Fundamental limit of microresonator field uniformity and slow light enabled ultraprecise displacement metrology.

We determine the fundamental limit of microresonator field uniformity. It can be achieved in a specially designed microresonator, called a bat microresonator, fabricated at the optical fiber surface. We show that the relative nonuniformity of an eigenmode amplitude along the axial length of an ideal bat microresonator cannot be smaller than 13, where ,, and are its refractive index, eigenmode wavelength, and -factor, respectively. For a silica microresonator with =10, this eigenmode has axial speed ∼10, where is the speed of light in vacuum, and its nonuniformity along length =100\unicode{x00B5}m at wavelength =1.5µm is ∼10. For a realistic fiber with diameter 100 µm and surface roughness 0.2 nm, the smallest eigenmode nonuniformity is ∼0.0003. As an application, we consider a bat microresonator evanescently coupled to high -factor silica microspheres, which serves as a reference supporting ultraprecise straight-line translation.