**4.1 Introduction to broadband CARS**

186 Photonic Crystals – Innovative Systems, Lasers and Waveguides

simpler way to generate favorable SC for CARS applications. The simulation results are shown in figure 9, where we can see that the SC generated by a PCF with two ZDW is quite good for

Fig. 8. Temporal-spectral distribution of SC when PCFs with lengthes of 10 cm (a), 20 cm (b), 25 cm (c), and 50 cm (d) pumped by laser pulse with pulse-width 30 fs, wavelength 780 nm,

(a) (b)

(c) (d)

Fig. 9. Temporal-spectral distribution of the SC when using the femtosecond laser pulse with a central wavelength of 780 nm, peak power of 10 kW and pulse-width of 50 fs (a), 100

By numerical simulations, we clearly understood the effects of the parameters of PCF and pumping laser pulse on the generation of SC. All simulation results provide us an intuitive

fs (b), 300 fs (c) and 500 fs (b) as seed pulse to pump a PCF with length of 10cm.

and peak power 10 kW [98].

CARS applications when the laser pulse width is 300fs, as shown in figure 9 (c).

The M-CARS spectroscopy was first demonstrated by Akhamnov et al., a part of CARS spectra of a sample can be simultaneously obtained [34]. In M-CARS, a broadband laser beam is used as the Stokes beam for providing a required spectral range. A narrow line-width laser beam is used as the pump and probe beam that determines the spectral resolution of the system. The multiplex molecular vibrational modes of a sample can be resonantly enhanced, the corresponding CARS signals can be detected simultaneously, the energy diagram of M-CARS shown in figure 10.

Fig. 10. Energy level diagram of M-CARS.

In the previous works, a narrowband and a broadband dye laser was used for the pump/probe and the Stokes beams respectively [36-38]. The recent progress in wavelengthtunable ultra-short pulse laser has been giving a powerful momentum to the development of M-CARS. The M-CARS micro-spectroscopy has been developed for fast spectral characterization of microscopic samples [35, 99, 100]. But because of the used laser limitation to the line-width, M-CARS is still unable to simultaneously obtain wider molecular

Ultra-Broadband Time-Resolved Coherent Anti-Stokes Raman Scattering

time is 10ps, the relaxation process of Qv is shown in figure 12.

resonantly enhanced by incident pump and Stokes pulses [107].

disappearance of the pump and Stokes laser pulses [107].

frequency is generated and can be expressed as [107]:

Spectroscopy and Microscopy with Photonic Crystal Fiber Generated Supercontinuum 189

where A is an integration constant. We can see that Qv decays exponentially with time immediately after disappearance of the pump and Stoke pulses. Assuming the dephasing

Fig. 11. Intensity of Qv amplitude versus time, when the vibration of active Raman mode is

Fig. 12. The free relaxation process of a molecular vibration mode immediately after

In the third phase, when the probe pulse reaches the focus with the delay time tD, it will be modulated by the resonantly enhanced molecular vibration. The signal field at anti-Stokes

> 222 *AS AS AS AS AS i kz*

 

*E nE <sup>i</sup> E NE <sup>Q</sup> <sup>e</sup> z ct nc Q*

*AS*

 

0

*AS P*

1

'

. (4.4)

vibrational spectra as required. With the progress of SC generation technique [85-87], especially with the advent of PCF [39], much wider spectra of M-CARS can be simultaneously obtained by broadening the spectral range of Stokes pulses with nonlinear optical fiber, such as the tapped optical fiber [101] or PCF [43, 44, 102]. By using a specially designed and achieved SC source, the simultaneously detectable spectral range of M-CARS spectroscopy and microscopy is greatly widened, which can be called the broadband CARS. Wider simultaneously detectable spectral range makes it possible to quickly distinguishing various components and real-time monitoring slight variations in a mixture [103-105]. At the same time, the system of the broadband CARS with SC is simplified and cost is reduced.

#### **4.2 Suppression of NRB noise in broadband CARS with SC**

In the M-CARS, NRB noise can not be avoided and many methods for suppressing it in a single-frequency CARS can also be used, but they can not be easily applied in the broadband CARS with SC, because of the complex polarization and phase of various spectral components in SC, as shown in section 3. The NRB noise can be eliminated with numerical fitting method by regarding it as a reference signal, but the Raman spectra of the samples are needed in advance [106].

