On the Rayleigh limit of the generalized Lorenz–Mie theory and its formal identification with the dipole theory of forces. I. The longitudinal case

Abstract

This work analytically shows that the dipole theory for longitudinal forces completely identifies with the Rayleigh limit of the generalized Lorenz–Mie theory (GLMT). To do so, the field components presented in the expressions for the time-average longitudinal optical force exerted on a dipolar dielectric scatterer are expanded in terms of spherical harmonic functions, and results are presented in terms of the beam shape coefficients, which carries the spatial properties of the optical field, using two distinct but complementary approaches. It is seen that, even though it is the total incident field that appears in the dipole theory of forces, only few poles actually contribute to the force exerted on the scatterer, as expected from the GLMT.