suppression can be achieved when a well-compressed, broadband continuum pulse,

**F**[

*E*

_{c}](

*t*), arrives at

*t*= 0. Under these conditions neither the 2-color resonant signal nor the NRB contributions are generated since all of these require that electric fields from all pulses (pump, Stokes, and probe) to have significant amplitude simultaneously. Survival of resonant signal in a 3-color CARS spectrum can be understood as being due to the presence of significant probe pulse field amplitude during the non-zero lifetime the vibrational coherence set up in the sample by the continuum pulse. The Raman response function decays slowly, on the time scale of the Raman dephasing time, which typically ranges several hundreds femtoseconds to several picoseconds [21

21. A. Morresi, L. Mariani, M. R. Distefano, and M. G. Giorgini, “Vibrational-Relaxation Processes in Isotropic Molecular Liquids - A Critical Comparison,” J. Raman Spectrosc. **26**, 179–216 (1995). [CrossRef]

**F**[

*E*

_{n}](

*t*) and the instantaneous electronic response for NRB contribution becomes negligible compared with that between

**F**[

*E*

_{n}](

*t*) and the Raman response. This makes the NRB free CARS spectrum available in the 3-color broadband CARS spectroscopy.

7. Y. J. Lee, Y Liu, and M. T. Cicerone, “Characterization of 3-color CARS in a 2-pulse broadband CARS spectrum,” Opt. Lett. **32**, 3370–3372 (2007). [CrossRef] [PubMed]

^{-1}) continuum pulse from a nonlinear fiber, and these continua generally contain multiple modes with higher order dispersion [22

22. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**, 1135–1184 (2006). [CrossRef]

## 3. Experimental setup

**32**, 3370–3372 (2007). [CrossRef] [PubMed]

23. Y. J. Lee and M. T. Cicerone, “Vibrational dephasing time imaging by time-resolved broadband coherent anti-Stokes Raman scattering microscopy,” Appl. Phys. Lett. **92**, 041108 (2008). [CrossRef]

*f*pulse shaper, where a reflecting spatial light modulator (CRI, SLM-640-D-NM) was used to control both amplitude and phase of probe pulses at 1.7 cm

^{-1}spectral resolution and 1% amplitude resolution. The continuum and probe beams were introduced co-linearly and with parallel polarization into a 1.3 NA oil immersion objective lens. The generated CARS signal was collected using a CCD spectrometer (PhotonMax, Roper Scientific).

## 4. Experimental results

*ps-fs*interference scheme shaped by controlling the amplitude and phase of the original femtosecond pulse (the blue dotted line) using the spatial light modulator. The phase of the narrow center region (the

*ps*component) is offset with respect to the phase of the other broad and low intensity region (the

*fs*component) by a value Δ

*ϕ*. Note that the pedestal

*fs*component is a broad Gaussian pulse with a narrow dip at the center. Figures 6(b) and 6(c) are measured broadband CARS spectra of Δ

*ϕ*= 0 and π respectively. As expected, the NRB is significantly reduced in the out-of-phase (Δ

*ϕ*= π) CARS spectrum. Also, the resonant peaks in the NRB-suppressed CARS spectrum become symmetrical and located at the resonance frequencies as in a spontaneous Raman spectrum, so that their center frequencies do not change with experimental conditions, which could help reliable analysis of crowded Raman spectrum of complex media. We note also that peaks at higher Raman shifts are significantly reduced in the NRB suppressed spectrum. This is consistent with the simulation results of 2- and 3-color interference CARS and the characteristics of 2- and 3-color CARS signals. The higher-frequency peaks are likely to have relatively more 2-color character (see Fig. 1), and only 3-color resonant CARS signals survive at the NRB suppressing condition in the

*ps-fs*interference scheme.

