can be evaluated. As $W$ is conventionally given in units of joules, $\tau$ in femtoseconds and $\lambda$ in nanometers, it is helpful to note that $$\left(\frac{I}{I_{\rm cr}}\frac{\lambda}{\lambda_c}\right)^3\frac{\tau}{\tau_c}\approx 3.40\cdot10^{11}\left(\frac{W[J]}{\tau[{\rm fs}]\,\lambda[{\rm nm}]}\right)^3 \tau[{\rm fs}]\,. \label{eq:J-fs-nm}$$

Before providing some explicit estimates of the numbers of photons resulting from the stimulated emission process attainable with present and near future high-intensity laser facilities, we focus on the directional emission characteristics encoded in the functions $h_{(p)}^\omega(u,\varphi)$. Let us emphasize again that – in the diffraction limit, and particularly for $f^\#=1$ – these characteristics are independent of the actual laser parameters, and thus, are the same for all lasers. For a polarization insensitive measurement of the emitted photons the relevant directional emission characteristics as a function $\varphi,\vartheta$ are described by $h^\omega(\cos\vartheta,\varphi)\sin\vartheta$; recall that $|\frac{{\rm d}u}{{\rm d}\vartheta}|=\sin\vartheta$. We depict them in Fig. \[fig:Ntotal\].

The total number $N^\omega_{\rm tot}$ of emitted photons of frequency $\omega\in\{\Omega,3\Omega\}$ is obtained straightforwardly from [Eq. ]{} with $u_2=-1$, $u_1=1$, $\varphi_1=0$ and $\varphi_2=2\pi$. This results in $$\left\{\begin{array}{c}
  \! N^\Omega_{\rm tot}\\
  \! N^{3\Omega}_{\rm tot}
 \end{array}\right\}
 \approx
 \left\{\begin{array}{c}
   2.94\cdot10^{7} \\
   8.48\cdot10^{-16}
 \end{array}\right\}\left(\frac{W[J]}{\lambda[{\rm nm}]}\right)^3\!\left(\frac{1}{\tau[{\rm fs}]}\right)^2 . \label{eq:res1}$$ As the $3\Omega$ signal is severely suppressed, we do not study it any further in the remainder of this paper.

It 