  High-order harmonics generated by bicircular laser field have helicities
which alternate between $+1$ and $-1$. In order to generate circularly
polarized high-harmonic pulses, which are important for applications, it is
necessary to achieve asymmetry in emission of harmonics having opposite
helicities. We theoretically investigated a wide range of bicircular field
component intensities and found areas where both the harmonic intensity is high
and the helicity asymmetry is large. We investigated the cases of
$\omega$--$2\omega$ and $\omega$--$3\omega$ bicircular fields and atoms having
the $s$ and $p$ ground states, exemplified by He and Ne atoms, respectively. We
have shown that for He atoms strong high harmonics having positive helicity can
be generated using $\omega$--$3\omega$ bicircular field with a much stronger
second field component. For Ne atoms the helicity asymmetry can be large in a
wider range of the driving field component intensities and for higher harmonic
orders. For the stronger second field component the harmonic intensity is
higher and the helicity asymmetry parameter is larger for higher harmonic
orders. The results for Ne atoms are illustrated with the parametric plots of
elliptically polarized attosecond high-harmonic field.
