Optimized White Reflectance in Photonic‐Network Structures

Abstract

freedom to tune light transport properties in these media. Indeed, shapes such as prolate ellipsoids or cylinders can be packed up to higher densities delaying the onset of spatial correlations at the cost of increased angular correlations. [10][11][12] Interestingly, both these aspects-namely, the high density and prevalent orientation exhibited by packed rods-can contribute to increase the overall turbidity, which makes cylinders particularly suited to realize highly turbid materials with a flat response over a broadband wavelength range. [13] Indeed, the smallest possible transport mean free path for a given refractive index contrast reported so far in the visible range has been obtained with GaP nanocylinders [14] and, for lower refractive index materials, claims of optimized scattering exist for the chitinous network structure of the Cyphochilus beetles. [5,13] In recent years, the latter has inspired an array of bio-mimicking materials attempting to reproduce its outstanding efficiency in terms of strong light scattering and limited material usage, taking advantage of a wide range of fabrication techniques including electro-spinning, super critical CO 2 foaming, polymer phase separation, and direct laser writing, [6,7,9,[15][16][17] to name a few.However, as opposed to nanoparticle systems, network materials are characterized by several additional aspects other than number density and spatial correlations, which makes it difficult to understand what key parameters should be optimized to design highly scattering network structures.Few notable examples include phase percolation, angular correlation, and network valence, all of which concur in determining their scattering properties. [13,[18][19][20] In this respect, simple generative models for photonic structures allowing to investigate the effects of these parameters separately are much needed to gain insight on their role and relevance.In this work, we describe a simple branching random walk (BRW) algorithm to generate random network structures inspired by that of the Cyphochilus beetle. Notably, the model allows to control and vary independently the volume fraction and degree of angular correlations without altering structural parameters such as the slab thickness, the shape, and aspect ratio of the constituent elements. The optical and transport properties of the generated structures have been investigated through finite difference time domain (FDTD) calculations and an inverse Monte Carlo (MC) approach, showing that the bright reflectance of the Cyphochilus beetle can be easily matched and surpassed by acting solely on the degree of anisotropy and the volume fraction of the network. To the best of our knowledge, this is the first rigorous demonstration of the key role played by structural anisotropy in highly reflective disordered samples.3D disordered networks are receiving increasing attention as they represent a versatile architecture for highly scattering materials. However, due to their complex morphology, little is known about the interplay betwee...

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.…”

Deterministic and Controllable Photonic Scattering Media via Direct Laser Writing

“…A priori knowledge of the internal structure makes it ideal for studies of light propagation that are sensitive to microscopic wave interference of light. [29] In the literature, several scattering media with deterministic geometry and scattering properties have been demonstrated using different nanofabrication techniques. Matoba et al [30] have created a large-volume deterministic scattering medium with laser micromachining, [31,32] but with undefined scattering strength.…”

Anisotropic silica colloids for light scattering

“…[7][8][9] The key parameters to its success are the anisotropic shape, dimensions and highly optimized filling fraction of the chitinous fibrils. 10,11 Recently, several groups attempted the fabrication of scattering networks with low refractive index polymers with performances comparable to the one of the Cyphochilus beetle. In particular, highly scattering material based on fibrillar-like networks were obtained by exploiting phase separation of polymers in a solvent mixture combined with kinetic arrest.…”

“…The selection of high aspect ratio rods was motivated by biological, 6 and numerical systems 10,11 which showcased the possibility of exploiting anisotropic building blocks for improved scattering efficiency in low refractive index media. It is important to note that the optical response of an ensemble of anisotropic colloids depends both on the single-particles properties (shape and dimensions) and by the structural ones (alignment and filling fraction).…”