  Chiral discrimination with high harmonic generation (cHHG method) has been
introduced in the recent work by R. Cireasa et al ( Nat. Phys. 11, 654 - 658,
2015). In its original implementation, the cHHG method works by detecting high
harmonic emission from randomly oriented ensemble of chiral molecules driven by
elliptically polarized field, as a function of ellipticity. Here we discuss
future perspectives in the development of this novel method, the ways of
increasing chiral dichroism using tailored laser pulses, new detection schemes
involving high harmonic phase measurements, and concentration-independent
approaches. Using the example of the epoxypropane molecule C$_3$H$_6$O (also
known as 1,2-propylene oxide), we show theoretically that application of
two-color counter-rotating elliptically polarized laser fields yields an order
of magnitude enhancement of chiral dichroism compared to single color
elliptical fields. We also describe how one can introduce a new functionality
to cHHG: concentration-independent measurement of the enatiomeric excess in a
mixture of randomly oriented left-handed and right-handed molecules. Finally,
for arbitrary configurations of laser fields, we connect the observables of the
cHHG method to the amplitude and phase of chiral response, providing a basis
for reconstructing wide range of chiral dynamics from cHHG measurements, with
femtosecond to sub-femtosecond temporal resolution.