As presented in above section, the time-resolved detection method can effectively eliminate the NRB noise by introducing a temporal delay between pump/Stokes pulses and probe pulse in order to temporally separate the resonant and nonresonant signals. In a T-CARS, three laser pulses, with frequencies at ωP, ωP', and ωS, are used as the pump, probe and Stokes pulses respectively. The generation process of CARS signals can be described in three phases [107]. In the first phase, the inherent molecular vibration of active Raman mode is driven by simultaneous pump and Stokes pulses and is resonantly enhanced when ΩR=ωP-ωS. The amplitude of resonantly enhanced molecular vibration is [108]:

$$\frac{\partial Q\_v}{\partial t} + \frac{Q\_v}{T\_2} = \frac{\mathrm{i}}{4m\Omega\_r} \left(\frac{\partial \alpha}{\partial Q}\right) E\_P E\_S^\* \left(1 - 2n\_a\right) \,\mathrm{}\tag{4.1}$$

where Qv is the amplitude of molecular vibration driven by the incident optical fields, T2 is the dephasing time of the resonant enhanced molecular vibrational state. When the simultaneous ultrashort laser pulses are used as the pump and Stokes pulses, the intensity changes of Qv with time is shown in figure 11. Qv increases during the period of incident laser pulses and reaches its maximum when the pump and Stokes pulses just disappear.

In the second phase, with the disappearance of incident laser pulses, the resonantly enhanced molecular vibration will rapidly return to its original state that can be regarded as a free relaxation process. Equation (4.1) can be rewritten as [107]:

$$\frac{\partial Q\_{\upsilon}}{\partial t} = -\frac{Q\_{\upsilon}}{T\_2}. \tag{4.2}$$

The solution of equation (4.2) is [107]:

$$\left\|Q\_{\upsilon}\right\|^{2} = A \exp\left(-2t/T\_{2}\right),\tag{4.3}$$

vibrational spectra as required. With the progress of SC generation technique [85-87], especially with the advent of PCF [39], much wider spectra of M-CARS can be simultaneously obtained by broadening the spectral range of Stokes pulses with nonlinear optical fiber, such as the tapped optical fiber [101] or PCF [43, 44, 102]. By using a specially designed and achieved SC source, the simultaneously detectable spectral range of M-CARS spectroscopy and microscopy is greatly widened, which can be called the broadband CARS. Wider simultaneously detectable spectral range makes it possible to quickly distinguishing various components and real-time monitoring slight variations in a mixture [103-105]. At the same time, the system of the broadband CARS with SC is simplified

In the M-CARS, NRB noise can not be avoided and many methods for suppressing it in a single-frequency CARS can also be used, but they can not be easily applied in the broadband CARS with SC, because of the complex polarization and phase of various spectral components in SC, as shown in section 3. The NRB noise can be eliminated with numerical fitting method by regarding it as a reference signal, but the Raman spectra of the

As presented in above section, the time-resolved detection method can effectively eliminate the NRB noise by introducing a temporal delay between pump/Stokes pulses and probe pulse in order to temporally separate the resonant and nonresonant signals. In a T-CARS, three laser pulses, with frequencies at ωP, ωP', and ωS, are used as the pump, probe and Stokes pulses respectively. The generation process of CARS signals can be described in three phases [107]. In the first phase, the inherent molecular vibration of active Raman mode is driven by simultaneous pump and Stokes pulses and is resonantly enhanced when

> *v v PS a r Q Q <sup>i</sup> EE n*

where Qv is the amplitude of molecular vibration driven by the incident optical fields, T2 is the dephasing time of the resonant enhanced molecular vibrational state. When the simultaneous ultrashort laser pulses are used as the pump and Stokes pulses, the intensity changes of Qv with time is shown in figure 11. Qv increases during the period of incident laser pulses and reaches its maximum when the pump and Stokes pulses just disappear.

