线性响应区内的等效介质理论
The equivalent medium theory within the linear response region
摘要：
本文利用线性响应理论提出了等效介质理论。发现在线性响应条件下，一系列不同折射率$n_{i}(ω)$和长度$d_{i}$的介质可以等效为一个体积平均折射率为$\frac{1}{D}\sum_{i=1}^{N}n_{i}(ω)d_{i}$、总长度为$D=\sum_{i=1i}^{N}d_{i}$的有效介质，其中$N$为不同介质的个数.基于这种等效理论，设计具有任意色散特性的有效介质是一种简单而实用的方法。作为一个例子，我们提出了一个建议，以获得增强或减少的折射率无吸收和大的色散没有明显的吸收，通过组装不同的线性色散增益和吸收介质。
英文摘要：
In this paper, we present the equivalent medium theory by using the linear response theory. It is found that, under the condition of the linear response, a series of different media with different refractive indices $n_{i}(ω)$ and lengths $d_{i}$ can be equivalent to an effective medium with the volume-averaged refractive index $\frac{1}{D}\sum_{i=1}^{N}n_{i}(ω)d_{i}$ and the total length $D=\sum_{i=1i}^{N}d_{i}$,where $N$ is the number of different media. Based on this equivalent theory, it is a simple but very useful method to design the effective medium with any desirable dispersion properties. As an example, we present a proposal to obtain the enhancement or reduction of the refractive index without absorption and the large dispersion without obvious absorption by assembling different linear dispersive gain and absorptive media.
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