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.

最近在离轴圆对称贝塞尔光束的情况下研究了广义Lorenz-Mie理论（GLMT）的Rayleigh极限，此后在轴上圆对称贝塞尔光束的情况下，在轴上情况更容易理解在GLMT的瑞利极限中施加的光学力的框架。本文将这种工作扩展到第一类非暗轴上轴对称光束的情况，其中包括零阶圆对称贝塞尔光束的情况和高斯光束局部模型的情况。展示了三种光学力，即传统的梯度力和散射力，以及另一种暂时称为非标准力的力。讨论了GLMT的Rayleigh极限与偶极力理论之间的关系，