  We outline a full-vectorial three-dimensional multi-mode matching technique
in a cylindrical coordinate system that addresses the mutual coupling among
multiple modes copropagating in a perturbed whispering-gallery-mode
microcavity. In addition to its superior accuracy in respect to our previously
implemented single-mode matching technique, this current technique is suitable
for modelling waveguide-to-cavity coupling where the influence of multi-mode
coupling is non-negligible. Using this methodology, a robust scheme for hybrid
integration of a microcavity onto a silicon-on-insulator platform is proposed.
