two physical (transversal) photon polarizations, we obtain $${\cal S}_{(p)}(\vec{k})
 =\frac{i}{\sqrt{2k^0}} \, \hat f^{\mu\nu}_{(p)}(k)\, \frac{\partial{\cal L}}{\partial F^{\mu\nu}}(-k)\,, \label{eq:Sp}$$ where $\frac{\partial{\cal L}}{\partial F^{\mu\nu}}(k)=\int{\rm d}^4 x\,{\rm e}^{-ikx}\frac{\partial{\cal L}}{\partial F^{\mu\nu}}(x)$, and we made use of the shorthand notation $\hat f^{\mu\nu}_{(p)}(k)=k^\mu\epsilon^{*\nu}_{(p)}(k)- k^\nu\epsilon^{*\mu}_{(p)}(k)$.

In the vicinity of its beam waist the electromagnetic field of a Gaussian laser beam, corresponding to a fundamental transverse electromagnetic ${\rm TEM}_{00}$ mode, polarized along $\vec{e}_{\rm x}$ and propagating along $\pm\vec{e}_{\rm z}$ can be approximately modeled by the following field configuration $$\begin{gathered}
 \vec{E}_\pm(x)=\pm{\cal E}\,\vec{e}_{\rm x}\,{\rm e}^{-\frac{4({\rm x}^2+{\rm y}^2)}{w^2}}{\rm e}^{-\frac{{\rm z}^2}{\zeta^2}}\cos\bigl(\Omega(t\mp {\rm z})\bigr), \nonumber\\
 \vec{B}_\pm(x)={\cal E}\,\vec{e}_{\rm y}\,{\rm e}^{-\frac{4({\rm x}^2+{\rm y}^2)}{w^2}}{\rm e}^{-\frac{{\rm z}^2}{\zeta^2}}\cos\bigl(\Omega(t\mp {\rm z})\bigr), \label{eq:beamfields}\end{gathered}$$ i.e., orthogonal electric and magnetic fields, which – for given space-time coordinates – are of the same magnitude, and become maximum for ${\rm x}={\rm y}={\rm z}=0$ (and $t=0$). Here, we have chosen the orientation of the electric and magnetic fields in such a way that the magnetic field vector points in the same direction ($\vec{e}_{\rm y}$) for both propagation directions $\pm\vec{e}_{\rm z}$; ${\cal E}>0$ denotes the electric/magnetic field amplitude. The transversal field profile in [Eq. ]{} is a Gaussian characterized by its full width $w$ at ${\rm e}^{-1}$ of its maximum. In longitudinal direction the fields feature a 