arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.07558physics.optics
收藏

介质腔光学模式的完全匹配层方法

Perfectly matched layer method for optical modes in dielectric cavities

Tianpeng Jiang, Yang Xiang

摘要:

光共振问题与定常的薛定谔方程有相似之处,但又有不同之处。共振问题中的特征函数是指数增长的,这是一个很大的挑战。我们给出了这种边界条件的物理解释,并引入完全匹配层(PML)方法将本征函数从指数增长转换为指数衰减。基于复拉伸技术,我们构造了一个非厄米哈密顿量的光学共振问题。我们成功地验证了有效性的哈密顿计算其本征值在圆形腔中,并与解析结果进行比较。我们也使用建议的哈密顿量来研究四余弦腔中例外点周围的模式演化。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