reference Bessel beam diameter.

Applicability of the OEi method to scattering interactions
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In this section, we demonstrate, on the basis of a numerical study, how the OEi method can equally be applied in some scattering interaction processes. Indeed, the OEi method presented above is applicable to free space propagation and can be directly extended to linear scattering processes where the optical interaction is expressed as a quadratic form of the field. As in the case of the smallest spot operator, the OEi of these light matter interactions can be used to determine the electromagnetic field profile delivering the largest or the smallest interaction strength. In this section, we show two numerical examples illustrating the cases presented in Table \[tab\]. The numerical modelling is performed using a finite element method (Comsol) and solving the fully vectorial monochromatic Maxwell’s equations in 3D. The structures considered here are embedded in a larger computational domain surrounded by perfectly matched layers. Figure \[fig:oei\] shows the electric field amplitude $|\bf E|$ for the different cases considered. To implement the OEi method, we determine the matrix operator with the help of equation . Here, we use angular spectral decomposition [@Richards:1959p2607] of the incident light field corresponding 