Computational approaches to scattering by microspheres

Volume 8, Issue 3 (December 2017), pp. 19–24

Download PDF

@article{jocse-8-3-3,
  author={Reed M. Hodges and Kelvin Rosado-Ayala and Maxim Durach},
  title={Computational approaches to scattering by microspheres},
  journal={The Journal of Computational Science Education},
  year=2017,
  month=dec,
  volume=8,
  issue=3,
  pages={19--24},
  doi={https://doi.org/10.22369/issn.2153-4136/8/3/3}
}

Mie theory is used to model the scattering off of wavelength-sized microspheres. It has numerous applications for many different geometries of spheres. The calculations of the electromagnetic fields involve large sums over vector spherical harmonics. Thus, the simple task of calculating the fields, along with additional analytical tools such as cross sections and intensities, require large summations that are conducive to high performance computing. In this paper, we derive Mie theory from first principles, and detail the process and results of programming Mie theory physics in Fortran 95. We describe the theoretical background specific to the microspheres in our system and the procedure of translating functions to Fortran. We then outline the process of optimizing the code and parallelizing various functions, comparing efficiencies and runtimes. The shorter runtimes of the Fortran functions are then compared to their corresponding functions in Wolfram Mathematica. Fortran has shorter runtimes than Mathematica by between one and four orders of magnitude for our code. Parallelization further reduces the runtimes of the Fortran code for large jobs. Finally, various plots and data related to scattering by dielectric spheres are presented.