In the second phase, with the disappearance of incident laser pulses, the resonantly enhanced molecular vibration will rapidly return to its original state that can be regarded as

> *Q Q t T*

 <sup>2</sup> <sup>2</sup> *Q A tT* exp 2

2

\*

, (4.1)

. (4.2)

, (4.3)

1 2

ΩR=ωP-ωS. The amplitude of resonantly enhanced molecular vibration is [108]:

4

*tT m Q* 

2

a free relaxation process. Equation (4.1) can be rewritten as [107]:

**4.2 Suppression of NRB noise in broadband CARS with SC** 

and cost is reduced.

samples are needed in advance [106].

The solution of equation (4.2) is [107]:

where A is an integration constant. We can see that Qv decays exponentially with time immediately after disappearance of the pump and Stoke pulses. Assuming the dephasing time is 10ps, the relaxation process of Qv is shown in figure 12.

Fig. 11. Intensity of Qv amplitude versus time, when the vibration of active Raman mode is resonantly enhanced by incident pump and Stokes pulses [107].

Fig. 12. The free relaxation process of a molecular vibration mode immediately after disappearance of the pump and Stokes laser pulses [107].

In the third phase, when the probe pulse reaches the focus with the delay time tD, it will be modulated by the resonantly enhanced molecular vibration. The signal field at anti-Stokes frequency is generated and can be expressed as [107]:

$$\frac{\partial E\_{AS}}{\partial z} + \frac{n\_{AS}}{c} \frac{\partial E\_{AS}}{\partial t} + \frac{a\_{AS}}{2} E\_{AS} = \frac{i o\_{AS}}{2 n\_{AS} c \varepsilon\_0} \left\lfloor \frac{1}{2} N \left( \frac{\partial a}{\partial Q} \right) E\_P Q\_o e^{-i\Lambda kz} \right\rfloor. \tag{4.4}$$

Ultra-Broadband Time-Resolved Coherent Anti-Stokes Raman Scattering

Spectroscopy and Microscopy with Photonic Crystal Fiber Generated Supercontinuum 191

ki

*P*'

The principle of broadband T-CARS spectroscopy has been presented in section 4.2. As discussed in section 3 and 4, the simultaneously detectable spectral range of a broadband T-CARS spectroscopy is limited by the simultaneously generated spectral range and its continuity in the SC. An ultra-broadband T-CARS spectroscopy based on optimized SC has been developed to simultaneously obtain CARS signals corresponding to various molecular vibrational modes and Raman free induction decays (RFID) of these molecular vibrational modes in a single measurement [43, 84]. The schematic of the broadband T-CARS spectroscopy is shown in figure 15. A femtosecond laser pulse of a mode-locked Ti:sapphire laser oscillator (Mira900, Coherent) is split into two parts by a beam splitter. One beam of the laser pulse, used as the seed pulse, is introduced into a PCF with geometric length of 180 mm and ZDW of 850 nm respectively. After passing through a long-pass filter, the residual spectral components of SC are used as the pump and the Stokes. Another beam is used as the probe pulse after passing through a narrow-band-pass filter. Two beams of the laser pulses are collinearly introduced into a microscope and tightly focused into a sample with an achromatic microscopy objective. The generated CARS signals in the forward direction, passing through a short-pass filter, are collected with the same microscope objective and detected by a fibre spectrometer. The delay time between SC pulse and probe pulse can be

Fig. 15. The schematic of the ultra-broadband T-CARS system. BS, beam splitter; Iso, optical isolator; NL, non-spherical lens; PCF, photonic crystal fibre; BC, beam combiner; MO1-3, microscopy objective; BPF, narrow-band-pass filter; LPF, long-pass filter; SPF, short-pass

With the ultra-broadband T-CARS spectroscopy, the time-resolved measurement is achieved by adjusting the delay time between the SC pulse and the probe pulse step by step [84]. The obtained time-resolved CARS spectral signals and CARS signals at specific delay

g

 *SP*

Fig. 14. Energy level diagram of the broadband T-CARS.

accurately adjusted by a kit of time delay line.

filter [84].

vi

ji

*ASi*

*i*

From the equation (4.4), we can find that the CARS signal field does not include the nonresonant component 3 *nr* that disappears with the end of the pump and Stokes pulses simultaneously. When the phase-matching condition is satisfied, Δk=0, the intensity changes of the CARS signal with time is shown in figure 13.

Fig. 13. Intensity of CARS signal changes with time [107].

