Chan Timothy Y M, Toader Ovidiu, John Sajeev
Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Apr;71(4 Pt 2):046605. doi: 10.1103/PhysRevE.71.046605. Epub 2005 Apr 7.
We describe the properties of three families of inversion-symmetric, large photonic band-gap (PBG) template architectures defined by iso-intensity surfaces in four beam laser interference patterns. These templates can be fabricated by optical interference (holographic) lithography in a suitable polymer photo-resist. PBG materials can be synthesized from these templates using two stages of infiltration and inversion, first with silica and second with silicon. By considering point and space group symmetries to produce laser interference patterns with the smallest possible irreducible Brillouin zones, we obtain laser beam intensities, directions, and polarizations which generate a diamond-like (fcc) crystal, a novel body-centered cubic (bcc) architecture, and a simple-cubic (sc) structure. We obtain laser beam parameters that maximize the intensity contrasts of the interference patterns. This optimizes the robustness of the holographic lithography to inhomogeneity in the polymer photo-resist. When the optimized iso-intensity surface defines a silicon to air boundary (dielectric contrast of 11.9 to 1), the fcc, bcc, and sc crystals have PBG to center frequency ratios of 25%, 21%, and 11%, respectively. A full PBG forms for the diamond-like crystal when the refractive index contrast exceeds 1.97 to 1. We illustrate a non-inversion symmetric PBG architecture that interpolates between a simple fcc structure and a diamond network structure. This crystal exhibits two distinct and complete photonic band gaps. We also describe a generalized class of tetragonal photonic crystals that interpolate between and extrapolate beyond the diamond-like crystal and the optimized bcc crystal. We demonstrate the extent to which the resulting PBG materials are robust against perturbations to the laser beam amplitudes and polarizations, and template inhomogeneity. The body centered cubic structure exhibits the maximum robustness overall.
我们描述了由四束激光干涉图案中的等强度面定义的三个反演对称的大光子带隙（PBG）模板结构族的特性。这些模板可以通过光学干涉（全息）光刻技术在合适的聚合物光刻胶中制造。PBG材料可以使用两步渗透和反演过程从这些模板合成，第一步用二氧化硅，第二步用硅。通过考虑点群和空间群对称性以产生具有尽可能小的不可约布里渊区的激光干涉图案，我们获得了能产生类金刚石（面心立方）晶体、一种新型体心立方（bcc）结构和简单立方（sc）结构的激光束强度、方向和偏振。我们获得了能使干涉图案的强度对比度最大化的激光束参数。这优化了全息光刻对聚合物光刻胶不均匀性的鲁棒性。当优化后的等强度面定义了硅与空气的边界（介电对比度为11.9比1）时，面心立方、体心立方和简单立方晶体的PBG与中心频率之比分别为25%、21%和11%。当折射率对比度超过1.97比1时，类金刚石晶体形成完整的PBG。我们展示了一种在简单面心立方结构和金刚石网络结构之间插值的非反演对称PBG结构。这种晶体展现出两个不同且完整的光子带隙。我们还描述了一类广义的四方光子晶体，它们在类金刚石晶体和优化后的体心立方晶体之间插值并外推。我们展示了所得PBG材料对激光束振幅和偏振以及模板不均匀性扰动的鲁棒程度。体心立方结构总体上表现出最大的鲁棒性。
