  Optical chirality (OC) - one of the fundamental quantities of electromagnetic
fields - corresponds to the instantaneous chirality of light. It has been
utilized for exploring chiral light-matter interactions in linear optics, but
has not yet been applied to nonlinear processes. Motivated to explore the role
of OC in the generation of helically polarized high-order harmonics and
attosecond pulses, we first separate the OC of transversal and paraxial beams
to polarization and orbital terms. We find that the polarization-associated OC
of attosecond pulses corresponds to that of the pump in the quasi-monochromatic
case, but not in multi-chromatic pump cases. We associate this discrepancy to
the fact that the polarization OC of multi-chromatic pumps vary rapidly in time
along the optical cycle. Thus, we propose new quantities, non-instantaneous
polarization-associated OC, and timescale-weighted polarization-associated OC,
that link the chirality of multi-chromatic pumps and their generated attosecond
pulses. The presented extension to OC theory should be useful for exploring
various nonlinear chiral light-matter interactions. For example, it stimulates
us to propose a tri-circular pump for generation of highly elliptical
attosecond pulses with a tunable ellipticity.
