We develop and experimentally verify a theoretical model for the total efficiency η0 of evanescent excitation and subsequent collection of spontaneous Raman signals by the fundamental quasi-TE and quasi-TM modes of a generic photonic channel waveguide. Single-mode silicon nitride (Si3N4) slot and strip waveguides of different dimensions are used in the experimental study. Our theoretical model is validated by the correspondence between the experimental and theoretical absolute values within the experimental errors. We extend our theoretical model to silicon-on-insulator (SOI) and titanium dioxide (TiO2) channel waveguides and study η0 as a function of index contrast, polarization of the mode and the geometry of the waveguides. We report nearly 2.5 (4 and 5) times larger η0 for the fundamental quasi-TM mode when compared to η0 for the fundamental quasi-TE mode of a typical Si3N4 (TiO2 and SOI) strip waveguide. η0 for the fundamental quasi-TE mode of a typical Si3N4, (TiO2 and SOI) slot waveguide is about 7 (22 and 90) times larger when compared to η0 for the fundamental quasi-TE mode of a strip waveguide of the similar dimensions. We attribute the observed enhancement to the higher electric field discontinuity present in high index contrast waveguides.