Torrese Guido, Taylor Jason, Hall Trevor J, Mégret Patrice
Service d'Electromagnétisme et de Télécommunications, Faculté Polytechnique de Mons, Mons, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 2):066616. doi: 10.1103/PhysRevE.73.066616. Epub 2006 Jun 16.
The effective medium theory is a useful approach for investigating the electromagnetic wave propagation in periodic multilayer slabs. It allows accurate computation of transmission and reflection spectra as well as of phase and group velocities. In this paper we derive an exact analytical expression for the energy velocity of a one-dimensional finite photonic crystal based on the effective medium approach. It accounts for the multiple reflections within the structure which results in the characteristic oscillations of the transmission spectrum. Our analytical expression holds for an arbitrary refractive index contrast and goes beyond the limits of the standard homogenization method. In order to validate our approach, results obtained by using the all-frequency effective energy velocity have been compared to those obtained using the transfer matrix method.
有效介质理论是研究电磁波在周期性多层平板中传播的一种有用方法。它能够精确计算透射和反射光谱以及相速度和群速度。在本文中，我们基于有效介质方法推导出了一维有限光子晶体能量速度的精确解析表达式。该表达式考虑了结构内部的多次反射，这导致了透射光谱的特征振荡。我们的解析表达式适用于任意折射率对比度，超越了标准均匀化方法的限制。为了验证我们的方法，已将使用全频有效能量速度获得的结果与使用转移矩阵法获得的结果进行了比较。
