Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨cos2θ⟩ directly from ⟨cos2θ2D⟩ by Fourier analysis

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, < cos(2)theta >, directly from its two-dimensional counterpart, < cos(2)theta(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)theta(2D)> trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of < cos(2)theta >. These additional frequency components can be identified and removed from the Fourier spectrum of < cos(2)theta(2D)>. By rescaling of the remaining frequency components, the Fourier spectrum of < cos(2)theta > is obtained and, finally, < cos(2)theta > is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the < cos(2)theta > trace from a measured < cos(2)theta(2D)> trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated < cos(2)theta > 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)theta(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)theta > and < cos(2)theta > in general.