Facile method to model the broadband optical response of imperfectly periodic nanotextures

Subwavelength nanotexturing creates opportunities to tailor the spectral response of an otherwise abrupt interface between two media. Precisely regimented unit cells choreograph the interference between incident and reflected electromagnetic wavefronts, orchestrating diffractive scattering and Fresnel losses. Recent years have witnessed the commercialization of nanotexturing as an alternative to conventional multilayer dielectrics and found applications ranging from photovoltaics to high-power laser optics and augmented reality headsets. Either purposefully or due to manufacturing tolerances, however, unit cell periodicities and vertical profiles are never perfectly uniform but subject to random displacements and unpredictable height variations. Ranging in magnitude from small (<0.1 nm) to large (>10 nm), periodicity imperfections distort the spectral response, especially at shorter wavelengths. Accurately predicting their impact is problematic because available mathematical models invariably assume or require the unit cells to be regimented perfectly across large distances. Although techniques such as the finite element method can simulate arbitrarily shaped structures, such routines are computationally intensive. In response, we introduce weighted rigorous coupled-wave analysis, a facile and computationally efficient method for simulating the optical response of imperfectly periodic nanostructures. The findings can be used to optimize the design of subwavelength 2D nanotextures within the context of manufacturing tolerances.