Chiral forces in longitudinally invariant dielectric photonic waveguides

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.