微谐振器场均匀性的基本限制和慢光使能的埃精确直线平移
Fundamental limit of the microresonator field uniformity and slow light enabled angstrom-precise straight-line translation
摘要：
我们确定的基本限制的微谐振器场均匀性。它可以实现在一个特殊设计的微谐振器，称为蝙蝠微谐振器，在光纤表面制造。我们表明，沿轴向长度$L$的本征模振幅的相对不均匀性的理想蝙蝠微谐振器不能小于${{\frac{1}{3}}}{π}^2n^4_r{λ}^{-4}Q^{-2}L^4$，其中$n_r,\ λ$和$Q$是它的折射率，本征模波长和Q因子。在没有损耗（$Q=\infty $）的情况下，该本征模具有与轴向坐标和零轴向速度无关的振幅（即，在$L$长度内停止）。对于具有$Q={10}^8$的石英微谐振器，该本征模具有轴向速度$\mathrm{\sim}$ 10 ${}^{-4}$ c，其中c是真空中的光速，并且其在波长$λ=1.5$微米处沿着100微米的长度的不均匀性是$\mathrm{\sim}$ 10 ${}^{-7}$。对于直径为100微米且表面粗糙度为0.2 nm的实际光纤，最小本征模非均匀性为$\mathrm{\sim}$ 0.0003。作为一个应用程序，我们认为蝙蝠微谐振器evanescently耦合到高Q因子的二氧化硅微球，作为一个参考，支持在超过一百微米的距离$L$埃精确的直线平移。
英文摘要：
We determine the fundamental limit of the 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 ${{\frac{1}{3}}}{π}^2n^4_r{λ}^{-4}Q^{-2}L^4$, where $n_r,\ λ$ and $Q$ are its refractive index, the eigenmode wavelength and Q-factor. In the absence of losses ($Q=\infty $), this eigenmode has the amplitude independent of axial coordinate and zero axial speed (i.e., is stopped) within the length $L$. For a silica microresonator with $Q={10}^8$ this eigenmode has the axial speed $\mathrm{\sim}$ 10${}^{-4}$c, where c is the speed of light in vacuum, and its nonuniformity along the length 100 micron at wavelength $λ=1.5$ micron is $\mathrm{\sim}$ 10${}^{-7}$. For a realistic fiber with diameter 100 micron and surface roughness 0.2 nm, the smallest eigenmode nonuniformity is $\mathrm{\sim}$ 0.0003. As an application, we consider a bat microresonator evanescently coupled to high Q-factor silica microspheres which serves as a reference supporting the angstrom-precise straight-line translation over the distance $L$ exceeding a hundred microns.
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