Periodic Reporting for period 1 - MALDIP (Machine Learning in Disordered Photonics)
Reporting period: 2020-06-01 to 2022-05-31
Creating highly scattering photonic materials from renewable and sustainable materials is outstanding scientific challenge. Structural colours, where the photonic response is based on nanoscopic structural features is a promising research field, compared to conventional pigment based colors, due to non-fadability of the material as long as the nanoscopic structures persist. In particular creating of structural white materials is of great importance since in the current commercial white paints the scattering components are often made from inorganic materials such as titanium dioxide TiO2 (refractive index n=2.6) which raise a number of safety and environmental concerns. Therefore discovering alternatives ways to produce safe and sustainable colored materials is of great importance and social impact, that has many important applications not only for paints and food additives but to medical imaging, solar cell efficiency etc.
In the field of structural colors, disordered photonics has grown increasing interest due to biological examples (such as the white beetles) where highly efficient scattering materials are achieved using low refractive index (RI) materials such as chitin and cellulose(n ~1.55$). The scattering strength of such random material depend not only on their refractive index, on the geometry and spatial distribution of its components. While the value of the refractive index is easy to obtain, the precise knowledge of the morphology of the sample in terms of size and special arrangement of the scattering elements is very challenging to determine and quantify.
The aims of this project were to 3D characterize and quantitatively model various disordered structures and combined with optical simulations understand how different structural features impact the optical properties to establish structure-property relationships.
In the field of structural colors, disordered photonics has grown increasing interest due to biological examples (such as the white beetles) where highly efficient scattering materials are achieved using low refractive index (RI) materials such as chitin and cellulose(n ~1.55$). The scattering strength of such random material depend not only on their refractive index, on the geometry and spatial distribution of its components. While the value of the refractive index is easy to obtain, the precise knowledge of the morphology of the sample in terms of size and special arrangement of the scattering elements is very challenging to determine and quantify.
The aims of this project were to 3D characterize and quantitatively model various disordered structures and combined with optical simulations understand how different structural features impact the optical properties to establish structure-property relationships.
The original intent was to have a larger focus on 3D characterization (researcher's main expertise) of existing photonic material samples in the host research group to cumulate a large database of different structures and their optical response to draw structure-property relationships. However it was soon realized, via extensive literature reviews, that there was vast amount of computational models developed (independently in separate scientific disciplines) to simulate various disordered structures that had been mostly unemployed in the field of disordered optics.
In other words, such in-silico approaches offered access to much broader range of interesting structures than what was trivially accessible via traditional chemical synthesis. More importantly the former was much more efficient as in-silico synthesis takes from few up to twenty minutes resulting direct 3D data. In comparison chemical synthesis is often tedious, and structural characterization required to obtain necessary 3D information wa likewise very time consuming.
The major draw back in the in-silico approach was that information on optical properties were relatively slow to obtain, where as scattering experiments deliver results from real world samples in usually matter of few minutes per sample. E.g.~a single optical simulations took up to four hours per sample on desktop pc. The situation was quickly addressed by the researcher by conducting the simulations on the Cambridge high performance cluster (HPC) which permitted the use of hundreds of CPU cores reducing the computation time to 30 minutes per sample, thus removing the computational bottle next.
The established workflow allowed us to investigate copious amounts different disordered systems. We decided to focus on 10 different structural morphologies, that represent a wide range of different disordered systems, in hundreds of different configurations (length scale, anisotropy, void content). During the course of the project we conducted over 4000 finite difference time domain (FDTD) optical simulations thanks to combination of in-silico synthesis and HPC resources.
In addition, the extensive literature survey allowed us to identify important tools, such as Minkowski functions, that can be used quantify structural differences in the simulated structures using comprehensive descriptors such as surface area, mean and Gaussian curvatures, and anisotropy value, which was essential for establishing structure-property relationships.
In other words, such in-silico approaches offered access to much broader range of interesting structures than what was trivially accessible via traditional chemical synthesis. More importantly the former was much more efficient as in-silico synthesis takes from few up to twenty minutes resulting direct 3D data. In comparison chemical synthesis is often tedious, and structural characterization required to obtain necessary 3D information wa likewise very time consuming.