In the T-CARS method, the resonant and nonresonant components have different temporal response characteristics. In order to effectively separate the resonant and nonresonant contributions and avoid the intensity loss of the CARS signal, the pulse-width of simultaneous pump ans Stokes pulse should be as short as possible and the rising edge of the probe pulse should be as steep as possible.

Recently the broadband T-CARS spectroscopy and microscopy with SC has been rapidly developed [43, 44], whose energy level diagram is shown in figure 14. In the broadband T-CARS, a well-designed SC is used as the pump and Stokes pulses and a temporally delayed laser pulse is used as the probe pulse. The simultaneously detectable spectral range and the spectral resolution are determined by the temporally overlapped spectral range of the SC and by the line-width of the probe pulse respectively. With the improvement of temporalspectral distribution of the SC, the simultaneously detectable spectral range of system can be further extended, which is called the ultra-broadband T-CARS and will be discussed in detail in the next section.

### **4.3 Ultra-broadband T-CARS spectroscopy with SC generated by PCF[84, 96]**

With a broadband T-CARS spectroscopy, we can obtain more specificities of the sample, not only the vibrational spectra reflecting the molecular structure and compositions, but also the dephasing time of various molecular vibrational modes reflecting the molecular responses to the external micro-environment, which are especially favorable for the study of the complicated interaction processes between molecules and their micro-environment such as solute-solvent interactions [108, 109], molecular dynamics[110-114], supramolecular structures[115] and excess energy dissipations in the fields of biology, chemistry and material science [64, 116-118].

Fig. 14. Energy level diagram of the broadband T-CARS.

190 Photonic Crystals – Innovative Systems, Lasers and Waveguides

From the equation (4.4), we can find that the CARS signal field does not include the

simultaneously. When the phase-matching condition is satisfied, Δk=0, the intensity changes

In the T-CARS method, the resonant and nonresonant components have different temporal response characteristics. In order to effectively separate the resonant and nonresonant contributions and avoid the intensity loss of the CARS signal, the pulse-width of simultaneous pump ans Stokes pulse should be as short as possible and the rising edge of

Recently the broadband T-CARS spectroscopy and microscopy with SC has been rapidly developed [43, 44], whose energy level diagram is shown in figure 14. In the broadband T-CARS, a well-designed SC is used as the pump and Stokes pulses and a temporally delayed laser pulse is used as the probe pulse. The simultaneously detectable spectral range and the spectral resolution are determined by the temporally overlapped spectral range of the SC and by the line-width of the probe pulse respectively. With the improvement of temporalspectral distribution of the SC, the simultaneously detectable spectral range of system can be further extended, which is called the ultra-broadband T-CARS and will be discussed in

With a broadband T-CARS spectroscopy, we can obtain more specificities of the sample, not only the vibrational spectra reflecting the molecular structure and compositions, but also the dephasing time of various molecular vibrational modes reflecting the molecular responses to the external micro-environment, which are especially favorable for the study of the complicated interaction processes between molecules and their micro-environment such as solute-solvent interactions [108, 109], molecular dynamics[110-114], supramolecular structures[115] and excess energy dissipations in the fields of biology, chemistry and

**4.3 Ultra-broadband T-CARS spectroscopy with SC generated by PCF[84, 96]**

*nr* that disappears with the end of the pump and Stokes pulses

nonresonant component 3

of the CARS signal with time is shown in figure 13.

Fig. 13. Intensity of CARS signal changes with time [107].

the probe pulse should be as steep as possible.

detail in the next section.

material science [64, 116-118].

The principle of broadband T-CARS spectroscopy has been presented in section 4.2. As discussed in section 3 and 4, the simultaneously detectable spectral range of a broadband T-CARS spectroscopy is limited by the simultaneously generated spectral range and its continuity in the SC. An ultra-broadband T-CARS spectroscopy based on optimized SC has been developed to simultaneously obtain CARS signals corresponding to various molecular vibrational modes and Raman free induction decays (RFID) of these molecular vibrational modes in a single measurement [43, 84]. The schematic of the broadband T-CARS spectroscopy is shown in figure 15. A femtosecond laser pulse of a mode-locked Ti:sapphire laser oscillator (Mira900, Coherent) is split into two parts by a beam splitter. One beam of the laser pulse, used as the seed pulse, is introduced into a PCF with geometric length of 180 mm and ZDW of 850 nm respectively. After passing through a long-pass filter, the residual spectral components of SC are used as the pump and the Stokes. Another beam is used as the probe pulse after passing through a narrow-band-pass filter. Two beams of the laser pulses are collinearly introduced into a microscope and tightly focused into a sample with an achromatic microscopy objective. The generated CARS signals in the forward direction, passing through a short-pass filter, are collected with the same microscope objective and detected by a fibre spectrometer. The delay time between SC pulse and probe pulse can be accurately adjusted by a kit of time delay line.

