Molecular effects in the ionization of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{F}}_2$ by intense laser fields

In this paper we study the response in time of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{F}}_2$ to laser pulses having a wavelength of $390\mathrm{nm}$. We find single-ionization suppression in ${\mathrm{O}}_2$ and its absence in ${\mathrm{F}}_2$, in accordance with experimental results at $\lambda =800\mathrm{nm}$. Within our framework of time-dependent density functional theory we are able to explain deviations from the predictions of intense-field many-body $S$-matrix theory (IMST). We confirm the connection of ionization suppression with destructive interference of outgoing electron waves from the ionized electron orbital. However, the prediction of ionization suppression, justified within the IMST approach through the symmetry of the highest occupied molecular orbital (HOMO), is not reliable since it turns out that—e.g., in the case of ${\mathrm{F}}_2$—the electronic response to the laser pulse is rather complicated and does not lead to dominant depletion of the HOMO. Therefore, the symmetry of the HOMO is not sufficient to predict ionization suppression. However, at least for ${\mathrm{F}}_2$, the symmetry of the dominantly ionized orbital is consistent with the nonsuppression of ionization.

Figure 1

Kohn-Sham orbital populations for ${\mathrm{N}}_2$ during interaction with a $24\text{‐}\text{cycle}$ laser pulse having a wavelength of $\lambda =390\mathrm{nm}$ and laser intensity (a) $I=1\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) $I=6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. For all laser intensities it is seen that the Kohn-Sham orbital having the same symmetry $\left(3{\sigma }_g\right)$ as the valence orbital of ${\mathrm{N}}_2$ shows the predominant response to the field.

Figure 2

Kohn-Sham orbital populations for ${\mathrm{O}}_2$ during interaction with a $24\text{‐}\text{cycle}$ laser pulse having a wavelength of $\lambda =390\mathrm{nm}$ and laser intensity (a) $I=1\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) $I=6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. For all laser intensities it is seen that the Kohn-Sham orbital having the same symmetry $\left(1{\pi }_g\right)$ as the valence orbital of ${\mathrm{O}}_2$ shows the predominant response to the field.

Figure 3

Kohn-Sham orbital populations for ${\mathrm{F}}_2$ during interaction with a $24\text{‐}\text{cycle}$ laser pulse having a wavelength of $\lambda =390\mathrm{nm}$ and laser intensity (a) $I=1\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, (b) $I=2\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, (c) $I=4\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, and (d) $I=6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. For all laser intensities, except $I=1\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, it is seen that the $3{\sigma }_g$ orbital predominantly responds to the field. At the lowest intensity the $1{\pi }_g$ antibonding orbital (having the same symmetry as the valence orbital of ${\mathrm{F}}_2$) is equally dominant with the $1{\pi }_u$ bonding orbital. These two orbitals respond almost identically at all laser intensities.

Figure 4

Kohn-Sham orbital populations for ${\mathrm{F}}_2$ during interaction with a $24\text{‐}\text{cycle}$ laser pulse having a wavelength of $\lambda =390\mathrm{nm}$ and an intensity of $I=2\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. In these calculations only the orbitals shown in each figure respond to the field. All other orbitals are frozen. It can clearly be seen in (c) that when only the $1{\pi }_u$ and $1{\pi }_g$ orbitals respond to the field is ionization suppressed. In (a) and (b) we see that the ionization of either the $1{\pi }_u$ or $1{\pi }_g$ is greater than that of the $3{\sigma }_g$ orbital. When the $3{\sigma }_g$, $1{\pi }_u$, and $1{\pi }_g$ orbitals respond, however, ionization of the $3{\sigma }_g$ orbital is dominant.

Figure 5

Kohn-Sham orbital populations for ${\mathrm{F}}_2$ during interaction with a $24\text{‐}\text{cycle}$ laser pulse having a wavelength of $\lambda =300\mathrm{nm}$ and intensity (a) $I=4\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) $I=6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. At this laser wavelength we see that the the orbital populations fall off exponentially, unlike the response at $\lambda =390\mathrm{nm}$ observed in Fig. 3. We conclude that the response at $\lambda =390\mathrm{nm}$ is due to the population of an intermediate resonance state.