Meiers Dominic T, von Freymann Georg
Opt Express. 2023 Sep 25;31(20):32067-32081. doi: 10.1364/OE.494653.
Considering light transport in disordered media, the medium is often treated as an effective medium requiring accurate evaluation of an effective refractive index. Because of its simplicity, the Maxwell-Garnett (MG) mixing rule is widely used, although its restriction to particles much smaller than the wavelength is rarely satisfied. Using 3D finite-difference time-domain simulations, we show that the MG theory indeed fails for large particles. Systematic investigation of size effects reveals that the effective refractive index can be instead approximated by a quadratic polynomial whose coefficients are given by an empirical formula. Hence, a simple mixing rule is derived which clearly outperforms established mixing rules for composite media containing large particles, a common condition in natural disordered media.
考虑到光在无序介质中的传播，该介质通常被视为一种有效介质，需要精确评估有效折射率。由于其简单性，麦克斯韦-加尼特（MG）混合规则被广泛使用，尽管其对远小于波长的粒子的限制很少能得到满足。通过三维时域有限差分模拟，我们表明MG理论对于大粒子确实失效。对尺寸效应的系统研究表明，有效折射率反而可以用一个二次多项式来近似，其系数由一个经验公式给出。因此，我们推导出了一个简单的混合规则，对于包含大粒子的复合介质，该规则明显优于已有的混合规则，而大粒子在天然无序介质中是一种常见情况。
