Figure 1

The slanted line indicates the intensity (as a function of frequency) at which an electron in a plane-wave field acquires so much ponderomotive energy that the $z_f$ intensity parameter of Eq. (3) is equal to one. This is a boundary between relativistic and nonrelativistic conditions. Starting at an arbitrary point in the nonrelativistic domain, a path showing the limit $I\to \infty$ must enter the relativistic domain, as must a path showing the limit $\omega \to 0$. The two limits will be very different. Since both limits correspond to the Keldysh $\gamma$ approaching zero, this means that the limit of very small $\gamma$ in a tunneling theory is not applicable to plane-wave (i.e., laser) fields.Reuse & Permissions

Figure 2

The line ${\beta }_0=1$ marks the low-frequency limit of dipole-approximation behavior, and $\omega =E_B$ marks the upper limit on the frequency for a tunneling description of ionization. (The value of $E_B$ is set to 0.5 as an illustration.) The shaded triangular area in the figure marks the region within which a tunneling theory can be applied to atomic ionization caused by a laser field.Reuse & Permissions

Figure 3

The region of applicability exhibited in Fig. 2 is here indicated on a diagram of $\gamma$ as a function of field intensity. The boundaries of this region depend on both the binding energy $E_B$ and the intensity parameter $z$ of Eq. (6), so the domain of applicability of tunneling cannot be described in terms of $\gamma$ alone.Reuse & Permissions