Rayleigh limit of generalized Lorenz-Mie theory for on-axis beams and its relationship with the dipole theory of forces. Part I: Non dark axisymmetric beams of the first kind, with the example of Gaussian beams

Abstract

The Rayleigh limit of the generalized Lorenz-Mie theory (GLMT) has been recently examined in the case of off-axis circularly symmetric Bessel beams, thereafter in the case of on-axis circularly symmetric Bessel beams, the on-axis case providing an easier framework for the understanding of the optical forces exerted in the Rayleigh limit of GLMT. This work is here extended to the case of non dark on-axis axisymmetric beams of the first kind This encompasses the case of zeroth-order circularly symmetric Bessel beams and the case of localized models of Gaussian beams. Three kinds of optical forces are exhibited, namely traditional gradient and scattering forces, plus another kind of forces which is for the time being denoted as non standard forces. The relationship between the Rayleigh limit of GLMT and the dipole theory of forces is discussed, to the best of our present understanding.