Abstract

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 ${\boldsymbol L}$ of an ideal bat microresonator cannot be smaller than $\frac{1}{3}{{\boldsymbol \pi}^2}{{\boldsymbol n}^4}{{\boldsymbol \lambda}^{- 4}}{{\boldsymbol Q}^{- 2}}{{\boldsymbol L}^4}$, where $n,{\boldsymbol \;\lambda}$, and ${\boldsymbol Q}$ are its refractive index, eigenmode wavelength, and $Q$-factor, respectively. For a silica microresonator with ${\boldsymbol Q} = {10^8}$, this eigenmode has axial speed $\sim 10^{-4}c$, where $c$ is the speed of light in vacuum, and its nonuniformity along length ${\boldsymbol L} = 100\; {\textbf{\unicode{x00B5}}\!\text{m}}$ at wavelength ${\boldsymbol \lambda} = 1.5{\boldsymbol \;\unicode{x00B5}\text{m}}$ is $\sim 10^{-7}$. For a realistic fiber with diameter 100 µm and surface roughness 0.2 nm, the smallest eigenmode nonuniformity is $\sim 0.0003$. 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.

© 2021 Optical Society of America

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