Resonant-state expansion applied to three-dimensional open optical systems
Resonant-state expansion applied to three-dimensional open optical systems
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DOI：
10.1103/physreva.90.013834
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发表时间：
2014-07-28
影响因子：
2.9
通讯作者：
Muljarov, E. A.
中科院分区：
文献类型：
--
作者：
Doost, M. B.;Langbein, W.;Muljarov, E. A.
共振态展开（RSE）是电动力学中的一种严格微扰方法，它适用于三维开放光学系统。结果使用解析可解的均匀介质球作为未扰动系统。由于任何破坏球对称性的扰动都会混合横电（TE）和横磁（TM）模式，因此RSE在这里扩展为包括TM模式和绿色函数的零频率极点。我们证明了有效性的RSE TM模式，通过验证其收敛到一个均匀的扰动球的精确结果。然后，我们应用RSE计算模式的选择扰动依次减少剩余的对称性，给出了半球和四分之一球形状的介电常数的变化。由于没有确切的解决方案是已知的，这些扰动，我们验证RSE的结果进行比较，最先进的有限元法（FEM）和时域有限差分（FDTD）求解器的结果。我们发现，对于选定的扰动，RSE提供了一个显着更高的精度比有限元法和FDTD为一个给定的计算工作量，证明其潜力，以取代目前使用的方法。我们还表明，在目前使用的方法相比，RSE是能够确定的扰动的一组选定的模式，通过使用有限的基础本地这些模式，这可以进一步减少计算工作量的数量级。
The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude.