## Abstract

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree,〈cos
^{2}Θ〉, directly from its two-dimensional counterpart, 〈cos
^{2}Θ
_{2D}〉. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent 〈cos
^{2}Θ
_{2D}〉 trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of 〈cos
^{2}Θ〉. These additional frequency components can be identified and removed from the Fourier spectrum of 〈cos
^{2}Θ
_{2D}〉. By rescaling of the remaining frequency components, the Fourier spectrum of 〈cos
^{2}Θ〉 is obtained and, finally, 〈cos
^{2}Θ〉 is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the 〈cos
^{2}Θ〉 trace from a measured 〈cos
^{2}Θ
_{2D}〉 trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated 〈cos
^{2}Θ〉 traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I
_{2} molecules. In addition, we present an efficient algorithm for calculating the matrix elements of 〈cos
^{2}Θ
_{2D}〉 and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of 〈cos
^{2}Θ
_{2D}〉 and 〈cos
^{2}Θ〉 in general.

Original language | English |
---|---|

Article number | 013905 |

Journal | Journal of Chemical Physics |

Volume | 147 |

Issue | 1 |

Number of pages | 10 |

ISSN | 0021-9606 |

DOIs | |

Publication status | Published - 7 Jul 2017 |

## Keywords

- ALIGNING MOLECULES
- 6J SYMBOLS
- FIELDS
- PHOTODISSOCIATION
- POLARIZATION
- DIFFRACTION
- PULSES
- 3J