Zimmerling Tyler J, Van Vien
Opt Lett. 2020 Feb 1;45(3):714-717. doi: 10.1364/OL.384552.
Hofstadter's butterfly spectrum, which characterizes the energy bands of electrons in a 2D lattice under a perpendicular magnetic field, has been emulated and experimentally characterized in periodic bandgap structures at microwave and acoustic frequencies. However, measurement of the complete spectrum at optical frequencies has yet to be demonstrated. Here, we propose a simple topological photonic structure based on a circular array of microrings with periodic resonant frequency detunings that can be implemented on an integrated optics platform. We show that this ring-of-rings structure exactly emulates the Harper equation and propose an experimental approach for measuring Hofstadter's butterfly spectrum at optical frequencies.
霍夫施塔特蝴蝶谱表征了二维晶格中电子在垂直磁场下的能带，已在微波和声学频率的周期性带隙结构中得到模拟和实验表征。然而，光学频率下完整谱的测量尚未得到证实。在此，我们提出一种基于具有周期性谐振频率失谐的微环圆形阵列的简单拓扑光子结构，该结构可在集成光学平台上实现。我们表明这种环中环结构精确地模拟了哈珀方程，并提出了一种在光学频率下测量霍夫施塔特蝴蝶谱的实验方法。
