Asymptotic and Numerical Techniques for Resonances of Thin Photonic Structures
Asymptotic and Numerical Techniques for Resonances of Thin Photonic Structures
复制标题
薄光子结构共振的渐近和数值技术
DOI：
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发表时间：
2008
影响因子：
1.9
通讯作者：
F. Santosa
中科院分区：
文献类型：
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作者：
Jay Gopalakrishnan;Shari Moskow;F. Santosa
本文讨论了光学谐振腔的谐振频率和辐射损耗的计算问题。光学谐振器的形式是具有可变介电特性的薄膜。这项工作提供了两种非常不同的方法来进行这样的计算。第一种是利用膜的小厚度和高折射率的渐近方法。我们推导出一个极限共振问题的厚度为零，并为一个简单的共振的情况下，找到一个一阶修正。极限问题和校正是在一个更少的空间维度，这可以使该方法非常有效。证明了渐近性的收敛估计。第二种方法，基于截断完全匹配层的有限元法，不限于薄结构。我们演示了使用这些方法的数值计算，进一步说明了它们的差异。渐近法通过求解一个密集的，但很小的，非线性特征值找到共振…
We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiting resonance problem as the thickness goes to zero, and for the case of a simple resonance, find a first order correction. The limiting problem and the correction are in one less space dimension, which can make the approach very efficient. Convergence estimates are proved for the asymptotics. The second approach, based on the finite element method with a truncated perfectly matched layer, is not restricted to thin structures. We demonstrate the use of these methods in numerical calculations which further illustrate their differences. The asymptotic method finds resonance by solving a dense, but small, nonlinear eige...