\[tab\] provides a list of common examples of such interactions. These interactions may be written in a general quadratic matrix form $$\label{eq:OEi1}
{m}^{(A)}(\mathbf{E},\mathbf{H})=\mathbf{a}^{\dagger}\mathbf{M}^{(A)}\mathbf{a}$$ where we considered a superposition of fields $\left\{\mathbf{E},\mathbf{H}\right\}  =\left\{\sum_{j=1}^{N}a_{j}\mathbf{E}_{j},\sum_{j=1}^{N}a_{j}\mathbf{H}_{j}\right\}$ and where $(A)$ labels the light-matter interaction defined in Table \[tab\]. The vectors $\mathbf{a}$ and $\mathbf{a}^{\dagger}$ are comprised of the superposition coefficients $a_{j}$ and their complex conjugates, respectively. The elements $M_{jk}^{(A)}$ of $\mathbf{M}^{(A)}$ are constructed by combining the respective fields $\{\mathbf{E}_{j},\mathbf{H}_{j}\}$ and $\{\mathbf{E}_{k},\mathbf{H}_{k}\}$ for $j,k=1\dots N$. More precisely, we have: $$\begin{aligned}
\label{eq:matrix}
4M_{jk}^{(A)}&=&{m}^{(A)}(\mathbf{E}_j+\mathbf{E}_k,\mathbf{H}_k+\mathbf{H}_k)-i{m}^{(A)}(\mathbf{E}_j+i\mathbf{E}_k,\mathbf{H}_k+i\mathbf{H}_k) \nonumber \\
&&-{m}^{(A)}(\mathbf{E}_j-\mathbf{E}_k,\mathbf{H}_k-\mathbf{H}_k)+i{m}^{(A)}(\mathbf{E}_j-i\mathbf{E}_k,\mathbf{H}_k-i\mathbf{H}_k). \end{aligned}$$ Given the Hermitian form of , we remark that the light-matter interaction $\mathbf{M}^{(A)}$ defines a spectrum of real eigenvalues $\lambda_{k}^{(A)}$ and associated eigenvectors $\mathbf{v}_{k}^{(A)}$. Each of these eigenvectors corresponds to a superposition of fields $\{\mathbf{E}_{j},\mathbf{H}_{j}\}$ termed here Optical Eigenmode (OEi). Crucially, we may now extremize the light-matter interaction considered; that is, the extremal eigenvalue $\lambda_{\textrm{ext}}^{(A)}$ and the associated eigenvectors $\mathbf{v}_{\textrm{ext}}^{(A)}$ deliver the superposition of fields $\left\{\mathbf{E}_{\textrm{ext}},\mathbf{H}_{\textrm{ext}}\right\}=
\left\{\sum_{j=1}^{N}v_{\textrm{ext},j}^{(A)}\mathbf{E}_{j},\sum_{j=1}^{N}v_{\textrm{ext},j}^{(A)}\mathbf{H}_{j}\right\}$ which extremizes the interaction $m^{(A)}$ while keeping the total field contributions constant $\mathbf{a}^{\dagger}\mathbf{a}=1$.

In this paper, we apply the OEi concept to minimize the size of a laser spot within a surface ROI. One way to define the spot size of a laser beam 