Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨𝖼𝗈𝗌𝟤 θ⟩ directly from ⟨𝖼𝗈𝗌𝟤 θ2D⟩ by Fourier analysis.

Abstract

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos2θ⟩, directly from its two-dimensional counterpart, ⟨cos2θ2D⟩. 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 ⟨cos2θ2D⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos2θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos2θ2D⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos2θ⟩ is obtained and, finally, ⟨cos2θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos2θ⟩ trace from a measured ⟨cos2θ2D⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos2θ⟩ 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 I2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos2θ2D 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 ⟨cos2θ2D⟩ and ⟨cos2θ⟩ in general.