论文标题
变形介电球的光学共振的摄动理论
Perturbation Theory of Optical Resonances of Deformed Dielectric Spheres
论文作者
论文摘要
注射到球形介电体中的光可以通过全部反射的机制非常有效地限制在球形介电体中。最限制的频率称为共振。如果身体的形状偏离了完美的球形形式，则共振会发生相应的变化。在本文中，开发了这种变形球的光学共振的扰动理论。这种开放系统的光学共振的特征是复杂的特征值，其中实际部分与共振光的频率以及虚构的部分有关，与能量泄漏从系统中泄漏。由于不受干扰且在分析上可解决方案的问题具有均匀的介电球体，并且对其特征值的校正被确定并包括二阶，以实现光线的任何极化。对于每个阶，光学共振的校正由有限维线性特征值方程确定，类似于量子力学中的堕落时间独立依赖性扰动理论。此外，得出了几何直观的适用性标准。为了检查所提出方法的有效性，将其应用于分析解决的问题并将其进行比较。
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the perfect spherical form the resonances change accordingly. In this thesis, a perturbation theory for the optical resonances of such a deformed sphere is developed. The optical resonances of such an open system are characterized by complex eigenvalues, where the real part relates to the frequency of the resonant light and the imaginary part to the energy leakage out of the system. As unperturbed and analytically solvable problem serves the homogeneous dielectric sphere, and the corrections to its eigenvalues are determined up to and including second order for any polarization of light. For each order, the corrections of the optical resonances are determined by a finite-dimensional linear eigenvalue equation, similar to degenerate time-independent perturbation theory in quantum mechanics. Furthermore, geometrically intuitive applicability criteria are derived. To check the validity of the presented method, it is applied and compared to an analytically solvable problem.
