On the interference of the scattered wave and the incident wave in light scattering problems with Gaussian beams

We consider the light scattering problem for a Gaussian beam and a (spherical) particle at arbitrary location. Within the beam cross section, the total electromagnetic field is the superposition of the incident beam and the scattered wave. Using the Generalized Lorenz-Mie Theory (GLMT) as a vehicle to access such scattering problems, we discuss the mathematical modeling of this interference at short, large but finite and infinite distances from the scatterer. We show how to eliminate the errors that can arise from improper modeling in the most straight-forward manner, that is superimposing the scattered wave with the closed-form expression for the Gaussian beam at a finite distance from the particle. GLMT uses a low order beam model ($s^1$), but using the known higher order models ($s^3$, $s^5$, $s^7$, ...) would not mitigate these errors as we discuss. The challenge lies in an appropriate description of the Gaussian beam at arbitrary distances from its focus, not in its description on the scale of a particle (located in or near the focus) nor in the expressions for the scattered field. Hence, the solutions described here can readily be extended to light scattering frameworks other than GLMT and are thus also relevant for non-spherical particles.