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arXiv physics/0511197physics.optics
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电磁系统中高折射率对比度变化的非微扰方法

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

Lars Rindorf, Niels Asger Mortensen

摘要:

我们提出了一种方法,正式计算\emph{exact}频率偏移的电磁场的折射率的任意变化。可能的折射率变化包括各向异性变化和边界偏移。简并本征模频率在所提出的方法中没有问题。这种方法依赖于算子代数来推导频率偏移的方程,最终以简单和物理上合理的形式出现。在数值上,方程表现良好,易于实现,并且可以非常快速地求解。像在微扰理论中一样,首先考虑一个参考系,然后用它来求解另一个相关但不同的系统。该方法的精度仅受参考系基函数的限制,对于一阶基组误差,频率引起的误差是二阶的。作为一个例子,我们应用我们的方法在空气孔直径的变化在光子晶体光纤的问题。

英文摘要:

We present a method that formally calculates \emph{exact} frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.

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