arXivDaily arXiv每日学术速递 周一至周五更新
arXiv physics/0406102physics.optics
收藏

含平面介质镜的三维矢量微腔问题的求解方法

Methods for 3-D vector microcavity problems involving a planar dielectric mirror

David H. Foster, Jens U. Nockel

摘要:

我们开发并演示了两种数值方法来解决这类开放腔问题,其中涉及一个弯曲的,圆柱对称的导电镜面对一个平面介质堆。这种圆顶形腔由于其将光紧密聚焦到平坦表面上而有用。第一种方法使用贝塞尔波基。从这种方法发展出一种双基方法,它最终使用多极基。每一种方法都适用于标量场和电磁矢量场,并给出了明确的“最终用户”公式。所有这些方法都完全通过其s和p偏振的2 \times 2传递矩阵来表征任意介质堆叠反射镜。我们解释我们的方法的理论和实践的局限性。非平凡的演示,包括一个堆栈诱导的效果(近退化拉盖尔-高斯模式的混合),可能会持续任意远到傍轴极限。处理了50 λ大的腔,远远超过了以前报道的任何矢量解。

英文摘要:

We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to their tight focusing of light onto the flat surface. The first method uses the Bessel wave basis. From this method evolves a two-basis method, which ultimately uses a multipole basis. Each method is developed for both the scalar field and the electromagnetic vector field and explicit ``end user'' formulas are given. All of these methods characterize the arbitrary dielectric stack mirror entirely by its 2\times2 transfer matrices for s- and p-polarization. We explain both theoretical and practical limitations to our method. Non-trivial demonstrations are given, including one of a stack-induced effect (the mixing of near-degenerate Laguerre-Gaussian modes) that may persist arbitrarily far into the paraxial limit. Cavities as large as 50 λare treated, far exceeding any vectorial solutions previously reported.

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。

↑