Minimum principles in electromagnetic scattering by aspherical aerosols

What is an aerosol shape causing minimal extinction among all particles of equal volume and randomly oriented?  Motivated by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (induced dipole moment) approximation, seeking to disentangle electric and geometric contributions. To that end, a simple proof is supplied of spherical optimality for a coated ellipsoidal particle and a monotonic increase with asphericity is shown in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections. Physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose linking low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions wash out the Mie resonances. This proposal is supported by the sum rule for integrated extinction. Implications for aerosol remote sensing are discussed.