Metric for three-dimensional alignment of molecules

In an effort to clarify the three-dimensional alignment dynamics of polyatomic molecules, we propose a single measure for the degree of angular confinement of such molecules. The measure proposed for three-dimensional orientation is the angle of the single rotation that takes the molecule to the desired target orientation. Further, taking into account the $D_2$ symmetry of a three-dimensionally aligned distribution, a symmetrized version of the measure is constructed that serves as a direct indicator of the degree of three-dimensional alignment of a distribution. The calculation of the rotational dynamics of iodobenzene under the influence of two cross-polarized laser pulses demonstrates the effectiveness of the proposed metric.

Figure 1

On the left, four equivalent target orientations for 3D alignment generated by $\pi$ rotations around the LF axes. On the right, two of eight possible perfectly antialigned orientations in 3D. The axis of rotation is the unit vector $(\widehat{X}+\widehat{Y}+\widehat{Z})/\sqrt{3}$. The remaining six can be generated from these two by $\pi$ rotations around the $X$, $Y$, and $Z$ axes.

Figure 2

Expectation values calculated using TDSE for one-pulse and two-pulse excitation of rotational wave packets. The single pulse and the first pulse of the two-pulse calculation are polarized along the $Z$ axis and peak at 0 ps; the second pulse is polarized along the $X$ axis and peaks at 3.8 ps. Each pulse has a Gaussian temporal envelope with a duration (full width at half maximum of the intensity) of 170 fs and a peak intensity of 8 TW/cm${}^2$. The rotational temperature of iodobenzene is 0.5 K. The insets show details of the initial alignment and the second $J$-type revival.

Figure 3

The expectation values of $\langle {\cos }^2\delta \rangle$ for the excitation schemes shown in Fig. 2. The evolution of 3D alignment can be seen directly in this variable. Apart from the initial 3D alignment after the second pulse, the overlap of $J$- and $K$-type revivals results in a substantial revival of 3D alignment at 710.2 ps.