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arXiv 0801.0562cond-mat.dis-nn
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无序光子晶体中的辐射能量传递

Radiative energy transfer in disordered photonic crystals

M. V. Erementchouk, L. I. Deych, H. Noh, H. Cao, A. A. Lisyansky

摘要:

描述无序光子晶体中的辐射转移的困难来自于必须平等地考虑介电函数的周期性调制和随机不均匀性引起的波散射。我们解决了这个困难,接近这个问题的立场上的一般多重散射理论在介质中的介电函数的任意规则的轮廓。我们使用的Bethe-Salpeter方程的一般渐近解,以表明,对于一个足够弱的无序的扩散限制在无序光子晶体提出的非相干叠加的模式的理想结构的权重成反比各自的群速度。辐射转移和扩散方程推导作为一个放松的长期尺度偏离这个限制分布。特别是,它表明,在一般情况下,扩散是各向异性的,除非晶体具有足够丰富的对称性,说,正方形晶格在2D或立方晶格在3D。在这种情况下,扩散是各向同性的,只有在这种情况下,无序的影响可以通过依赖于频率的单个平均自由程来表征。

英文摘要:

The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random inhomogeneities. We resolve this difficulty by approaching this problem from the standpoint of the general multiple scattering theory in media with arbitrary regular profile of the dielectric function. We use the general asymptotic solution of the Bethe-Salpeter equation in order to show that for a sufficiently weak disorder the diffusion limit in disordered photonic crystals is presented by incoherent superpositions of the modes of the ideal structure with weights inversely proportional to the respective group velocities. The radiative transfer and the diffusion equations are derived as a relaxation of long-scale deviations from this limiting distribution. In particular, it is shown that in general the diffusion is anisotropic unless the crystal has sufficiently rich symmetry, say, the square lattice in 2D or the cubic lattice in 3D. In this case, the diffusion is isotropic and only in this case the effect of the disorder can be characterized by the single mean-free-path depending on frequency.

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