  Optical forces can be chiral when they exhibit opposite signs for the two
enantiomeric versions of a chiral molecule or particle. Such forces could be
eventually used to separate enantiomers, which could find application in
numerous disciplines. Here, we analyze numerically the optical chiral forces
arising in the basic element of photonic integrated circuitry: a dielectric
waveguide with rectangular cross-section. Such waveguides are inherently
lossless thus generating chiral forces that are invariant in the longitudinal
direction and therefore enable enantiomeric separation over long (cm-scale)
distances. Assuming Brownian motion in a liquid environment, we calculate first
the force strength and time span needed to perform the separation of chiral
nanoparticles as a function of the radii. Then we analyze the chiral forces
produced by the fundamental quasi-TE guided mode in a silicon nitride waveguide
and show that it can lead to enantiomeric separation via the transverse spin at
short wavelengths (405 nm). At longer wavelengths (1310 nm), the proper
combination of degenerate quasi-TE and quasi-TM modes would result in a
quasi-circularly polarized mode with intrinsic chirality (helicity), leading to
chiral gradient forces that also enable the enantiomeric separation of smaller
nanoparticles. We report particle tracking simulations where the optical force
field produced by a quasi-TE and a quasi-circular mode proved to separate
enantiomers under a time span of two seconds. Our results suggest the viability
of enantiomeric separation using simple photonic integrated circuits, though
different wavelength windows should be selected according to the nanoparticle
size.