Fig. 15. The schematic of the ultra-broadband T-CARS system. BS, beam splitter; Iso, optical isolator; NL, non-spherical lens; PCF, photonic crystal fibre; BC, beam combiner; MO1-3, microscopy objective; BPF, narrow-band-pass filter; LPF, long-pass filter; SPF, short-pass filter [84].

With the ultra-broadband T-CARS spectroscopy, the time-resolved measurement is achieved by adjusting the delay time between the SC pulse and the probe pulse step by step [84]. The obtained time-resolved CARS spectral signals and CARS signals at specific delay

Ultra-Broadband Time-Resolved Coherent Anti-Stokes Raman Scattering

 1016cm-1 Fitting curve T/2 = 2.68ps

 1608cm-1 Fitting curve T/2 = 0.65ps

<sup>012345678</sup> 0.0

<sup>012345678</sup> 0.0

**Time (ps)**

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

**Normalized Intensity (%)**

**Time (ps)**

**(c)**

1.0 **(a)**

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

**Normalized Intensity (%)**

**Normalized Intensity (%)**

one as a function of τ and fitted to equation (4.5) in figure 17 (a)-(e) respectively [84].

Spectroscopy and Microscopy with Photonic Crystal Fiber Generated Supercontinuum 193

*IA T*

where T is the vibrational dephasing time responding to each molecular vibrational mode; A0 is a constant; τ is the delay time. The normalized intensities of five typical peaks corresponding to typical molecular vibrational modes for pure benzonitrile, at the wavenumbers of 1016 cm-1, 1190 cm-1, 1608 cm-1, 2248 cm-1 and 3090 cm-1, are plotted one by

 

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

 3090cm-1 Fitting curve T/2 = 0.35ps

**Normalized Intensity (%)**

<sup>012345678</sup> 0.0

Fig. 17. Vibrational dephasing processes and their relevant dephasing times of various molecular vibrational modes for pure liquid benzonitrile shown in (a)-(e) respectively, with the solid line corresponding to the change of CARS signal with delay time and the

dash dot line representing the fitting curve to a single exponential function [84].

**Time (ps)**

In a benzonitrile-methanol-ethanol mixture solution, the benzonitrile molecule is regarded as the target molecule. The normalized intensities of three typical peaks corresponding to

1.0 **(e)** 

**Normalized Intensity (%)**

<sup>0</sup> exp 2 , (4.5)

<sup>012345678</sup> 0.0

<sup>012345678</sup> 0.0

**Time (ps)**

**Time (ps)**

 **(d)**

**(b)**

 1190cm-1 Fitting curve T/2 = 0.71ps

 2248cm-1 Fitting curve T/2 = 0.52ps

time of pure benzonitrile and mixture solution are shown in figure 16. The molecular vibrational spectra for pure liquid benzonitrile in the range of 380-4000 cm-1 can be simultaneously obtained without any tuning of the system and its characteristics. The NRB noise can be effectively suppressed through tuning the delay time. For the pure benzonitrile, the obvious peaks at wavenumbers of 1016 cm-1, 1190 cm-1, 1608 cm-1, 2248 cm-1 and 3090 cm-1 correspond to C-C-C trigonal breathing, C-H in plane bending, C-C in plane stretching, C≡N stretching, and C-H stretching vibrational modes respectively [119]. In the mixture, the peaks at wavenumbers of 1016 cm-1, 2248 cm-1 and 3090 cm-1 of benzonitrile can be apparently seen [120]. Other peaks correspond to the typical molecular vibrational modes of methanol and ethanol. We can easily and accurately distinguish the various components in the mixture. The spectral resolution, depending on the line-width of the probe pulse and spectral resolution of the spectrometer, is 14 cm-1 in this case.

