  Whispering-gallery microcavities have been used to realize a variety of
efficient parametric nonlinear optical processes through the enhanced
light-matter interaction brought about by supporting multiple high quality
factor and small modal volume resonances. Critical to such studies is the
ability to control the relative frequencies of the cavity modes, so that
frequency matching is achieved to satisfy energy conservation. Typically this
is done by tailoring the resonator cross-section. Doing so modifies the
frequencies of all of the cavity modes, that is, the global dispersion profile,
which may be undesired, for example, in introducing competing nonlinear
processes.Here, we demonstrate a frequency engineering tool, termed multiple
selective mode splitting (MSMS), that is independent of the global dispersion
and instead allows targeted and independent control of the frequencies of
multiple cavity modes. In particular, we show controllable frequency shifts up
to 0.8 nm, independent control of the splitting of up to five cavity modes with
optical quality factors $\gtrsim 10^5$, and strongly suppressed frequency
shifts for untargeted modes. The MSMS technique can be broadly applied to a
wide variety of nonlinear optical processes across different material
platforms, and can be used to both selectively enhance processes of interestand
suppress competing unwanted processes.
