  We theoretically investigate several types of plasmonic slot waveguides for
enhancing the measured signal in Raman spectroscopy, which is a consequence of
electric field and Purcell factor enhancements, as well as an increase in
light-matter interaction volume and the Raman signal collection efficiency. An
intuitive methodology is presented for calculating the accumulated Raman
enhancement factor of an ensemble of molecules in waveguide sensing, which
exploits an analytical photon Green function expansion in terms of the
waveguide normal modes, and we combine this with a quantum optics formalism of
the molecule-waveguide interaction to model Raman scattering. We subsequently
show how integrated plasmonic slot waveguides can attain significantly higher
Raman enhancement factors: $\sim$5.3$\times$ compared to optofluidic fibers and
$\sim$3.7$\times$ compared to planar integrated dielectric waveguides, with a
device size and thus analyte volume of at least three-orders of magnitude less.
We also provide a comprehensive comparison between the different types of
plasmonic slot waveguides based on the important figures-of-merit, and
determine the optimal approaches to maximize Raman enhancement.
