论文标题
介电腔中光学模式的完全匹配的层方法
Perfectly matched layer method for optical modes in dielectric cavities
论文作者
论文摘要
光学共振问题与时间稳定的Schrödinger方程相似，但不同。一个大挑战是共振问题中的本征函数正在成倍增长。我们对这种边界条件提供了物理解释，并引入了完美匹配的层（PML）方法，以将特征函数从指数增长转化为指数率。基于复杂的拉伸技术，我们为光学共振问题构建了一个非热的哈密顿量。我们通过计算圆形腔中的特征值并与分析结果进行比较来成功验证哈密顿量的有效性。我们还使用拟议的哈密顿量来研究四骨腔中特殊点的模式演变。
The optical resonance problem is similar to but different from time-steady Schrödinger equation. One big challenge is that the eigenfunctions in resonance problem is exponentially growing. We give physical explanation to this boundary condition and introduce perfectly matched layer (PML) method to transform eigenfunctions from exponential-growth to exponential-decay. Based on the complex stretching technique, we construct a non-Hermitian Hamiltonian for the optical resonance problem. We successfully validate the effectiveness of the Hamiltonian by calculate its eigenvalues in the circular cavity and compare with the analytical results. We also use the proposed Hamiltonian to investigate the mode evolution around exceptional points in the quad-cosine cavity.
