Wubs Martijn, Suttorp L G, Lagendijk A
Complex Photonic Systems, Faculty of Science and Technology, University of Twente, NL-7500 AE Enschede, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jan;69(1 Pt 2):016616. doi: 10.1103/PhysRevE.69.016616. Epub 2004 Jan 30.
The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.
先前为标量波所发展的平面散射体概念得到了推广，从而涵盖了光的偏振。从矢量波的 Lippmann - Schwinger 形式体系出发，我们表明在以一致方式定义 T 矩阵之前，格林函数必须进行正则化。正则化之后，对于由任意数量的平行平面构成、处于任意位置且每个平面可具有不同光学性质的有限结构，可精确确定光学模式和格林函数。该模型应用于由规则间隔的相同平面组成的有限晶体这一特殊情况，在此情况下解析方法可进一步拓展，仅留下少量数值计算任务。该形式体系用于计算有限光子晶体内外及附近与位置和取向相关的自发发射率。结果表明，标量波和矢量波的发射率及反射特性可能有很大差异。晶体的有限尺寸会影响发射率。对于靠近平面的平行偶极子，向导模的发射会在频率相关的发射率中产生一个峰值。
