arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1011.0109physics.opticscond-mat.dis-nncond-mat.mes-hall
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无序光子晶体的电磁模式

Electromagnetic modes of a disordered photonic crystal

Vincenzo Savona

摘要:

我们提出了一个系统的数值方法来计算无序光子晶体的本征模和相关的本征频率,其特征在于,否则周期性的介电分布的小波动。场本征模展开相应的周期性结构的布洛赫模式的基础上,和由此产生的本征值问题是对角化的截断的基础上,包括有限数量的布洛赫带。布洛赫模式展开对于在给定频率范围内非常扩展的无序结构的模式建模非常有效,因为只有光谱上接近的带必须包括在基集中。通过对增加的带集重复对角化,可以容易地验证收敛性。作为例证,我们应用该方法的W1线缺陷波导和L3耦合腔波导,都基于一个光子晶体平板与三角形晶格的圆孔。计算并表征了由无序引起的局域模的本征频率、空间场分布和辐射损失率。对于W1波导,我们表明,辐射损耗,在底部的空间均匀的引导带,是由一个小的杂交与布洛赫模式的空间奇数带,引起的混乱,尽管他们的频率分离。布洛赫模式展开法有着非常广泛的应用:它也可以用来精确地计算具有周期介电常数系统调制的结构的模式,例如在几种高Q腔的设计中。

英文摘要:

We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on the basis of Bloch modes of the corresponding periodic structure, and the resulting eigenvalue problem is diagonalized on a truncated basis including a finite number of Bloch bands. The Bloch-mode expansion is very effective for modeling modes of very extended disordered structures in a given frequency range, as only spectrally close bands must be included in the basis set. The convergence can be easily verified by repeating the diagonalization for an increased band set. As illustrations, we apply the method to the W1 line-defect waveguide and to the L3 coupled-cavity waveguide, both based on a photonic crystal slab with a triangular lattice of circular holes. We compute and characterize the eigenfrequencies, spatial field profiles and radiation loss rates of the localized modes induced by disorder. For the W1 waveguide, we demonstrate that radiation losses, at the bottom of the spatially-even guided band, are determined by a small hybridization with Bloch modes of the spatially-odd band, induced by disorder in spite of their frequency separation. The Bloch-mode expansion method has a very broad range of applications: it can be also used to accurately compute the modes of structures with systematic modulations of the periodic dielectric constant, as in several designs of high-Q cavities.

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