Gao Hanhong, Zhang Baile, Johnson Steven G, Barbastathis George
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Opt Express. 2012 Jan 16;20(2):1617-28. doi: 10.1364/OE.20.001617.
We design an all-dielectric Lüneburg lens as an adiabatic space-variant lattice explicitly accounting for finite film thickness. We describe an all-analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass-band regime. This method calculates the effective refractive index of the infinite-height lattice from effective medium theory, then embeds a medium of the same effective index into a slab waveguide of finite height and uses the waveguide dispersion diagram to calculate a new effective index. The results are compared with the conventional numerical treatment - a direct band diagram calculation, using a modified three-dimensional lattice with the superstrate and substrate included in the cell geometry. We show that the analytical results are in good agreement with the numerical ones, and the performance of the thin-film Lüneburg lens is quite different than the estimates obtained assuming infinite height.
我们设计了一种全介质吕讷堡透镜，作为一种绝热空间变体晶格，明确考虑了有限的薄膜厚度。我们描述了一种全解析方法，用于补偿通带 regime 中亚波长介电结构的有限高度。该方法根据有效介质理论计算无限高晶格的有效折射率，然后将具有相同有效折射率的介质嵌入有限高度的平板波导中，并使用波导色散图计算新的有效折射率。将结果与传统的数值处理方法——直接带图计算进行比较，该计算使用了一种修改后的三维晶格，其单元几何结构中包括上层和下层。我们表明，解析结果与数值结果吻合良好，并且薄膜吕讷堡透镜的性能与假设无限高度时获得的估计值有很大不同。
