Article 5a), I2 (Fig. You are using a browser version with limited support for CSS. \hfill \end{array}$$, \(P^{(3)}(\omega ,\Delta T) = P^{(3)}(2\pi c\tilde \nu ,{\mathrm{\Delta }}T)\), $$\begin{array}{*{20}{l}} {P_{{\mathrm{NVRB}}}^{(3)}(\omega ,{\mathrm{\Delta }}T)} \hfill & \propto \hfill & { - \eta _{{\mathrm{NVRB}}}\mathop {\int}\limits_{ - \infty }^\infty d \omega _1\mathop {\int}\limits_{ - \infty }^\infty d \omega _2} \hfill \\ {} \hfill & {} \hfill & { \times {\textstyle{{\hat A_{\mathrm{P}}(\omega _1,{\mathrm{\Delta }}T)\hat A_{\mathrm{P}}(\omega _2,{\mathrm{\Delta }}T)\hat A_{\mathrm{S}}^ \ast (2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} - \omega + \omega _1 + \omega _2,0)} \over {\left( {\omega _{\mathrm{P}} + \omega _1 - \bar \omega _{ea}} \right)\left( {2\omega _{\mathrm{P}} + \omega _1 + \omega _2 - \bar \omega _{ea}} \right)\left( {\omega - \bar \omega _{ea}} \right)}}}}, \hfill \end{array}$$, \(\tilde \nu _{ea} = 2\tilde \nu _{\mathrm{P}}\), \(\hat E_{\mathrm{P}}(\omega ) = E_{\mathrm{P}} \cdot \delta (\omega - \omega _{\mathrm{P}})\), \(\hat E_{\mathrm{S}}(\omega ) = E_{\mathrm{S}} \cdot \delta (\omega - \omega _{\mathrm{S}})\), $$\begin{array}{*{20}{l}} {P_{{\mathrm{CARS}}}^{(3)}(\omega )} \hfill & \propto \hfill & { - \frac{{\eta _{CARS}E_P^2E_S^ \ast }}{{(\omega _P - \bar \omega _{ba})(\omega - \omega _P - \bar \omega _{ca})(\omega - \bar \omega _{da})}}} \hfill \\ {} \hfill & = \hfill & {\chi _{CARS}^{(3)}E_P^2E_S^ \ast }; \hfill \end{array}$$, $$\begin{array}{*{20}{l}} {P_{{\mathrm{NVRB}}}^{(3)}(\omega )} \hfill & \propto \hfill & { - \frac{{\eta _{{\mathrm{NVRB}}}E_{\mathrm{P}}^2E_{\mathrm{S}}^ \ast }}{{(\omega _{\mathrm{P}} - \bar \omega _{ea})(2\omega _{\mathrm{P}} - \bar \omega _{ea})(\omega - \bar \omega _{ea})}}} \hfill \\ {} \hfill & = \hfill & {\chi _{{\mathrm{NVRB}}}^{(3)}E_{\mathrm{P}}^2E_{\mathrm{S}}^ \ast }, \hfill \end{array}$$, $$\begin{array}{*{20}{l}} {I(\omega _{{\mathrm{as}}})^{{\mathrm{NR}}}} \hfill & \sim \hfill & {|P_{{\mathrm{NVRB}}}^{(3)}|^2 + |P_{{\mathrm{CARS}}}^{(3)}|^2 + 2\Re (P_{{\mathrm{NVRB}}}^{(3)})\Re (P_{{\mathrm{CARS}}}^{(3)})} \hfill \\ {} \hfill & \propto \hfill & {|\chi _{{\mathrm{NVRB}}}^{(3)}|^2 + |\chi _{{\mathrm{CARS}}}^{(3)}|^2 + 2\Re (\chi _{{\mathrm{NVRB}}}^{(3)})\Re (\chi _{{\mathrm{CARS}}}^{(3)})} \hfill, \end{array}$$, \(\left( {\frac{{\mu _{ba}\mu _{cb}\mu _{cd}\mu _{ad}}}{{|\mu _{ea}|^4}} < < 1} \right)\), \(\left( {\frac{{n_{{\kern 1pt} {\mathrm{CARS}}}}}{{n_{{\kern 1pt} {\mathrm{NVRB}}}}} < < 1} \right)\), \((\omega _{\mathrm{P}} - \bar \omega _{ba})\), $$\begin{array}{*{20}{l}} {I(\omega _{{\mathrm{as}}})^{\mathrm{R}}} \hfill & {\sim |P_{{\mathrm{NRVB}}}^{(3)}|^2 + |P_{{\mathrm{CARS}}}^{(3)}|^2 + 2\Im (P_{{\mathrm{NRVB}}}^{(3)})\Im (P_{{\mathrm{CARS}}}^{(3)})} \hfill \\ {} \hfill & { \propto |\chi _{{\mathrm{NRVB}}}^{(3)}|^2 + |\chi _{{\mathrm{CARS}}}^{(3)}|^2 + 2\Im (\chi _{{\mathrm{NRVB}}}^{(3)})\Im (\chi _{{\mathrm{CARS}}}^{(3)})} \hfill, \end{array}$$, \(\left( {\chi _{{\mathrm{CARS}}}^{(3)}/\chi _{{\mathrm{NRVB}}}^{(3)}} \right)\), \(\tilde \nu _{ca} = 1580\,{\mathrm{cm}}^{ - 1}\), \(\frac{{\eta _{{\mathrm{CARS}}}}}{{\eta _{{\mathrm{NVRB}}}}} = (3.0 \pm 0.7) \times 10^{ - 5}\), \(\frac{{\eta _{{\mathrm{CARS}}}}}{{\eta _{{\mathrm{NVRB}}}}}\), \(\frac{{|\chi _{{\mathrm{CARS}}}^{(3)}|}}{{|\chi _{{\mathrm{NRVB}}}^{(3)}|}}\sim 1.3\), \(\tilde \nu _2 - \tilde \nu _{\mathrm{P}}\sim \tilde \nu _{\mathrm{G}}\), $$I = I_1 - I_2 + \frac{{\tilde \nu _2 - \tilde \nu _1}}{{\tilde \nu _3 - \tilde \nu _1}}(I_3 - I_1){,}$$, \(\tilde \nu _1 = \tilde \nu _{\mathrm{P}} + 1545\,{\mathrm{cm}}^{ - 1}\), \(\tilde \nu _2 = \tilde \nu _{\mathrm{P}} + 1576\,{\mathrm{cm}}^{ - 1}\), \(\tilde \nu _3 = \tilde \nu _{\mathrm{P}} + 1607\,{\mathrm{cm}}^{ - 1}\), \(|\tilde \nu _{1,3} - \tilde \nu _{\mathrm{G}}|\), \(C = \frac{{\overline I _{\mathrm{g}} - \overline I _{\mathrm{s}}}}{{\overline I _{\mathrm{s}}}}\), \(\left( {\overline I _{\mathrm{s}} \gg 0} \right)\), $$\begin{array}{*{20}{l}} {P^{(3)}(t)} \hfill & \propto \hfill & {N\mathop {\int}\limits_0^\infty d \tau _3\mathop {\int}\limits_0^\infty d \tau _2\mathop {\int}\limits_0^\infty d \tau _1{\cal{E}}(t - \tau _3)} \hfill \\ {} \hfill & {} \hfill & { \times {\cal{E}}(t - \tau _2 - \tau _3){\cal{E}}(t - \tau _1 - \tau _2 - \tau _3)S^{(3)}(\tau _1,\tau _2,\tau _3)} \hfill, \end{array}$$, $$\begin{array}{*{20}{l}} {S^{(3)}(\tau _1,\tau _2,\tau _3)} \hfill & \propto \hfill & {\left( i \right)^3Tr\left\{ {\mu (\tau _1 + \tau _2 + \tau _3)} \right.} 4df. Here, we use two 1ps pulses (see inset of Fig. This condition is common in the case of a weak vibrational resonant contribution \(\left( {\frac{{\mu _{ba}\mu _{cb}\mu _{cd}\mu _{ad}}}{{|\mu _{ea}|^4}} < < 1} \right)\), as in the case of low concentrations of oscillators \(\left( {\frac{{n_{{\kern 1pt} {\mathrm{CARS}}}}}{{n_{{\kern 1pt} {\mathrm{NVRB}}}}} < < 1} \right)\). Soavi, G. et al. 4ac. However, these vibrational signatures are also characteristic of molecules within anatomical tissue such as the brain, making it increasingly useful and applicable for . 17, 34473451 (2017). To obtain Fano, U. Due to its gapless nature, several interfering electronic and phononic transitions concur to generate its optical response, preventing to retrieve spectral profiles analogous to those of spontaneous Raman. Coherent Raman spectroscopy with a fiber-format femtosecond oscillator. Similarly, the vibrationally resonant FWM, I2, originating from concurrent CARS and NVRB processes (Fig. Spontaneous and coherent anti-Stokes Raman spectroscopy of human gastrocnemius muscle biopsies in CH-stretching region for discrimination of peripheral artery disease. Nat. 5, 5309 (2014). Rapid multiplex coherent anti-Stokes Raman scattering (CARS) spectroscopy in the high-wavenumber (HW) region shows great advantages in real-time dynamic process visualizations, clinical diagnosis, . Coherent anti-Stokes Raman scattering (CARS) signals, based on the mixing of four waves in a nonlinear optical process, are much stronger than Raman signals and thus more suited