Coherent wave propagation through a sparse concentration of particles


  • Gary S. Brown


The Foldy-Twersky integral equation (FTIE) for the coherent field propagating through a sparsely populated, random, uncorrelated distribution of particles is solved to show that the average field inside any particle is a plane wave. This result is in conflict with the average single-particle integral equation, which dictates that the average internal field cannot, in general, be a plane wave. The conflict is resolved by examining the conditions under which the average single-particle-scattering amplitudes resulting from the two integral equations are nearly equal. The major implications of this analysis are that (1) the classical Foldy result for the propagation constant of the coherent field follows directly from the FTIE and its implicit assumptions regardless of the electrical or physical properties of the particles and (2) the FTIE only applies to situations where the effects of multiple scattering upon the coherent field are negligible.