On light scattering by large solid particles with wavelength-scale surface roughness

Natural particles often exhibit multiscale surface roughness, which affects their light-scattering characteristics. Such particles can be found in various environments, including regoliths on asteroid and lunar surfaces, comae of active asteroids and comets, planetary atmospheres, and planetary disks. However, micro-scale surface roughness effects are often overlooked in modeling efforts. Light scattering by large solid particles is typically modeled using geometric or physical optics approximations, which only account for large scale roughness while neglecting wavelength-scale roughness effects.  In this study, we investigate the impact of  micro-scale surface roughness on light scattering characteristics by comparing a numerically exact electromagnetic solution to the geometric optics approximation. 

We implement a Surface Integral Equation (SIE) method to compute the numerically exact solution. Specifically, we discretize the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation using the Galerkin method, and accelerate the solution using the Multilevel Fast Multipole Algorithm (MLFMA)  (Chew et al. 2001). The MLFMA-accelerated SIE solution proves efficient for solid particles with moderately rough surfaces, as the number of unknowns scales with the surface area. This represents a significant advantage over volumetric methods such as the discrete-dipole approximation or finite-element method where the number of unknowns scales with the volume of the scatterer. For computing the geometric optics solution, we employ the open-source SIRIS4 software (Väisänen et al. 2019).

We generate surface roughness using a self-affine transformation, characterized by the Hurst exponent. We employ the open-source software Pyrough (Itaney et al. 2024) which allows us to create rough surface spheres with varying Hurst exponents. Pyrough produces a rough surface sphere shape model in the form of a triangular mesh, which serves as input for both the MLFMA-SIE and SIRIS4 solvers. This approach enables us to compare the solutions obtained from MLFMA-SIE and SIRIS4 for identical particle shape and investigate the impact of micro-scale roughness on light-scattering characteristics. 

Acknowledgements: This work was supported by the German Research Foundation (DFG) grant no. 517146316.

References:

W.C. Chew, et al. 2001, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, Inc., USA.

H. Iteney, et al. 2024, Pyrough: A tool to build 3D samples with rough surfaces for atomistic and finite-element simulations, Comp. Phys. Comm., 295, 108958.

T. Väisänen, et al. 2020, JQSRT  241, 106719.