手性是自然界中一种普遍而又特殊的现象，近年来手性检测在生物制药，化学，光学等领域的重要性愈发凸显，成为科学研究的热点。回音壁模式光学微腔因其具有超高的品质因子和极小的模式体积，已经成为光与物质相互作用的重要平台，在微纳光子学领域有很多应用。现有的手性光学检测手段由于手性光学效应本身较弱，且需要一定的作用空间，对于微量样品的手性检测仍然存在较大挑战。而传统的回音壁模式微腔具有镜像对称面，对于其在手性检测上的应用存在很大的限制。在此背景下，本文考虑使用手性调制的回音壁模式微腔作为手性检测的平台，构建了手性材料微结构的有限元仿真框架，分析了回音壁微腔的手性微扰理论，并对手性材料二维圆腔和手性液体填充的微泡腔及手性检测进行了仿真，取得了一些研究进展，主要包括：

(1) 通过麦克斯韦方程组和手性材料的唯象本构关系推导了手性材料中的电磁场，并构建出了适用于有限元仿真软件的手性材料微结构的仿真框架。使用有限元仿真框架对手性材料的二维圆腔进行了有限元仿真，发现了腔模的偏振与模式手性参数P 之间具有非常强烈的依赖关系，在微腔内外部手性不同时，微腔模式谐振频率随手性不同方向的变化会产生了非对称的模式移动响应。通过谐振腔的微扰理论，推导出了适用于TE与TM模式强耦合情况下的回音壁微腔手性微扰理论，并与之前的仿真结果进行了对照。

(2) 在得到手性材料二维圆腔仿真的一系列结论后，对检测机制上更具优势的内部填充手性液体的微泡腔进行了有限元仿真。微泡腔的内部填充手性溶液会影响其腔模的偏振态以及光场分布。对微泡腔的壁厚进行改变，发现微泡腔的壁厚变薄的同时，其对于回音壁模式光场的限制也越来越小，不在壁内的光场占总光场的比例有较为明显的提高。我们研究了不同壁厚的手性微泡腔与外部旋光性b₁的依赖关系，很明显的看出随着微泡腔壁厚的降低，其模式的特征频率与外部环境中手性的依赖关系越来越强。且这种模式对于外部环境中不同方向的手性其特征频率的响应是相反的，这更有利于进行高精度的手性检测并确定其方向，证明了其在手性检测中的潜力。

Chirality is a prevalent and distinctive phenomenon in nature. In recent years, the importance of chirality detection has been increasingly emphasized in fields such as biopharmaceuticals, chemistry, and optics, making it a hotspot in scientific research. Whispering-gallery-mode optical microcavities, due to their ultra-high quality factors and extremely small mode volumes, have become important platforms for the interaction between light and matter, with numerous applications in the field of micro and nanophotonics. Existing methods for chirality detection face significant challenges in detecting chiral effects due to their inherent weakness and the requirement of certain interaction spaces, particularly for the detection of trace samples. Moreover, traditional whispering-gallery-mode microcavities possess mirror-symmetry planes, imposing significant limitations on their applications in chirality detection. Against this backdrop, thesis considers the use of chirally modulated whispering gallery mode microcavities as a platform for chirality detection. A finite element simulation framework for chiral material microstructures is constructed, and the chirality-induced perturbation theory of whispering-gallery-mode microcavities is analyzed. Simulations of chirality detection are conducted for two-dimensional circular cavities with chirality-modified materials and microbubbles filled with chiral liquids, resulting in some research advancements, primarily including:

(1) The electromagnetic field within chiral materials is derived through the Maxwell's equations and the phenomenological constitutive relationship of chiral materials. A simulation framework suitable for finite element software is established for chiral material microstructures. Finite element simulations of two-dimensional circular cavities with chiral materials reveal a strong dependence between cavity mode polarization and the mode chirality parameter P. When the chirality inside and outside the microcavity differs, the resonance frequency of cavity modes exhibits asymmetric mode shift responses with respect to different chirality directions. Perturbation theory of resonant cavities is derived, applicable for strong coupling cases of TE and TM modes in whispering-gallery-mode microcavities, and compared with previous simulation results.

(2) Following a series of conclusions obtained from simulations of two-dimensional circular cavities with chiral materials, finite element simulations are conducted for microbubbles filled with internally advantageous chiral liquids for the detection mechanism. The internal filling of chiral solutions in microbubbles affects the polarization state of cavity modes and the distribution of optical fields. By varying the thickness of microbubble walls, it is observed that as the wall thickness decreases, the restriction on the whispering-gallery-mode optical field within the walls diminishes, leading to a significant increase in the proportion of optical field outside the walls. The dependency relationship between microbubble thickness and the external optical rotation b₁ is studied, demonstrating that as the microbubble wall thickness decreases, the dependence of mode characteristic frequencies on external chiral environments becomes stronger. Moreover, the response of these modes to the chirality in different directions within the external environment is opposite, facilitating high-precision chirality detection and determination of its direction, thus demonstrating its potential in chirality detection.