TIME-DEPENDENT THEORY OF RAMAN SCATTERING WITH PULSES

Abstract

In this thesis, we develop a real-time dependent theory of Raman scattering for a pulse-mode laser within second-order perturbation theory and using the wavepacket terminology. Both spontaneous and stimulated Raman emission are considered in detail. An exact rate equation of spontaneous Raman emission with a pulse is proposed. In the case of CW excitation, this rate equation can correctly reduce to the time-frame equivalent of the well-known Kramers-Heisenberg-Dirac expression. We provide a consistent picture which treats the two-photon process from short pulse to long pulse (including CW limit) and for both on-resonance and off-resonance excitation. We also show how Shapiro's ( J. Chem. Phys. 99, 2453 (1903); Femtosecond Chemistry Vol. 1, edited by J. Manz and Wöste (VCH Publishers, Weinheim, 1995), pp.321-351) approximate energy-frame result for pulse excitation can be derived from the exact time-frame expression. The theory is applied to continuum Raman scattering for short and long pulses and varying pulse carrier frequency. The Raman spectrum, spontaneous and stimulated Raman probabilities, and the transient rate of emission are calculated. All results obtained can be explained by the wavepacket created on the excited state surface and the correlation function. Fluorescence-like emission peak which remains fixed as the incident frequency is tuned near resonance occurs only in the case of ultrashort pulses, whose pulse, durations are very much shorter than the dissociation time. Such an ultrashort. pulse, leaves a real wavepacket. in the Franck-Condon region of the excited state surface after the pulse has passed. ln all other cases, Raman-like peaks which track linearly with the pulse carrier frequency are obtained. All components of Raman spectrum have the same nodal structures as the moduli of their corresponding correlation functions. It is also shown that the rate of Raman emission as a function of time and pulse carrier frequency, from an initial ground vibrational state to various final vibrational states, is structureless for all pulses, and for pulses that are longer than the dissociation time the rate also decays with the pulses. This is contrary to Shapiro's report of recurring resonance fluorescence type structures at long times after the pulse has vanished. We explain why such structures are unphysical for continuum Raman scattering. Finally, the results for excitation from the first. excited vibrational state are also presented. The emission rate as a function of time has the symmetry of the correlation function, but as a function of detuning it has the symmetry of the modulus of the vibrational state in the Raman process with the lower quantum number. For an ultrashort pulse, this structure may be smoothened out due to a wide enough energy spectrum.