Ultrafast Raman loss spectroscopy (URLS) is equivalent to anti-Stokes femtosecond stimulated Raman spectroscopy (FSRS), using a broadband probe pulse that extends to the blue of the narrow bandwidth Raman pump, and can be described as inverse Raman scattering (IRS). Using the Feynman dual time-line diagram, the third-order polarization for IRS with finite pulses can be written down in terms of a four-time correlation function. An analytic expression is obtained for the latter in the harmonic approximation which facilitates computation. We simulated the URLS of crystal violet (CV) for various resonance Raman pump excitation wavelengths using the IRS polarization expression with finite pulses. The calculated results agreed well with the experimental results of S. Umapathy et al., J. Chem. Phys. 133, 024505 (2010). In the limit of monochromatic Raman pump and probe pulses, we obtain the third-order susceptibility for multi-modes, and for a single mode we recover the well-known expression for the third-order susceptibility, χ(IRS) ((3)), for IRS. The latter is used to understand the mode dependent phase changes as a function of Raman pump excitation in the URLS of CV.
Femtosecond stimulated Raman spectroscopy (FSRS) typically uses a picosecond Raman pump and a ∼10 fs probe pulse. Such an ultrashort probe pulse is akin to a delta function (supercontinuum) pulse and the expressions for the third-order polarization simplifies with a reduction in the four-time correlation function to a three-time correlation function. Assuming multimode harmonic potentials for the ground and excited states of the molecule, we obtain analytic expressions for the three-time correlation functions which facilitate the computation of the third-order polarizations for resonance Raman scattering, hot luminescence, and inverse Raman scattering terms, which contribute to the FSRS spectra from the ground vibrational state. The effects of Raman pump pulse temporal width, the vibrational dephasing time, the homogeneous damping constant, and the inhomogeneous damping constant on the Raman Stokes spectrum are also more readily studied. The resonance FSRS spectra of rhodamine 6G from the ground vibrational state with various resonance excitation wavelengths were calculated using a delta probe and shown to account well for the recent experimental results of Frontiera et al., J. Chem. Phys. 2008; 129: 064507 for both the Stokes and anti-Stokes bands, as well as of Shim et al., ChemPhysChem. 2008; 9: 697.
I would like to thank my supervisor Prof. Lee Soo-Ying for his guidance and assistance throughout this entire project. Prof. Lee taught me how to find a scientific problem and to solve the problem. During the research, he provided invaluable advice on constructing models, data analysis, and paper writing. He is knowledgable and his ability of focusing on big picture kept me from overthinking technicalities. I am thankful for all the skills he has taught me. I would like to express my genuine gratitude to Dr. Sun Zhigang and Dr. Lu Yunpeng for their assistance and support. Dr. Sun Zhigang was an excellent tutor, without his help and patience it would be very hard for me to get close to these projects. Dr. Lu Yunpeng helped me a lot on debugging the codes and he gave me some wonderful suggestions. Thanks to all the talented and pleasant colleague Dr. Niu Kai, Zhao Bin, Li Xiuting, Song Hongwei and others in the Physics and Applied Physics department. I gratefully acknowledge the helpful discussions with them. Without them, life as a PhD student for these years would be very dull and monotonous. Finally, I would like to express my deepest gratitude to my family for their emotional support and encouragement. My parents, my husband and my brother, they are a great source of inspiration throughout the duration of my studies.
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