Theoretical analysis of anharmonic coupling and cascading Raman signals observed with femtosecond stimulated Raman spectroscopy

We present a classical theoretical treatment of a two-dimensional Raman spectroscopy based on the initiation of vibrational coherence with an impulsive Raman pump and subsequent probing by two-pulse femtosecond stimulated Raman spectroscopy (FSRS). The classical model offers an intuitive picture of the molecular dynamics initiated by each laser pulse and the generation of the signal field traveling along the probe wave vector. Previous reports have assigned the observed FSRS signals to anharmonic coupling between the impulsively driven vibration and the higher-frequency vibration observed with FSRS. However, we show that the observed signals are not due to anharmonic coupling, which is shown to be a fifth-order coherent Raman process, but instead due to cascades of coherent Raman signals. Specifically, the observed vibrational sidebands are generated by parallel cascades in which a coherent anti-Stokes or Stokes Raman spectroscopy (i.e., CARS or CSRS) field generated by the coherent coupling of the impulsive pump and the Raman pump pulses participates in a third-order FSRS transition. Additional sequential cascades are discussed that will give rise to cascade artifacts at the fundamental FSRS frequencies. It is shown that the intended fifth-order FSRS signals, generated by an anharmonic coupling mechanism, will produce signals of approximately 10(-4) DeltaOD (change in the optical density). The cascading signals, however, will produce stimulated Raman signal of approximately 10(-2) DeltaOD, as has been observed experimentally. Experiments probing deuterochloroform find significant sidebands of the CCl(3) bend, which has an E type symmetry, shifted from the A(1) type C-D and C-Cl stretching modes, despite the fact that third-order anharmonic coupling between these modes is forbidden by symmetry. Experiments probing a 50:50 mixture of chloroform and d-chloroform find equivalent intensity signals of low-frequency CDCl(3) modes as sidebands shifted from both the C-D stretch of CDCl(3) and the C-H stretch of CHCl(3). Such intermolecular sidebands are allowed in the cascade mechanism, but are expected to be extremely small in the fifth-order frequency modulation mechanism. Each of these observations indicates that the observed signals are due to cascading third-order Raman signals.