Fig. 16. Intensities of time-resolved CARS signals of pure benzonitrile and at the delay time of 3 ps (a). Intensities of time-resolved CARS signals of benzonitrile-methanol-ethanol mixture solution and at the delay time of 4 ps (b) detected with the ultra-broadband T-CARS spectroscopy [84].

By extracting the time evolutions of CARS signals corresponding to the molecular vibrational modes for a pure liquid benzonitrile and mixture, the RFID processes of various molecular vibrational modes can be measured at the same time. The dephasing times of various molecular vibrational modes can be obtained by fitting the data to a single exponential function as:

time of pure benzonitrile and mixture solution are shown in figure 16. The molecular vibrational spectra for pure liquid benzonitrile in the range of 380-4000 cm-1 can be simultaneously obtained without any tuning of the system and its characteristics. The NRB noise can be effectively suppressed through tuning the delay time. For the pure benzonitrile, the obvious peaks at wavenumbers of 1016 cm-1, 1190 cm-1, 1608 cm-1, 2248 cm-1 and 3090 cm-1 correspond to C-C-C trigonal breathing, C-H in plane bending, C-C in plane stretching, C≡N stretching, and C-H stretching vibrational modes respectively [119]. In the mixture, the peaks at wavenumbers of 1016 cm-1, 2248 cm-1 and 3090 cm-1 of benzonitrile can be apparently seen [120]. Other peaks correspond to the typical molecular vibrational modes of methanol and ethanol. We can easily and accurately distinguish the various components in the mixture. The spectral resolution, depending on the line-width of the probe pulse and

Fig. 16. Intensities of time-resolved CARS signals of pure benzonitrile and at the delay time of 3 ps (a). Intensities of time-resolved CARS signals of benzonitrile-methanol-ethanol mixture solution and at the delay time of 4 ps (b) detected with the ultra-broadband T-CARS

By extracting the time evolutions of CARS signals corresponding to the molecular vibrational modes for a pure liquid benzonitrile and mixture, the RFID processes of various molecular vibrational modes can be measured at the same time. The dephasing times of various molecular vibrational modes can be obtained by fitting the data to a single

spectral resolution of the spectrometer, is 14 cm-1 in this case.

spectroscopy [84].

exponential function as:

$$I(\tau) = A\_0 \exp\left(-2\tau/T\right),\tag{4.5}$$

where T is the vibrational dephasing time responding to each molecular vibrational mode; A0 is a constant; τ is the delay time. The normalized intensities of five typical peaks corresponding to typical molecular vibrational modes for pure benzonitrile, at the wavenumbers of 1016 cm-1, 1190 cm-1, 1608 cm-1, 2248 cm-1 and 3090 cm-1, are plotted one by one as a function of τ and fitted to equation (4.5) in figure 17 (a)-(e) respectively [84].

Fig. 17. Vibrational dephasing processes and their relevant dephasing times of various molecular vibrational modes for pure liquid benzonitrile shown in (a)-(e) respectively, with the solid line corresponding to the change of CARS signal with delay time and the dash dot line representing the fitting curve to a single exponential function [84].

In a benzonitrile-methanol-ethanol mixture solution, the benzonitrile molecule is regarded as the target molecule. The normalized intensities of three typical peaks corresponding to

Ultra-Broadband Time-Resolved Coherent Anti-Stokes Raman Scattering

**5. Sub-diffraction-limited CARS microscopy** 

bio-molecular movement and interaction imaging.

diffraction limit as [124]:

**5.1 Methods of improving spatial resolution of CARS microscopy** 

Spectroscopy and Microscopy with Photonic Crystal Fiber Generated Supercontinuum 195

distinguishing various kinds of components and understanding the mechanisms of chemical reactions in a dynamic process. The latter is very helpful for explanation of both solvent dynamics and solute-solvent interactions in the fields of biology, chemistry and material science. The question is whether we can reach above goal in the near future by optimizing the temporal-spectral distribution of the SC? Our answer is positive. As what we have known the existing molecules have the Raman wave-numbers in the range of about tens to 5000 cm-1, which means that the simultaneously generated Stokes wavelength bandwidth should be not less than 350nm. As we have given in section 3 that the bandwidth of the simultaneously generated SC can be greater than 400nm, therefore it is very promising to achieve label-free microscopic imaging technique with high contrast and chemical specificity based on the simultaneously obtained complete molecular vibrational spectra.

