Propagation invariant beams, also known as “non-diffracting beams”, propagate indefinitely without changing their transverse intensity distribution. These optical fields are well-known plane waves, the Bessel beams, Mathieu beams and Weber beams. These invariant beams correspond the solutions of the solutions of the Helmholtz wave equation in Cartesian, circular cylindrical, parabolic cylindrical, and elliptical cylindrical coordinates, respectively. These non-diffracting beams have a large quantity of applications in fundamental and applied science in areas such as quantum mechanics, acoustic optics, nonlinear optics, optical tweezers, fluid dynamics optical communications, among others.  In the first part of the talk, I will present briefly a description of the electromagnetic field for propagation invariant beams using scalar potentials. Fundamental dynamical quantities are obtained such as: energy density, Poynting vector, Maxwell stress tensor.

 In the second part of the talk is focused on a fundamental relation in scattering theory, the so-called optical cross-section theorem or simply the Optical Theorem (OT), which describes the rate at which energy is distributed from a probing incident wave field by scattering object, due to re-radiation and absorption by the scattered. I discuss and show an expression for the optical theorem based on classical electromagnetic theory, for probe sources given in terms of propagation invariant beams and is obtained a general expression for the differential scattering cross section using the integral scattering amplitude approximation in the far field. Some examples are given for the scattering Rayleigh approximation.