One-Billion-Particle electromagnetic Scattering Problem

Consider one billion spherical particles (radius r) randomly located in a finite, spherical medium (radius R) in free space in an incident electromagnetic plane wave field (wavelength λ, wave number k=2π/λ). Show the ensemble-averaged 4×4 Mueller scattering matrix interrelating the four Stokes parameters (I = (I,Q,U,V)) of the incident field and the scattered field when the size parameter (x=kr) and complex refractive index (m) of the individual spherical particles are x=1.76 and m=1.50+i10-4 and when the volume fraction of the spherical particles in the spherical medium is v=20%.

You may consider an exact or an approximate solution, or a measurement. If the one-billion-particle challenge cannot be met, compute or measure the scattering matrix for a finite medium composed of the maximum number of spherical particles accessible for your method.


The problem and the solution attempts will be discussed at a one-day workshop on Friday, August 19th, 2016. The workshop is organized as a part of the EMTS 2016 conference and its Multiple Scattering session. The workshop is open and free of charge. If interested to join, please e-mail tentative registration to Dr. Antti Penttilä. The workshop will be held at the University of Helsinki and organized by the ERC SAEMPL project.


Kumpula Campus, Physicum lobby

  • 09:30 Coffee

Kumpula Campus, Physicum, room E207

  • 10:00 Antti Penttilä, Opening
  • 10:05 Daniel Mackowski, Multi-sphere T-matrix method and its capabilities
  • 10:20 Johannes Markkanen, FMM-accelerated T-matrix implementation
  • 10:35 Dimitrios Tzarouchis, TBA
  • 10:50 Xavier Faget, TBA
  • 11:05 Jukka Räbinä, Exact solution with the Discrete Exterior Calculus for a limited problem
  • 11:20 Maxim Yurkin, Exact solution, capabilities of discrete-dipole approximation code ADDA
  • 11:35 Karri Muinonen, Radiative-transfer solution with incoherent scattering
  • 11.50 Antti Penttilä, Exact solutions for reduced problems vs. approximate radiative-transfer solutions

12.15-13.30, lunch, Kumpula Campus, Dynamicum

  • 13:30 Open discussion
    • future prospects
    • joint article for Radio Science

End by 15:00


The Helsinki University Faculty of Science is located at the Kumpula Campus. It can be reached by several bus lines from the Helsinki or Pasila railway stations, by tram lines 6 and 8, or by bus number 506 from Otaniemi. Please see the Journey Planner for details, the street address for the campus is "Gustaf Hällströmin katu 2a".



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