*ps-ps*interference scheme, where the phases of the two spectral components are independently controlled. Figures 7(b) and 7(c) show interference CARS spectra of c-hexane at Δ

*ϕ*= 0 and π. These spectra also show features consistent with our simulations, such as significantly reduced NRB contribution and relatively high peak intensity at lower Raman shift, although the Δ

*Ω*

_{ps}and Δ

*Ω*

_{c}values were not optimized for the maximum peak intensity. The vertical lines in Fig. 7(c) indicate known spontaneous Raman resonant frequencies. We note that there appear to be many more “peaks” in the CARS spectrum in Fig. 7(b), due to spectral intensity undulations of the continuum used. Where the NRB is suppressed in Fig. 7(c), the spurious “peaks” disappear, and actual peaks become evident, slightly above the noise.

*Ω*

_{fs}/Δ

*Ω*

_{ps}= 9.7, the intended ratio of pulse intensity,

*I*

^{0}

_{fs}/

*I*

^{0}

_{ps}, was 0.01 for the data in Fig. 6. While the SLM we used provides approximately 1% amplitude control, we used pulse light that was outside the antireflection coating range of the SLM, and we were able to obtain ratios only as small as 0.14. Figure 3 shows that deviations from the optimal value of

*I*

^{0}

_{fs}/

*I*

^{0}

_{ps}result in decreased resonant signal recovery and increased NRB. We experienced similar difficulties in preparing the

*ps-ps*geminate pulses. Most of these problems could be avoided in an optimized experimental setup.

**32**, 3370–3372 (2007). [CrossRef] [PubMed]

25. B. von Vacano, L. Meyer, and M. Motzkus, “Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy,” J. Raman Spectrosc. **38**, 916–926 (2007). [CrossRef]

## 5. Discussion

8. F. Ganikhanov, C. L. Evans, B. G. Saar, and X. S. Xie, “High-sensitivity vibrational imaging with frequency modulation coherent anti-Stokes Raman scattering (FM CARS) microscopy,” Opt. Lett. **31**, 1872–1874 (2006). [CrossRef] [PubMed]

6. H. A. Rinia, M. Bonn, and M. Muller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B **110**, 4472–4479 (2006). [CrossRef] [PubMed]

26. M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express **15**, 15207–15213 (2007). [CrossRef] [PubMed]

*I*

_{CARS}, is proportional to the square of the sum of nonresonant and resonant susceptibility,

*I*

_{CARS}∝ |

*χ*

_{NR}^{(3)}+

*χ*

_{R}^{(3)}|

^{2}= |

*χ*

_{NR}^{(3)}|

^{2}+ |

*χ*

_{R}^{(3)}|

^{2}+2

*χ*

_{NR}^{(3)}Re(

*χ*

_{R}^{(3)}). When the resonant signal is weak, i.e., |

*χ*

_{R}^{(3)}|≪|

*χ*

_{NR}^{(3)}|, the CARS signal intensity is approximately proportional to (|

*χ*

_{NR}^{(3)}|

^{2}+ 2

*χ*

_{NR}^{(3)}Re(

*χ*

_{R}^{(3)})), and the nonresonant component serves to amplify the resonant signal intensity through the cross-term, 2

*χ*

_{NR}^{(3)}Re(

*χ*

_{R}^{(3)}) .

*I*

_{CARS})

^{1/2}. At low signal intensities, where dark noise would dominate, the noise is independent of signal intensity and a small amount of NRB may be beneficial as it could be used to amplify the resonant signal above the dark noise and improve the S/N of the measurement. On the other hand, there is little benefit in increasing signal levels through increased NRB beyond the point at which shot noise dominates because both the resonant signal and the noise increase with (

*I*

_{NRB})

^{1/2}. Furthermore, an excessively large NRB contribution increases the ratio between the total signal, (|

*χ*

_{NR}^{(3)}|

^{2}+ 2

*χ*

_{NR}^{(3)}Re(

*χ*

_{R}^{(3)})), and resonant signal, (2

*χ*

_{NR}^{(3)}Re(

*χ*

_{R}^{(3)})), limiting sensitivity due to finite dynamic range of detectors and analog-to-digital converters. We note that in the large NRB contribution limit, the measured

*I*

_{CARS}is linearly proportional to a sample concentration of interest while in the NRB-free limit,

*I*

_{CARS}is quadratically proportional to a sample concentration. This can be both advantageous and disadvantageous depending on applications.