As well known, there is a theoretical limitation of the spatial resolution for any far-field optical microscopes because of the existence of light diffraction. Ernst Abbe defined the

> *n NA*

where *d* is the resolvable minimum size, λ is the wavelength of incident light, n is the refraction index of the medium being imaged in, φ is the aperture angle of the lens, and NA is the numerical aperture of the optical lens. It is obvious that for an optical microscope, d is the theoretical limit of spatial resolution. The samples' spatial features, smaller than approximately half the wavelength of the used light, would never be able to be resolved.

In recent years, in order to meet the requirements on the study of life science and material science, ones have found several ways to overcome the optical diffraction limit and obtained sub-diffraction limited spatial resolution theoretically. In fluorescence microscopy, the success of the resolution enhancement techniques relies on the ability to control the emissive properties of fluorophores with a proper optical beam. The most important developments for breaking through the diffraction barrier are sub-diffraction-limited resolution fluorescent imaging techniques, such as photo activated localization microscopy (PALM) [125], stochastic optical reconstruction microscopy (STORM) [126], and stimulated emission depletion (STED) microscopy [127, 128], which have opened up notable prospect for sub-cellular structure and

As one of label-free nonlinear imaging techniques, the spatial resolution of CARS microscopy is higher (about 300nm lateral resolution) than the one of traditional linear optical microscopy, but it is still a diffraction-limited imaging technique. Today, how to achieve a sub-diffractionlimited CARS microscopy has become one of attractive topics all over the world. Compared with developments of the fluorescence nanoscopy, the method for breaking through the

In 2009, Beeker et al. firstly presented a way to obtain a sub-diffraction-limited CARS microscopy in theory [129]. With the density matrix theoretical calculations, they found that

diffraction limitation in CARS microscopy is still under theoretical research.

, (5.1)

0.61 sin 2

*d*

typical molecular vibrational modes for benzonitrile, at the wavenumbers of 1016 cm-1, 2248 cm-1 and 3090 cm-1, are plotted one by one as a function of τ and fitted to equation (4.5) in figure 18 (a)-(c), respectively.

Fig. 18. Vibrational dephasing processes and their corresponding dephasing times of various molecular vibrational modes for benzonitrile in benzonitrile-methanol-ethanol mixture solution shown in (a)-(c) respectively, with the solid line corresponding to the variation of CARS signal with delay time and the dash dot line representing the single exponential fitting curve [84].

From experimental results, the intensities of the CARS signals corresponding to different molecular vibrational modes attenuate exponentially against the delay time in a large dynamic range. By fitting the intensity data of the CARS signal to a single exponential function for the molecular vibrational modes at different wave-numbers, half of vibrational dephasing time T/2 can be worked out as shown in figure 17, which are consistent with the previously published data [43, 121-123]. But in a benzonitrile-methanol-ethanol mixture solution, the experimental results show that the influence of solvent on the property of solute is reflected not by the Raman peak position but by the variations of the vibrational dephasing times for different molecular vibrational modes.

#### **4.4 Simultaneously obtaining the complete molecular vibrational spectra**

As discussed above, the simultaneously detectable spectral range of the ultra-broadband T-CARS with SC depends on the quality of the SC. It is of importance to simultaneously obtain the complete molecular vibrational spectra and the dephasing times of various molecular vibrational modes of the sample. The former is very useful for effectively and accurately distinguishing various kinds of components and understanding the mechanisms of chemical reactions in a dynamic process. The latter is very helpful for explanation of both solvent dynamics and solute-solvent interactions in the fields of biology, chemistry and material science. The question is whether we can reach above goal in the near future by optimizing the temporal-spectral distribution of the SC? Our answer is positive. As what we have known the existing molecules have the Raman wave-numbers in the range of about tens to 5000 cm-1, which means that the simultaneously generated Stokes wavelength bandwidth should be not less than 350nm. As we have given in section 3 that the bandwidth of the simultaneously generated SC can be greater than 400nm, therefore it is very promising to achieve label-free microscopic imaging technique with high contrast and chemical specificity based on the simultaneously obtained complete molecular vibrational spectra.