The major draw back in the in-silico approach was that information on optical properties were relatively slow to obtain, where as scattering experiments deliver results from real world samples in usually matter of few minutes per sample. E.g.~a single optical simulations took up to four hours per sample on desktop pc. The situation was quickly addressed by the researcher by conducting the simulations on the Cambridge high performance cluster (HPC) which permitted the use of hundreds of CPU cores reducing the computation time to 30 minutes per sample, thus removing the computational bottle next.
The established workflow allowed us to investigate copious amounts different disordered systems. We decided to focus on 10 different structural morphologies, that represent a wide range of different disordered systems, in hundreds of different configurations (length scale, anisotropy, void content). During the course of the project we conducted over 4000 finite difference time domain (FDTD) optical simulations thanks to combination of in-silico synthesis and HPC resources.
In addition, the extensive literature survey allowed us to identify important tools, such as Minkowski functions, that can be used quantify structural differences in the simulated structures using comprehensive descriptors such as surface area, mean and Gaussian curvatures, and anisotropy value, which was essential for establishing structure-property relationships.
Together previously mentioned three elements; in silico synthesis, Minkowski functions, and HPC FDTD simulations provided us with all the necessary elements to conduct systematic investigation accross different disordered structures.
Initially we expected to observe quite different reflectance properties among the various structures. To our surprise, all the sctructures converged on similar behaviour (reflectance) in terms of topologicially invariant features (filling fraction of the solid content, lenght scale). The optimal filling fraction was revealed to be determined by RI difference with optimal value 50\% at low RI difference, and decreasing optimal filling fraction with increasing RI difference. This has major implications from an industrial perspective; as the choise of the material determines the optimal filling fraction and thus material requirements.
Further more it was discovered that the most signifficant factor explaining the remaining differences in reflectancces between different disordered structures was universally accounted by the average mean curvature value of the structures. In addition we also demonstrated how equal reflectance could then be achieved introducing structural anisotropy (orientation dependent).
In conclusion our results are beyond state of the art in several ways. It's the first systematic study of creating brilliant whiteness based on large variety of disordered structures. We demonstrate topological invariance, universal predictors for explaining remaining diffrences, how to quantity structural properties (including anistropy) and their roles, and offer an approximate solution on optimal conditions to maxime scattering efficiency regardless of the choise of topology. Therefore we consider our contribution for creating of artificial pigments invaluable from both theoretical and industrial perspective, as our investigation reveal than only reletively few features have (length scale, filling fraction and anistropy) to be tuned for optimal reflectance as brilliant whiteness is achievable from multiple starting points.
Initially we expected to observe quite different reflectance properties among the various structures. To our surprise, all the sctructures converged on similar behaviour (reflectance) in terms of topologicially invariant features (filling fraction of the solid content, lenght scale). The optimal filling fraction was revealed to be determined by RI difference with optimal value 50\% at low RI difference, and decreasing optimal filling fraction with increasing RI difference. This has major implications from an industrial perspective; as the choise of the material determines the optimal filling fraction and thus material requirements.
Further more it was discovered that the most signifficant factor explaining the remaining differences in reflectancces between different disordered structures was universally accounted by the average mean curvature value of the structures. In addition we also demonstrated how equal reflectance could then be achieved introducing structural anisotropy (orientation dependent).
In conclusion our results are beyond state of the art in several ways. It's the first systematic study of creating brilliant whiteness based on large variety of disordered structures. We demonstrate topological invariance, universal predictors for explaining remaining diffrences, how to quantity structural properties (including anistropy) and their roles, and offer an approximate solution on optimal conditions to maxime scattering efficiency regardless of the choise of topology. Therefore we consider our contribution for creating of artificial pigments invaluable from both theoretical and industrial perspective, as our investigation reveal than only reletively few features have (length scale, filling fraction and anistropy) to be tuned for optimal reflectance as brilliant whiteness is achievable from multiple starting points.