## 6. Conclusion

*ps-fs*scheme and the

*ps-ps*scheme. In both schemes, the resonant CARS signal from only the “3-color” CARS mechanism is recovered with minimal attenuation while the resonant signal from “2-color” CARS mechanism becomes negligible when the NRB contribution is suppressed. We have discussed optimization conditions for the signal intensity and shape of resonant peaks. Experimental CARS spectra of c-hexane and benzonitrile obtained by preliminary measurements are consistent with the simulation results, showing NRB-suppressed CARS spectra.

## Acknowledgment

## Footnotes

* | Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States |

## References and links

1. | A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. |

2. | C. L. Evans, E. O. Potma, M. Puoris’haag, D. Cote, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA |

3. | J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B |

4. | T. W. Kee and M. T. Cicerone, “Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. |

5. | G. I. Petrov and V. V. Yakovlev, “Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy,” Opt. Express |

6. | H. A. Rinia, M. Bonn, and M. Muller, “Quantitative multiplex CARS spectroscopy in congested spectral regions,” J. Phys. Chem. B |

7. | Y. J. Lee, Y Liu, and M. T. Cicerone, “Characterization of 3-color CARS in a 2-pulse broadband CARS spectrum,” Opt. Lett. |

8. | F. Ganikhanov, C. L. Evans, B. G. Saar, and X. S. Xie, “High-sensitivity vibrational imaging with frequency modulation coherent anti-Stokes Raman scattering (FM CARS) microscopy,” Opt. Lett. |

9. | J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-stokes raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B |

10. | J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. |

11. | A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. |

12. | C. L. Evans, E. O. Potma, and X. S. N. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ |

13. | E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. |

14. | D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. |

15. | B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B |

16. | T. W. Kee, H. X. Zhao, and M. T. Cicerone, “One-laser interferometric broadband coherent anti-Stokes Raman scattering,” Opt. Express |

17. | J. P. Ogilvie, E. Beaurepaire, A. Alexandrou, and M. Joffre, “Fourier-transform coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. |

18. | H. Kano and H. Hamaguchi, “Dispersion-compensated supercontinuum generation for ultrabroadband multiplex coherent anti-Stokes Raman scattering spectroscopy,” J. Raman Spectrosc. |

19. | G. L. Eesley, |

20. | D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, “Narrow-band coherent anti-stokes Raman signals from broad-band pulses,” Phys. Rev. Lett. |

21. | A. Morresi, L. Mariani, M. R. Distefano, and M. G. Giorgini, “Vibrational-Relaxation Processes in Isotropic Molecular Liquids - A Critical Comparison,” J. Raman Spectrosc. |

22. | J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. |

23. | Y. J. Lee and M. T. Cicerone, “Vibrational dephasing time imaging by time-resolved broadband coherent anti-Stokes Raman scattering microscopy,” Appl. Phys. Lett. |

24. | Certain equipment is identified in this Letter to specify adequately the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology, nor does it imply that the equipment is necessarily the best available for this purpose. |

25. | B. von Vacano, L. Meyer, and M. Motzkus, “Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy,” J. Raman Spectrosc. |

26. | M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express |

**OCIS Codes**

(300.6230) Spectroscopy : Spectroscopy, coherent anti-Stokes Raman scattering

(320.5540) Ultrafast optics : Pulse shaping

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: October 14, 2008

Revised Manuscript: November 28, 2008

Manuscript Accepted: December 4, 2008

Published: December 23, 2008

**Citation**

Young Jong Lee and Marcus T. Cicerone, "Single-shot interferometric approach to
background free broadband coherent anti-
Stokes Raman scattering spectroscopy," Opt. Express **17**, 123-135 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-123

