MORPHOLOGICAL COMPLEXITY AND ORGANIZATIONAL DISORDER OF RANDOM ANTIREFLECTIVE STRUCTURED SURFACES

Random antireflective surface nanostructures (rARSS) enhance transmission by reducing the electromagnetic impedance between optical indices across a boundary, serving as alternatives for traditional coating techniques. Understanding and quantifying the role of randomness of the surface nanostructures remain elusive, without a comprehensive model that can accurately predict the wideband spectral response of randomly nanostructured surfaces based on causal physical principles. Effective-medium approximations (EMA) emulate the randomly structured surface as a sequence of homogeneous film layers, failing to predict the critical (or cut-off) wavelength above which the enhancement effect is observed and below which bidirectional optical scatter is prominent. Analyzing near-field or far-field radiance due to wavefront propagation through randomly nanostructured surfaces requires high computational budgets, which are challenging for randomly distributed features with varying-scale boundary conditions.
Deterministic periodicity is considered a sufficient surface geometrical descriptor for regular (or long-range repetitive) nanostructured surfaces, whereas characterizing random surface features is based on first-order statistical evaluations or macroscopic averages, such as autocorrelation lengths, which introduce significant ambiguity in subwavelength scales. What constitutes the "randomness" of rARSS, beyond standard surface topography measures, is subjective. Conventional optical surface structure characterization, disregards aspects of nanoscale morphological attributes, mainly spatial configuration or organization, due to resolution limitations of metrological instruments. The organizational aspect of nanostructured features can significantly impact the macroscopic Fresnel reflectivity radiance, bidirectional scattering, and axial transmission enhancement (cooperative-interference effect).
In this work, transverse granule population distributions and their corresponding granular organization at the nanoscale, is determined using a variation of the Granulometric image processing technique. Various rARSS surfaces were fabricated, resulting in unique surface modifications and spectral performance, as observed with respectively scanning electron microscope (SEM) micrographs and spectral photometry. The approach to quantify randomness or complexity of the nanostructures, presented in this work, is based on Shannon’s entropy principles. Resolution limitations from conventional characterization techniques using non-invasive confocal microscopy and spectroscopic ellipsometry is discussed. Statistical quantification of nano-structural randomness using Shannon’s entropy is proposed as a solution to characterize the unique degree of disorder on the surfaces. A figure-of-merit is derived and computed from surface organization state variables, and it is proposed as a heuristic parameter to predict the transition from spectral scattering to the transmission enhancement region. This multivariate problem is addressed by accounting for the conditional probability dependence of granule populations as functions of granule dimensions and their corresponding proximity distributions, thereby laying the foundations for a surface microcanonical ensemble model, establishing a link between surface morphological descriptors and spectral variables.