  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 appearing 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.
