Variational principle for scattering of light by dielectric particles

We exploit two fundamental properties of the dipole interaction matrix A (symmetry with respect to reversal of incident beam direction and interchange of any pair of dipoles) to construct two functionals. The connection with the minimum energy theorem and cross section suggests that our numerical algorithm will search for a physical quantity, and hence it would be efficient and stable. In this Letter we have made the crudest use of the variational principle. The practical limit for the current version of our numerical scheme is a dipole array (with fourfold symmetry) of order N ~10,000 atoms. Since the phase difference between neighboring atoms should be ≤1/3 rad for reliable results, this limits the scattering parameter 2πa/λ to ≤10. The storage required is ~20N real numbers, and the time is ~1x10^-6 N^2 min on a CDC 7600. Note that the main advantage with the current method is that we do not need to store the A matrix with order N^2 elements.