Direct Measurement of the Angular Dependence of Ionization for ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{CO}}_2$ in Intense Laser Fields

We experimentally measure the ionization probability as a function of alignment angle of three molecules in intense laser fields: nitrogen, oxygen, and carbon dioxide. Unlike atoms, molecules have a rotational degree of freedom. By controlling the alignment of the molecule relative to the laser field, molecules offer additional ways to understand strong-field ionization. The angular dependence of ionization directly maps to the orbital symmetry of each molecule. Carbon dioxide is seen to have a very sharp preference for ionization when aligned at 45 degrees to the laser field, in significant disagreement with current theories.

Figure 1

Alignment distribution of ${\mathrm{CO}}_2$ molecules with respect to the polarization axis of the aligning beam (horizontal). The dots are the measured angular distribution $A(\vartheta )$ calculated from the vector difference between the velocities of the correlated pairs of ${\mathrm{O}}^{2+}$ and ${\mathrm{O}}^{3+}$ fragments. The dashed line is the best fit to $A(\vartheta )=1+a/\sqrt{{cos}^2\vartheta +{ϵ}^2{sin}^2\vartheta }$. The two limiting cases of the actual alignment distribution, $A_1(\theta )$ (no realignment) and $A_2(\theta )$ (complete realignment into the polarization plane), are also shown.

Figure 2

Measured ionization yield $M(\alpha )$ as a function of the angle $\alpha$ between the polarization axes of the aligning and the ionizing beams for (a) ${\mathrm{N}}_2$, (b) ${\mathrm{O}}_2$, and (c) ${\mathrm{CO}}_2$. The error bars in the ionization yields are estimated from the results of different experimental runs. The solid lines are the best fits using the corresponding functional forms shown in Fig. 3. The peak laser intensities and the degrees of alignment, $⟨{cos}^2\vartheta ⟩$, are, respectively: (a) $1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, 0.77; (b) $1.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, 0.78; (c) $1.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, 0.73.

Figure 3

Angular dependence of the ionization signal $S(\theta )$ after deconvolution with the alignment distribution: (a) ${\mathrm{N}}_2$, (b) ${\mathrm{O}}_2$, and (c) ${\mathrm{CO}}_2$. The curves are the result of the best fit of Eq. (1) to the measured yields in Fig. 2 using parameterized $S(\theta )$ (see text). The results are shown for the two limiting cases of the alignment distribution (as shown in Fig. 1 for ${\mathrm{CO}}_2$): $A_1(\theta )$, no realignment (solid line), and $A_2(\theta )$, complete realignment (dash-dotted line). The dotted line is the ionization signal calculated with the molecular ADK model and the experimental intensity distribution.