  The generation of high-order harmonics in a medium of chiral molecules driven
by intense bi-elliptical laser fields can lead to strong chiroptical response
in a broad range of harmonic numbers and ellipticities [D. Ayuso et al, J.
Phys. B 51, 06LT01 (2018)]. Here we present a comprehensive analytical model
that can describe the most relevant features arising in the high-order harmonic
spectra of chiral molecules driven by strong bi-elliptical fields. Our model
recovers the physical picture underlying chiral high-order harmonic generation
based on ultrafast chiral hole motion and identifies the rotationally invariant
molecular pseudoscalars responsible for chiral dynamics. Using the chiral
molecule propylene oxide as an example, we show that one can control and
enhance the chiral response in bi-elliptical high-order harmonic generation by
tailoring the driving field, in particular by tuning its frequency, intensity
and ellipticity, exploiting a suppression mechanism of achiral background based
on the linear Stark effect.
