Humblet's angular momentum decomposition applied to radiation torque on metallic spheres using the Hagen–Rubens approximation

Abstract

When a circularly polarized electromagnetic wave is scattered by an isotropic sphere, Humblet's decomposition from 1943 is helpful for understanding why the axial projection of the spin-angular momentum gives incomplete information concerning the total radiated angular momentum. Humblet asserted that some field angular momentum is orbital angular momentum (OAM). This distinction, applied here to Mie scattering, gives insight into why classical electromagnetic radiation torque is proportional to absorbed power for isotropic spheres. It also reveals the direct measurability (from Stokes parameters) of spin contributions to the radiated angular momentum. This approach is applied to metallic spheres in circularly polarized illumination modeled with Lorenz–Mie theory using the Hagen–Rubens approximation (1903) in which the real and imaginary components of the sphere's refractive index are equal in magnitude. That approximation is often useful for terahertz and lower frequencies. It was helpful to compare a spin efficiency factor Qspin with the canonical scattering efficiency factor Qsca for varying sphere sizes at a fixed frequency. A small-size limiting case Qsca/Qspin = 2 is recovered associated with a common interpretation of electric dipole-related torque. For larger sizes, the OAM contribution increases giving Qsca/Qspin > 2. Van de Hulst's scattering calculations for metal spheres are also reproduced.Dedicated in memory of Seattle Pacific University Professor James H. Crichton (1937–1999).