  We fabricate a liquid-core liquid-clad microcavity that is coupled to a
standard tapered fiber, and then experimentally map the whispering-gallery
modes of this droplet resonator. The shape of our resonator is similar to a
thin prolate spheroid, which makes space for many high-order transverse modes,
suggesting that some of them will share the same resonance frequency. Indeed,
we experimentally observe that more than half of the droplet's modes have a
sibling having the same frequency (to within linewidth) and therefore
exhibiting a standing interference-pattern.
