Wan Congshan, Gaylord Thomas K, Bakir Muhannad S
Appl Opt. 2016 Dec 10;55(35):10006-10015. doi: 10.1364/AO.55.010006.
The interlayer waveguide grating coupling efficiencies under angular (rotational) misalignments are simulated using the 3D rigorous coupled-wave analysis (3D-RCWA) together with the RCWA equivalent-index-slab (RCWA-EIS) method. As examples of conical diffraction, rotations about the two coordinate axes, x and z, defined by the vectors [1 0 0] and [0 0 1], respectively, as well as an arbitrary axis, defined by the vector [2 2 1], are simulated for binary rectangular-groove gratings. The interlayer grating coupling efficiency is approximated by the product of the top- and bottom-grating diffraction efficiencies (DEs). It is found that the bottom-grating DEs decrease about 25% when the bottom grating is rotated ±0.1 rad (5.73°) about the z-axis. DEs slightly increase (5% to 10% depending on the grating structures) when the bottom grating is rotated ±0.1 rad about the x-axis. This is consistent with the diffraction behavior of an over-modulated grating. When the bottom grating is rotated about the vector [2 2 1], the change in DEs is asymmetric with a 100% decrease at a rotation angle -0.1 rad and a 67% decrease at a rotation angle +0.1 rad. The method is shown to be computationally efficient and numerically stable for grating structures with optimized parameters, and the resulting bottom-grating diffraction efficiencies demonstrate similar trends as those calculated by the 3D finite-difference time-domain simulations. The procedure presented can be directly used in the analysis and design of interlayer waveguide grating coupling for optical interconnects in high-density integrated electronics.
使用三维严格耦合波分析（3D-RCWA）以及RCWA等效折射率平板（RCWA-EIS）方法，模拟了角向（旋转）失准情况下的层间波导光栅耦合效率。作为锥形衍射的示例，针对二元矩形槽光栅，分别模拟了绕由向量[1 0 0]和[0 0 1]定义的两个坐标轴x和z的旋转，以及绕由向量[2 2 1]定义的任意轴的旋转。层间光栅耦合效率由顶部和底部光栅的衍射效率（DE）的乘积近似得出。研究发现，当底部光栅绕z轴旋转±0.1 rad（5.73°）时，底部光栅的DE下降约25%。当底部光栅绕x轴旋转±0.1 rad时，DE略有增加（根据光栅结构，增加5%至10%）。这与过调制光栅的衍射行为一致。当底部光栅绕向量[2 2 1]旋转时，DE的变化是不对称的，在旋转角度为-0.1 rad时下降100%，在旋转角度为+0.1 rad时下降67%。结果表明，该方法对于具有优化参数的光栅结构在计算上是高效且数值稳定的，并且所得的底部光栅衍射效率显示出与通过三维时域有限差分模拟计算得出的结果相似的趋势。所提出的过程可直接用于高密度集成电子器件中光互连的层间波导光栅耦合的分析和设计。
