Abstract The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total matrix to solve for all the fields at all the interfaces simultaneously and an expansion in the Bloch-like modes of a periodic artificially repeated system. We apply both methods to obtain the reflectance spectra of multilayered chirped structures composed of nanostructured porous silicon (PS). Both methods yield reliable and numerically stable results. The former allows an analysis of the field within all layers while the latter is much more efficient computationally, allowing the design of novel structures and the optimization of their parameters. We compare numerical and experimental results across a wide spectral range from the infrared to the ultraviolet.

中文翻译：

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大型非周期耗散多层系统光学特性的稳定计算

摘要 在吸收存在的情况下，大型非周期性多层系统的传递矩阵的计算可能会变得不稳定。我们讨论了这种不稳定性的起源，并探索了两种克服它的方法：使用总矩阵同时求解所有界面上的所有场，以及在周期性人工重复系统的类布洛赫模式中展开。我们应用这两种方法来获得由纳米结构多孔硅 (PS) 组成的多层啁啾结构的反射光谱。这两种方法都能产生可靠且数值稳定的结果。前者允许对所有层内的场进行分析，而后者在计算上效率更高，允许设计新颖的结构并优化其参数。