Wang Ken Kang-Hsin, Ye Zhen
Wave Phenomena Laboratory and Center of Complex Systems, Department of Physics, National Central University, Chungli, Taiwan 32054, Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046608. doi: 10.1103/PhysRevE.68.046608. Epub 2003 Oct 22.
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan et al. [J. Opt. Soc. Am. B 10, 391 (1993)]. A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of, and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with traveling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases where the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems [Asatryan et al., Phys. Rev. E 67, 036605 (2003)].
在本文中，我们按照埃尔多安等人[《美国光学学会会刊B》10, 391 (1993)]之前提出的模型，讨论电磁波在由电偶极子阵列组成的二维随机系统中的输运现象。我们给出了一组自洽方程，该方程考虑了系统中的多次散射，然后进行数值求解。在频域中发现了一个强局域化区域。针对不同参数，如填充因子和系统尺寸，研究了局域化区域内、边缘附近以及几乎局域化区域外的输运性质。结果表明，在局域化区域内，波被困在发射源附近。同时，扩散波呈现出一种直观但预期的图像。也就是说，随着越来越多的随机散射发生，它们随传播路径增加，随后达到饱和，然后当传播路径足够大时开始指数衰减，这表明了局域化效应。对于频率接近局域化区域边界或在其之外的情况，将扩散波的结果与扩散近似进行了比较，但与其他系统[阿萨特良等人，《物理评论E》67, 036605 (2003)]相比，一致性不太理想。
