The notion that Stimulated Brillouin Scattering (SBS) is primarily defined by bulk material properties has been overturned by recent work on nanoscale waveguides. It is now understood that boundary forces of radiation pressure and electrostriction ap
pearing in such highly confined waveguides can make a significant contribution to the Brillouin gain. Here, this concept is extended to show that gain enhancement does not require nanoscale or subwavelength features, but generally appears where optical and acoustic fields are simultaneously confined near a free surface or material interface. This situation routinely occurs in whispering gallery resonators (WGRs), making gain enhancements much more accessible than previously thought. To illustrate this concept, the first full-vectorial analytic model for SBS in WGRs is developed, including optical boundary forces, and the SBS gain in common silica WGR geometries is computationally evaluated. These results predict that gains $10^4$ times greater than the predictions of scalar theory may appear in WGRs even in the 100 um size range. Further, trapezoidal cross-section microdisks can exhibit very large SBS gains approaching $10^2$ m$^{-1}$W$^{-1}$. With resonant amplification included, extreme gains on the order of $10^{12}$ m$^{-1}$W$^{-1}$ may be realized, which is $10^8$ times greater than the highest predicted gains in linear waveguide systems.
