The purpose of this Addendum is to provide some clarifications and additional discussions related to the formalism of the generalized Lorenz–Mie theories in two-dimensions presented in the manuscript (Mitri F G 2017 J. Opt. 19 065403). The generalized formalism provides exact mathematical expressions that are used to compute the optical scattering, and time-averaged radiation force and torque of any light-sheets of arbitrary wavefront illuminating a homogeneous dielectric cylindrical particle of arbitrary geometrical cross-section, suspended in a lossless medium of wave propagation. In particular, it is emphasized here that concerning the analytical derivations and calculations based on far-field limits of the scattering, the Poynting vector formalism can only be utilized to determine the optical radiation force vector and its components, a result that is commensurate with the same outcome of an analysis based on the integration of the time-averaged Maxwell stress tensor. Nevertheless, in the far-field, the Poynting vector formalism is not valid to evaluate the optical radiation torque because it is radial, and the integration of its moment over a surface of large radius enclosing the particle leads to a zero torque, not in agreement with the derivation based on Maxwell’s stress tensor. Therefore, the analytical expression required to derive the optical radiation torque component (either in the near-field or far-field limits of the scattering, which lead to equivalent expressions without any approximations in the case of a lossless medium of wave propagation) should always involve the integration of the moment of the time-averaged Maxwell stress tensor.