Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

Abstract

structure factor) and their specific characteristics (form factor and refractive index). [1][2][3][4] Therefore, most efforts to control light propagation in random systems have been focused upon the optimization of isotropic spatial correlations in highrefractive index systems. These studies had a remarkable impact in many fundamental [5][6][7][8][9][10][11][12][13][14][15][16] and applied phenomena. [17][18][19][20][21] However, the role of anisotropy in multiple scattering systems has been overlooked. In fact, despite the well-known analytical solution for the single scattering, [4,22] the response of an ensemble of randomly arranged anisotropic particles has not been theoretically investigated. The same is valid for the presence of anisotropic structural correlations. Similarly, recent experimental works focused on the fabrication and optical characterization of anisotropic, disordered materials but without proving the role of anisotropy in scattering optimization. [23][24][25][26][27][28][29][30] Here, we study the effect of structural and single-particle anisotropy on the opacity of a material and identify the criteria to improve scattering over a large parameter space, including filling fraction and refractive index. Our work proves that ensembles of uncorrelated, anisotropic particles outperform their isotropic counterpart both for low-and high-refractive indices. In addition, anisotropic, low-refractive index systems not only require a lower amount of material to maximize scattering than isotropic media, but they also exhibit a whiteness comparable to those of high-refractive index materials.Our results showcase how to exploit natural resources (e.g., biopolymers) to replace commercially available white enhancers, made from inorganic high-refractive materials (e.g., TiO 2 ), which have recently raised safety concerns. [31,32] Moreover, our work unveils why anisotropy is an evolutionary-chosen mechanism to optimize scattering in biological systems. Results and DiscussionTo establish a comparison between different disordered materials, we numerically investigated the optical properties of 2D media (see Sections S1 and S2 in the Supporting Information). Exploiting a 2D numerical approach allows to independently vary the structural and form factors of a system, and therefore to disentangle their role in scattering optimization, while avoiding computational burden. In particular, we systematically The ability to manipulate light-matter interaction to tailor the scattering properties of materials is crucial to many aspects of everyday life, from paints to lighting, and to many fundamental concepts in disordered photonics. Light transport and scattering in a granular disordered medium are dictated by the spatial distribution (structure factor) and the scattering properties (form factor and refractive index) of its building blocks. As yet, however, the importance of anisotropy in such systems has not been considered. Here, a systematic numerical survey that disentangles and quantifies the role of different kinds...

Angular‐Independent Photonic Pigments via the Controlled Micellization of Amphiphilic Bottlebrush Block Copolymers

“…Disordered 2D structures with short‐range correlation were generated using a recently developed inverse design algorithm, as discussed in detail by Jacucci et al. [ 49 ] This algorithm allows for the simulation of inverse photonic glasses whose single‐particle (size distribution) and structural (correlation length) properties can be controlled independently. Input parameters were derived from correlation analysis of the SEM cross‐section images in Figure 2, as discussed in the Supporting Information.…”

Light Management with Natural Materials: From Whiteness to Transparency

“…Therefore, their appearance results from the interplay between: 1) the single-scatterer properties as the scattering cross-section; 2) the ensemble properties as the filling fraction (i.e., the volume percentage occupied by the scatterers), the average orientation of the scatterers, and the structure factor (i.e., the spatial organization of the scatterers). [6,7] The appearance of a disordered material (which is defined as system where the structure factor does not exhibit longrange order) is directly determined by the optical thickness (OT). This parameter is defined as the ratio between the physical thickness of a medium and the transport mean free path, that is, the average distance over which light loses memory of its initial direction.…”

“…Different numerical algorithms have been recently developed to separate these contributions and gain insight into the scattering optimization process. [6,7,28] By exploring a large parameter space for single-particle and ensemble configurations, Jacucci et al demonstrated that optimized ensembles of anisotropic scatterers outperform the scattering efficiency of their isotropic counterpart. [6] In detail, this result is valid when the anisotropic system exhibits an orientational order where the long axis of the scatterers is on average perpendicular to the incoming beam, [6,7] as showcased by the Cyphochilus beetle.…”

Optical costs and benefits of disorder in biological photonic crystals

“…and L. stigma enhances the brightness through increased out-of-plane scattering. [138][139][140]143 Moreover, this evolutionarily optimised scattering has drawn interest for paper coating technologies through a bioinspiration approach. 144 Other longhorn beetles, such as Celosterna pollinosa sulfurea, Phosphorus virescens and Trictenotoma childreni, also combine disordered structures with yellow and uorescent pigments in order to produce a range of yellow hues.…”