general corresponds to the $\textrm{Range of interest}=\textrm{ROI}$ of the measure. In the optical momentum case, it corresponds to a closed surface surrounding the scattering object with $\bf F \cdot \bf u$ representing the optical force in the direction defined by the unit vector $\bf u$. For surface integrals, $\bf n$ is the normal unit vector to the surface considered. The definition of the electromagnetic energy density is ${\cal E}=1/2 (\epsilon_0\bf E\cdot \bf E^*+\mu_0\bf H\cdot \bf H^*)$. []{data-label="tab"}

For our proof-of-principle studies described in the remainder of the paper, we also applied the scalar version of the OEi method where a set of scalar fields $E_{i}$ is considered in order to determine the IO and SSO as $$\label{eq:OEi4}
M_{jk}^{(0)}=\int_S E_{j}^{\ast}E_{k}\;d\sigma$$ and $$\label{eq:OEi5}
M_{jk}^{(2)}=\int_S \mathbf{r}^{2}E_{j}^{\ast}E_{k}\;d\sigma,$$ respectively. These scalar expressions are equivalent to the respective vector versions listed in Table \[tab\] and determined through equation . The scalar version of the optimimum OEi  explicitly reads $$\label{eq:OEi6}
E_{\min}=\sum_{j=1}^{N}\sum_{k=1}^{N}\frac{v_{\min,k}^{(2)}v_{k,j}^{(0)}}{\sqrt{\lambda_{k}^{(0)}}}\cdot E_{j}.$$

Smallest focal spot using Laguerre Gaussian beams {#s:sec33}
-------------------------------------------------

Using a superposition of LG beams we can minimize the size of a focal spot using the representation of the SSO in cylindrical coordinates. It is important to note at this point that we only retain 