Modeling broad-spectrum response of hierarchical photonic materials: Development and comparison of radiative transfer methods

Photonic materials with a prescribed response over multiple spectral bands are essential to applications such as energy harvesting and thermal management. Engineering the response over such a wide range of wavelengths is difficult because these materials have hierarchical structures, which make it challenging to predict and optimize the spectral response. To address this challenge, we develop and compare several optical models aimed at capturing multiscale effects, and we apply these models to understanding the response of microgeodes---dielectric microshells encapsulating nanowires. Among the models, we find that an intensity-based transfer matrix method, newly developed in this work, provides the best agreement with experimentally observed spectra. In particular, it substantially improves the prediction of reflectance at short wavelengths, where the other models significantly underestimate the experimental values, resulting in an overall improvement across the full spectrum. We show that this model has superior predictive performance because it accounts for the interdependent scattering contributions from nanowires and microshells, while circumventing the need to specify reflectance conditions at the boundaries of the microgeode film. This approach could be used to explore the large design space of possible structures in microgeodes and other hierarchically structured, broad-spectrum materials.