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### References

- A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999). [CrossRef]
- C. L. Evans, E. O. Potma, M. Puoris'haag, D. Cote, C. P. Lin, and X. S. Xie, "Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy," Proc. Natl. Acad. Sci. USA 102, 16807-16812 (2005). [CrossRef] [PubMed]
- J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "Multiplex coherent anti-stokes Raman scattering microspectroscopy and study of lipid vesicles," J. Phys. Chem. B 106, 8493-8498 (2002). [CrossRef]
- T. W. Kee and M. T. Cicerone, "Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 29, 2701-2703 (2004). [CrossRef] [PubMed]
- G. I. Petrov and V. V. Yakovlev, "Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy," Opt. Express 13, 1299-1306 (2005). [CrossRef] [PubMed]
- H. A. Rinia, M. Bonn, and M. Muller, "Quantitative multiplex CARS spectroscopy in congested spectral regions," J. Phys. Chem. B 110, 4472-4479 (2006). [CrossRef] [PubMed]
- Y. J. Lee, Y Liu, and M. T. Cicerone, "Characterization of 3-color CARS in a 2-pulse broadband CARS spectrum," Opt. Lett. 32, 3370-3372 (2007). [CrossRef] [PubMed]
- F. Ganikhanov, C. L. Evans, B. G. Saar, and X. S. Xie, "High-sensitivity vibrational imaging with frequency modulation coherent anti-Stokes Raman scattering (FM CARS) microscopy," Opt. Lett. 31, 1872-1874 (2006). [CrossRef] [PubMed]
- J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, "An epi-detected coherent anti-stokes raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity," J. Phys. Chem. B 105, 1277-1280 (2001). [CrossRef]
- J. X. Cheng, L. D. Book, and X. S. Xie, "Polarization coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 26, 1341-1343 (2001). [CrossRef]
- A. Volkmer, L. D. Book, and X. S. Xie, "Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay," Appl. Phys. Lett. 80, 1505-1507 (2002). [CrossRef]
- C. L. Evans, E. O. Potma, and X. S. N. Xie, "Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility ?(3) for vibrational microscopy," Opt. Lett. 29, 2923-2925 (2004). [CrossRef]
- E. O. Potma, C. L. Evans, and X. S. Xie, "Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging," Opt. Lett. 31, 241-243 (2006). [CrossRef] [PubMed]
- D. Oron, N. Dudovich, and Y. Silberberg, "Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy," Phys. Rev. Lett. 90, 213902 (2003). [CrossRef] [PubMed]
- B. C. Chen and S. H. Lim, "Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy," J. Phys. Chem. B 112, 3653-3661 (2008). [CrossRef] [PubMed]
- T. W. Kee, H. X. Zhao, and M. T. Cicerone, "One-laser interferometric broadband coherent anti-Stokes Raman scattering," Opt. Express 14, 3631-3640 (2006). [CrossRef] [PubMed]
- J. P. Ogilvie, E. Beaurepaire, A. Alexandrou, and M. Joffre, "Fourier-transform coherent anti-Stokes Raman scattering microscopy," Opt. Lett. 31, 480-482 (2006). [CrossRef] [PubMed]
- H. Kano and H. Hamaguchi, "Dispersion-compensated supercontinuum generation for ultrabroadband multiplex coherent anti-Stokes Raman scattering spectroscopy," J. Raman Spectrosc. 37, 411-415 (2006). [CrossRef]
- G. L. Eesley, Coherent Raman Spectroscopy (Pergamon Press, Oxford 1981).
- D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, "Narrow-band coherent anti-stokes Raman signals from broad-band pulses," Phys. Rev. Lett. 88, 063004 (2002). [CrossRef] [PubMed]
- A. Morresi, L. Mariani, M. R. Distefano, and M. G. Giorgini, "Vibrational-Relaxation Processes in Isotropic Molecular Liquids - A Critical Comparison," J. Raman Spectrosc. 26, 179-216 (1995). [CrossRef]
- J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
- Y. J. Lee and M. T. Cicerone, "Vibrational dephasing time imaging by time-resolved broadband coherent anti-Stokes Raman scattering microscopy," Appl. Phys. Lett. 92, 041108 (2008). [CrossRef]
- Certain equipment is identified in this Letter to specify adequately the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology, nor does it imply that the equipment is necessarily the best available for this purpose.
- B. von Vacano, L. Meyer, and M. Motzkus, "Rapid polymer blend imaging with quantitative broadband multiplex CARS microscopy," J. Raman Spectrosc. 38, 916-926 (2007). [CrossRef]
- M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, "Shot noise limited heterodyne detection of CARS signals," Opt. Express 15, 15207-15213 (2007). [CrossRef] [PubMed]

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