for microscopy applications that require real-time imaging [ 11 ]. Wu, J. Lett. Kumar, V. et al. In the biological field21,24, a wealth of studies has demonstrated the potential of CARS for fast imaging21,22,25, with pixel acquisition times as low as24 ~0.16s, thus allowing for video-rate microscopy24. Baldacchini, T. & Zadoyan, R. In situ and real time monitoring of two-photon polymerization using broadband coherent anti-Stokes Raman scattering microscopy, Opt. 2) to explore FWM in SLG and few-layer graphene (FLG). USA 107, 1499915004 (2010). We also demonstrated that CARS can be used for vibrational imaging with contrast equivalent to spontaneous Raman microscopy and signal levels as large as those of the third-order nonlinear response. Quantitative, Comparable Coherent Anti-Stokes Raman Scattering (CARS) Spectroscopy: Correcting Errors in Phase Retrieval J Raman Spectrosc. FLG nonlinear optical microscopy. CAS Coherent anti-Stokes Raman spectroscopy of single and multi-layer graphene, \(1/\delta t \sim 15\,{\mathrm{cm}}^{ - 1}\), \(\left( {\tilde \nu - \tilde \nu _{\mathrm{P}}} \right)\), \(( {\tilde \nu _{1,2,3} - \tilde \nu _{\mathrm{P}} = 1545,1576,1607{\mathrm{cm}}^{ - 1}})\), $$I(\omega _{{\mathrm{as}}}) \propto |P_{{\mathrm{CARS}}}^{(3)}(\omega _{{\mathrm{as}}}) + P_{{\mathrm{NVRB}}}^{(3)}(\omega _{{\mathrm{as}}})|^2.$$, \(P^{(3)} \propto E_{\mathrm{P}}^2E_{\mathrm{S}}^ \ast\), \(P_{{\mathrm{NVRB}}}^{(3)} \propto E_{\mathrm{P}}^2(t - \Delta T)E_{\mathrm{S}}^ \ast (t)\), \(P_{{\mathrm{CARS}}}^{(3)} \propto E_{\mathrm{P}}(t - {\mathrm{\Delta }}T)E_{\mathrm{S}}^ \ast (t){\int}_{ - \infty }^t E_{\mathrm{P}}(t{\prime} - {\mathrm{\Delta }}T)e^{ - t{\prime}/\tau }dt{\prime}\), \(P_{{\mathrm{CARS}}}^{(3)}/P_{{\mathrm{NVRB}}}^{(3)}\), \(E_{\mathrm{P}}(t,{\mathrm{\Delta }}T) = A_{\mathrm{P}}(t,{\mathrm{\Delta }}T)e^{ - i\omega _{\mathrm{P}}t}\), \(E_{\mathrm{S}}(t,0) = A_{\mathrm{S}}(t,0)e^{ - i\omega _{\mathrm{S}}t}\), \(\hat E_{\mathrm{P}}(\omega ,{\mathrm{\Delta }}T) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{P}}(t,{\mathrm{\Delta }}T)e^{i\omega t}dt\), \(\hat E_{\mathrm{S}}(\omega ,0) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{S}}(t,0)e^{i\omega t}dt\), \(P_{{\mathrm{CARS}}}^{(3)}(\omega ,\Delta T)\), $$ {P_{{\mathrm{CARS}}}^{(3)}(\omega ,{\mathrm{\Delta }}T) \propto - \eta _{{\kern 1pt} {\mathrm{CARS}}}\mathop {\int}\limits_{ - \infty }^\infty d \omega _3\mathop {\int}\limits_{ - \infty }^\infty d \omega _2\mathop {\int}\limits_{ - \infty }^\infty} {d \omega _1} \\ \times{{ \hat A_{\mathrm{P}}(\omega _3,{\mathrm{\Delta }}T)\hat A_{\mathrm{P}}(\omega _1,{\mathrm{\Delta }}T)\hat A_{\mathrm{S}}^ \ast (\omega _2,0)\delta (\omega - 2\omega _P + \omega _S - \omega _3 - \omega _1 + \omega _2)} \over {\left( {\omega _{\mathrm{P}} + \omega _3 - \bar \omega _{ba}} \right)\left( {\omega _{\mathrm{P}} - \omega _{\mathrm{S}} + \omega _3 - \omega _2 - \bar \omega _{ca}} \right)\left( {2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} + \omega _3 - \omega _2 + \omega _1 - \bar \omega _{da}} \right)}},$$, \(\bar \omega _{ij} = \omega _{ij} - i\gamma _{ij} = \omega _i - \omega _j - i\gamma _{ij}\), $$\begin{array}{*{20}{l}} {P_{{\mathrm{CARS}}}^{(3)}(\omega ,{\mathrm{\Delta }}T)} \hfill & \propto \hfill & { - \eta _{{\mathrm{CARS}}}\mathop {\int}\limits_{ - \infty }^\infty d \omega _1\mathop {\int}\limits_{ - \infty }^\infty d \omega _3} \hfill \\ {} \hfill & {} \hfill & { \times {\textstyle{{\hat A_{\mathrm{P}}(\omega _3,{\mathrm{\Delta }}T)\hat A_P(\omega _1,{\mathrm{\Delta }}T)\hat A_{\mathrm{S}}^ \ast (2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} - \omega + \omega _3 + \omega _1,0)} \over {\left( {\omega _{\mathrm{P}} + \omega _3 - \bar \omega _{ba}} \right)\left( {\omega - \omega _{\mathrm{P}} - \omega _1 - \bar \omega _{ca}} \right)\left( {\omega - \bar \omega _{da}} \right)}}}}. Research - sandia.gov A dichroic mirror reflects the SP in order to measure its intensity (Is) with a powermeter (P). For such systems, resonance CARS spectroscopy is a suitable tool to obtain resonance Raman information via the anti-Stokes, coherent spectroscopic method. Article In both processes, the optical response consists of a field emitted at the anti-Stokes frequency4 as=2PS. Abstract Coherent anti-stokes Raman scattering (CARS) microscopy is a label-free chemical imaging modality capable of interrogating local molecular composition, concentration, and even orientation.. Chemphyschem 8, 21562170 (2007). The same combination of optical fields used for CARS can generate another FWM signal, a nonvibrationally resonant background (NVRB)2, Fig. Coherent anti-Stokes Raman spectroscopy. Fiber-format CARS spectroscopy by spectral compression of femtosecond pulses from a single laser oscillator. (5), is a complex quantity: the real part has a dispersive lineshape, while the imaginary part peaks at ca. Sidorov-Biryukov, D. A. et al. Extracting for each image pixel I1 (Fig. developed the modeling and carried out the numerical simulations with contribution from A.V. Nature 459, 820823 (2009). Sci. Abstract Coherent anti-Stokes Raman scattering (CARS) microscopy using linearly chirped femtosecond laser pulses and spectrally and time-integrated detection is discussed both theoretically and experimentally. The NVRB polarization, defined by Eq. Lett. Authors Charles H Camp Jr 1 , Young Jong Lee 1 , Marcus T Cicerone 1 Affiliation B 19, 13631375 (2002). Examples of such paramagnetic systems are free radicals such as NO, OH, and CH2 and transition-metal ions like Fe(H2O)63+ and Cr(CN)64. Nature Communications (Nat Commun) By Fourier transform, the fields can be expressed in the frequency domain as \(\hat E_{\mathrm{P}}(\omega ,{\mathrm{\Delta }}T) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{P}}(t,{\mathrm{\Delta }}T)e^{i\omega t}dt\) and \(\hat E_{\mathrm{S}}(\omega ,0) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{S}}(t,0)e^{i\omega t}dt\), which can be used to calculate \(P_{{\mathrm{CARS}}}^{(3)}(\omega ,\Delta T)\) as20,53.
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