On longitudinal radiation pressure cross-sections in the generalized Lorenz–Mie theory and their numerical relationship with the dipole theory of forces

Abstract

A recent work devoted to the longitudinal optical forces exerted by circularly symmetric Bessel beams on point-like particles in the Rayleigh regime of the generalized Lorenz–Mie theory (GLMT) confirmed the existence of nonstandard forces (named axicon forces in the context of Bessel beams) that seemingly cannot be expressed in terms of scattering and gradient forces traditionally discussed in the framework of the dipole theory of forces. These results lead to this question: Do the Rayleigh limit of the GLMT and the dipole theory of forces actually agree, or are they in disagreement? If so, the Rayleigh limit of the generalized Lorenz–Mie theory would have to be preferred because it provides a highly accurate formulation. To find a definitive answer to the question, numerical comparisons done between optical forces exerted in both frameworks demonstrated an extremely accurate agreement up to 1000 decimal places. This leads to the conjecture that the Rayleigh limit of GLMT might indeed exactly identify with the usual dipole theory of forces.