Nanomesh:A Python workflow tool for generating meshes from image data

Create 2d and 3d meshes from experimental imaging data.</p

Uniform line fillings

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.Comment: 10 pages, 12 figures; v3: restructured paper, more references, more graph

Computation of Optical Properties of Real Photonic Band Gap Crystals as Opposed to Utopian Ones

Computational methods are essential in the design and analysis of three-dimensional (3D) photonic crystals [1]. These methods predict the physical properties of a particular design before elaborate nanomanufacturing. However, any manufactured crystal device inevitably differs from the design [2], [3]. These differences are not included in modelled crystals that we therefore call “utopian”, which are typically assumed to be infinite for computational reasons. Therefore, the inevitable differences between experimental measurements and theoretical predictions can be explained by two sources, the imperfect model and the effects of manufacturing. The central problem is that the current knowledge and methods are not sufficient for attributing the differences to either cause, which hampers a systematic approach to improving device performance and thus device applications. Here, we aim to improve the understanding of manufacturing effects by using the structure of a real photonic crystal as input for computations, thereby including all real manufacturing defects

Non-utopian optical properties computed of a tomographically reconstructed real photonic band gap crystal

State-of-the-art computational methods combined with common idealized structural models provide an incomplete understanding of experiments on real nanostructures, since manufacturing introduces unavoidable deviations from the design. We propose to close this knowledge gap by using the real structure of a manufactured crystal as input in computations to obtain a realistic comparison with observations on the same nanostructure. We demonstrate this approach on the structure of a real silicon inverse woodpile photonic bandgap crystal, obtained by previous synchrotron X-ray imaging. A 2D part of the dataset is selected and processed into a computational mesh suitable for a Discontinuous Galerkin Finite Element Method (DGFEM) to compute optical transmission spectra that are compared to those of a utopian crystal, i.e., a hypothetical model crystal with the same filling fraction where all pores are identical and circular. The nanopore shapes in the real crystal differ in a complex way from utopian pores, leading to a complex transmission spectrum with significant frequency speckle in and beyond the gap. The utopian model provides only a limited understanding of the spectrum: while it accurately predicts low frequency finite-size fringes and the lower band edge, the upper band edge is off, it completely misses the presence of speckle, the domination of speckle above the gap, and possible Anderson localized states in the gap. Moreover, unlike experiments where only external probes are available, numerical methods allow to study all fields everywhere. While the pore shapes hardly affect the fields at low frequency, major differences occur at high frequency such as localized fields deep inside the real crystal. In summary, using only external measurements and utopian models may give an erroneous picture of the fields and the LDOS inside a real crystal, which is remedied by our new approach