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This paper theoretically treats the spontaneous resonant inelastic scatteringof Laguerre-Gauss (LG) beams from the totally symmetric vibrations of complexpolyatomic molecules within the semi-classical framework. We develop aninteraction Hamiltonian that accounts for the position of the molecule withinthe excitation beam to derive the effective differential scatteringcross-section of a classical LG beam from a molecule using the frequency domainthird order nonlinear optical response function. To gain physical insight intothis scattering process, we utilize a model vibronic molecule to study thechanges to this scattering process. For specific molecular parameters includingvibrational frequency and relative displacement of the involved electronicstates, this investigation shows that an incident LG beam asymmetricallyenhances one of two participating excitation transitions causing modulation ofthe interference present in the scattering process. This modulation allows apathway to coherent control of resonant inelastic scattering from complex,poly-atomic molecules. We discuss the possible application of this control tothe resonant x-ray inelastic scattering (RIXS) of small poly-atomic moleculescentral to applications ranging from single molecule electronics to solarenergy science.

Examining resonant inelastic spontaneous scattering of classical Laguerre-Gauss beams from molecules