# Spectroscopic Ellipsometry and Optical Modelling of Structurally Colored Opaline Thin-Films
## 1 Introduction  
Ellipsometry is well established as an advanced optical characterization tool, by which the key parameters of thin-film materials (such as thickness, surface roughness, and complex refractive index) may be determined over macroscopic areas by a non-invasive, non-destructive method, and potentially tracked in real time [1; 2; 3; 4]. In addition to high precision metrology of monolithic planar layers of (for example) oxides in microelectronics [5; 6; 7], ellipsometric models can be developed towards single parameter, high-throughput monitoring of key processing tolerances, such as thickness uniformity and interfacial roughness, in other thin-film manufacturing processes. This is indeed pertinent where \"roll-to-roll\" (R2R) approaches may be applied, such as in large area organic photovoltaic (OPV) cells [8; 9; 10].  
Amongst the many candidate smart materials and functional coatings, where ellipsometry could be used as an in-line monitor, are periodic optical materials with engineered photonic and light scattering properties [11; 12]. Such photonic structures are of significantly greater optical complexity than simple dielectric layers, usually consisting of a 2D or 3D periodicity of the order of the wavelength of light. In many manifestations, the active layer may be considered as being a form of bulk heterostructure and, importantly, coloration results from structural resonance rather than oscillator absorption from pigments [13; 14; 15]. Hence, a key research goal in this area is to use detailed ellipsometric studies on suitable target materials to provide correlated measurements of optical constants, and to develop the most appropriate and robust optical models to describe these systems.  
In this paper, a suitable target thin-film material, \"Polymer opals\" (POs), are therefore investigated. These consist of polymeric nanosphere composites, utilizing a core-interlayer-shell (CIS) approach, which may be shear-ordered into large-scale flexible opals [16; 17]. In a number of our earlier reports, the emulsion polymerization synthesis of CIS particles (see Figure 1a) with rigid cross-linked polystyrene (PS) spheres, capped by a softer poly-ethylacrylate (PEA) shell via a poly-methylmethacrylate (PMMA) grafting layer, has been developed [18; 19]. The net refractive index contrast (\(\Delta n\)) between the PS core and PEA shell material is therefore 0.11-0.12, with \(\overline{n}\approx 1.52\). Engineered approaches to generating shear-induced ordering of the particle ensembles into characteristic random-hcp lattices havebeen a particular focus, and bending-induced oscillatory shear (BIOS [20], as illustrated in Figure 1b) has been notably successful in producing high-quality low-defect polymer opals with structural color resonances across the UV/visible and near-infrared regions. These resonances are tunable both by variation of the particle size and mechano-chromically, making POs an attractive platform for next generation coatings and R2R compatible functional materials [21,22].  
Here, the method of spectroscopic ellipsometry is applied to the exemplar POs system, across a range of thin-film samples with intense resonant structural color. Building upon earlier reported multilayer ellipsometric models of the system [23], a quasi-model encompassing the inherent degree of sample disorder and key properties of effective refractive-index and index-contrast is developed to elucidate the correlation between the ellipsometric parameters and the shear-induced opaline crystallinity. These approaches offer reliable means of in-line tracking of the sample quality, homogeneity, and engineering tolerance of such complex periodic nanomaterials in large scale processing and applications. Other candidate technologies for non-contact in-line monitoring of POs, in various current states of viability, might include hyperspectral imaging [24] and coherence tomography [25,26]; ellipsometry may in future be used as either a complementary or an alternative method to these.