Description of molecular chirality and its analysis with high harmonic generation

To clarify the microscopic origin of chirality-induced optical effect, we develop an analytical method that extracts the chiral part of the Hamiltonian of molecular electronic states. We demonstrate this method in a model chiral molecule consisting of two helically stacked $N$-sided regular polygons, and compare it with numerical calculation for chiral discrimination via high harmonic generation (HHG) of the same molecule. The discrimination signal here is the Kuhn $g$ factor, the difference between the harmonic intensity from the bicircular laser field and that from its reflected laser field normalized by their average. The $g$ factor is a pseudoscalar quantity that reflects the chirality of the molecule. As a result, we find that the $g$ factor becomes large over a wide range of harmonic orders making HHG suitable for chiral discrimination. We further find that to increase the difference of harmonic intensity from the above two fields, the unnormalized $g$ factor, the increase of capacity to generate the longitudinal dipole moment is more advantageous than maximizing the transverse-to-longitudinal conversion efficiency via the optimization of molecular chirality. We speculate this criteria may be extended to other optical and current-induced processes relevant to the chiral molecules and materials.