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 L of an ideal bat microresonator cannot be smaller than 1/3 pi(2)n(4)lambda(-4) Q(-2)L(4), where n, lambda, and Q are its refractive index, eigenmode wavelength, and Q-factor, respectively. For a silica microresonator with Q = 10(8), this eigenmode has axial speed similar to 10(-4)c, where c is the speed of light in vacuum, and its nonuniformity along length L = 100 mu m at wavelength lambda = 1.5 mu m is similar to 10(-7). For a realistic fiber with diameter 100 mu m and surface roughness 0.2 nm, the smallest eigenmode nonuniformity is similar to 0.0003. As an application, we consider a bat microresonator evanescently coupled to high Q-factor silica microspheres, which serves as a reference supporting ultraprecise straight-line translation. (C) 2021 Optical Society of America

Automated summary

The study determines the fundamental limit of microresonator field uniformity and investigates the relative nonuniformity of an eigenmode amplitude in an ideal bat microresonator. The smallest eigenmode nonuniformity for a realistic fiber is about 0.0003.