No abstract

Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes' solution by the principle of maximum ignorance. We analyse the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space in between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords.

between different materials and causes a part of the light to deviate from its original path. A sufficiently thick medium with a high density of such interfaces acts as a multiple-scattering material. The light transport through and interaction with the scattering medium is characterized by two characteristic length scales: the scattering mean free path ℓ sc and the transport mean free path ℓ tr. The scattering mean free path quantifies the mean distance between subsequent scattering events. The mean distance that the incident light propagates before its direction is scrambled is the transport mean free path ℓ tr. Scattering media with L > ℓ tr > λ, where L is its physical thickness and λ

We discuss the design and fabrication of deterministic photonic scattering media using direct laser writing. Static measurements and light transport calculations validate that the light scattering parameters match the design model.