  We show that the fundamental eigenmode of a shallow optical bottle
microresonator (also called a SNAP microresonator) can be made exceptionally
uniform along its axial length. The introduced microresonator has the effective
radius variation resembling the profile of a bat with ears and wings.
Remarkably, reduction of the axial size of this microresonator by cutting the
wings does not alter the uniformity of its fundamental eigenmode. Being of
general interest, our findings pave a way for improving the perceptibility of
micro/nanoparticle sensing. These results also suggest a bottle microresonator
suitable for accurate assembling of quantum emitters near the maximum of its
eigenmode important in cavity quantum electrodynamics.
