Achieving high molecular alignment and orientation for CH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_3$$\end{document}3F through manipulation of rotational states with varying optical and THz laser pulse parameters

Increasing interest in the fields of high-harmonics generation, laser-induced chemical reactions, and molecular imaging of gaseous targets demands high molecular “alignment” and “orientation” (A&O). In this work, we examine the critical role of different pulse parameters on the field-free A&O dynamics of the CH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_3$$\end{document}3F molecule, and identify experimentally feasible optical and THz range laser parameters that ensure maximal A&O for such molecules. Herein, apart from rotational temperature, we investigate effects of varying pulse parameters such as, pulse duration, intensity, frequency, and carrier envelop phase (CEP). By analyzing the interplay between laser pulse parameters and the resulting rotational population distribution, the origin of specific A&O dynamics was addressed. We could identify two qualitatively different A&O behaviors and revealed their connection with the pulse parameters and the population of excited rotational states. We report here the highest alignment of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {\mathrm{cos}^2\theta }\rangle = 0.843$$\end{document}⟨cos2θ⟩=0.843 and orientation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {\mathrm{cos}(\theta )}\rangle = 0.886$$\end{document}⟨cos(θ)⟩=0.886 for CH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_3$$\end{document}3F molecule at 2 K using a single pulse. Our study should be useful to understand different aspects of laser-induced unidirectional rotation in heteronuclear molecules, and in understanding routes to tune/enhance A&O in laboratory conditions for advanced applications.

. Population of ith rotational state calculated using main Eq. 5 for different temperatures for 800 nm pulse. Rest of the pulse parameters are specified in main Table. 2.
states (J = 1, 3 for M = 0) to higher J states (J = 17 − 20 for M = 0 and J = 18, 19 for M = −1, 1) on increasing the FWHM from 0.5 ps to 1 ps. On further increase in FWHM from 1 ps to 1.5 ps we observe a reverse shift in population, to lower J states (J = 10 − 15 for M = 0) however, in all cases the population on |J = 20, M = [−1, 0, 1]⟩ appears to localize in all cases. Furthermore, for FWHM of 1.5 ps to 2 ps the population is distributed on both lower-(J = 0 − 5) and higher (J = 10 − 20) lying states. SI Fig. S7 shows the time-dependent populations that reveal the intricate dynamics leading to the de-excitation. Comparing the time-dependent populations with Fig. S6, we can also see the effect of the field strength on the excitation process. When the field strength is large, (de)-excitation occurs, but the populations do not change when the field strength is zero. The maximal A&O curves show a local minimum at FWHM= 1.5 ps, which also indicates a change in the nature of excitation of rotational states. To analyze further deeper insight into the behaviour of A&O with different THz pulse widths we have plotted the Fourier-transform of the pulses in SI Fig. S6. Changing only the FWHM affects both the spectral bandwidth and the total energy deposited by the pulse. As shown in SI Fig. S6, the FWHM=0.5 ps pulse covers a wide energy range, but has relatively low strength throughout compared to the other pulses. Hence, the population of high-J states is not very high for this case (see Fig S5). The bandwidth of longer pulses becomes narrower, which effect -on its own-decreases the excitation since the pulse covers only a narrower range of rotational transitions. However, the pulse energy of the longer pulses is bigger than that of the 0.5 ps pulse, which overcompensates the effect of the narrow bandwidth, leading to high degree of excitation and anomalous A&O behaviour.

Testing the effect of intensity
The analysis of population distributions (see Fig. S8 and SI Fig. S9) leads us to understand that with increase in THz pulse intensity a broad range of J space is excited. On increasing the THz pulse intensity from 6×10 −4 TW/cm 2 to 0.2 TW/cm 2 (see main Fig. 3(II) for population distribution of 0.2 TW/cm 2 and Fig. S8 for rest) the population, having a broad distribution in J space, seems to be gradually shifted to higher J values. On the other hand, for 0.3 TW/cm 2 and 0.5 TW/cm 2 the total number of excited J states remain the same (up to J = 29) but the highest populated |J = 24, M = 0⟩ state shifts to |J = 23, M = 0⟩ state, and the population becomes localized to a few J states. For these intensities, the observed fast oscillations in the A&O , see main Fig. 3 (b), and Fig. 4 (b), originates from the J ↔ J + 2 and J ↔ J + 1 beatings for higher J states.

Testing the effect of frequency
With increase in THz pulse frequency, the central frequency shifts to higher energy (see main Fig. 3(III) Fig. S11) and thus, for attaining resonance with a particle rotational excitation state, the frequency has to be tuned suitable. The spectral bandwidth for THz pulse with frequency ≤1 THz in Fig. S11, show sharp rise in field strength for lower energy and then gradual decrease for higher energy. This indicates that the chances for higher J states to populate is higher for such laser pulse. The heat maps in Fig. S10 also shows increase in population of higher J states (≤ 10) on increase in frequency from 0.1 THz to 1 THz. On further increase in frequency the nature of the spectral bandwidth is reverse and shows a slow increase in field strength for lower energy and with central frequency at higher energy. If the frequency is greater than 2.0 THz, then the bandwidth of pulse does not cover the transitions of the low-J states, therefore, the excitation process cannot start and only low excitation can be achieved.

Effects from vibrational averaging
Herein we check the effect of vibrational averaging of the molecular parameters, and its impact on the laser-induced rotational dynamics. The rotational revivals for the optical pulse using the equilibrium parameters versus that using the vibrationally averaged molecular parameters, show negligible effect on the degree of alignment. For the THz pulse we repeated the simulation using vibrationally averaged rotational constants and dipole moment for the T =2 K, I=0.2 TW/cm 2 , FWHM=0.5 ps, frequency=0.5 THz and CEP=π/2 case, a pulse which resulted in a large orientation. The results are as shown below. We find that the maximal alignment and orientation obtained with the vibrationally averaged and the equilibrium parameter sets are rather similar to each other, however very slight drift in the revivals is observed with increasing time, due to slight change in rotational constants under vibrational averaging.
The vibrationally averaged parameters were obtained by adding -0.07688 cm −1 and -0.00813 cm −1 corrections from our previous work [J. Comput. Chem.43, 519-538 (2022)] to the equilibrium values of B z and B x =B y rotational constants, respectively, and -0.01391 D to the equilibrium dipole moment. Since, the polarizability values for vibrationally averaged conditions were not simulated we use the same polarizablity as used throughout this article, α ∥ as 2.524 Å 3 and α ⊥ as 2.296 Å 3 . The pulse parameters giving highest achieved molecular alignment for 800 nm pulse, and molecular A&O for THz pulse (using equilibrium molecular parameters) were used to test the effect of vibrational averaging. The 800 nm pulse parameters are: FWHM of 150 fs, intensity of 100 TW/cm 2 and temperature of 2K. The THz pulse parameters used are: FWHM of 0.5 ps, intensity of 0.2 TW/cm 2 , CEP of π/2, frequency of 0.5THz at 2K temperature. M = 0 M = -1 M states 2 ps Figure S5. Population of ith rotational state calculated using main Eq. 5 for different FWHM of THz pulse. Rest of the pulse parameters are specified in Table. 3