表面反射对随机介质内透射本征值统计和能量分布的影响
Impact of surface reflection on transmission eigenvalue statistics and energy distributions inside random media
摘要：
表面反射对通过随机介质的透射率和随机介质内的能量分布的影响通常用开放样品的输入端和输出端的边界外推长度$z_b, z_b'$来描述，该长度是样品内的能量密度外推为零时超出样品表面的距离。样品边界处反射的重要性在透射率的缩放中起着关键作用。在这里，我们考虑的影响，表面反射的传播扩散波的透射本征值（DTE）的分布的修改。我们回顾了我们的发现，在分析形式的DTE的样本长度等于$|z_b-z_b'|$点的过渡。对于边界反射较强的非对称性，最高透射本征值严格小于1。样品内部的平均透射率和能量密度分布仍然可以用样品长度$L$和样品两侧的边界外推长度$z_b, z_b'$来描述。对于局域波，我们发现样本内的能量密度分布是一个片段的分布，将在一个较长的样本长度$L+z_b+z_b'$。这些结果提出了通过改变边界反射率来控制扩散系统和局域系统中的波干涉的新方法。
英文摘要：
The impact of surface reflection upon transmission through and energy distributions within random media has generally been described in terms of the boundary extrapolation lengths $z_b, z_b'$ at the input and output end of an open sample, which are the distance beyond the sample surfaces at which the energy density within the sample extrapolates to zeroThe importance of reflection at the sample boundaries plays a key role in the scaling of transmission. Here we consider the impact of surface reflection on the propagation of diffusive waves in terms of the modification of the distribution of transmission eigenvalues (DTE). We review our finding of a transition in the analytical form of the DTE at the point that the sample length equals $|z_b-z_b'|$. The highest transmission eigenvalue for stronger asymmetry in boundary reflection is strictly smaller than unity. The average transmission and profiles of energy density inside the sample can still be described in terms of the sample length, $L$, and the boundary extrapolation lengths on both sides of the sample, $z_b, z_b'$. For localized waves, we find the energy density profile within the sample is a segment of the distribution that would be found in a longer sample with length $L+z_b+z_b'$. These results suggest new ways of controlling wave interference in both diffusive and localized systems by varying boundary reflectivity.
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