Longitudinal chiral forces in photonic integrated waveguides to separate particles with realistically small chirality

Chiral optical forces exhibit opposite signs for the two enantiomeric versions of a chiral molecule or particle. If large enough, these forces might be able to separate enantiomers all optically, which would find numerous applications in different fields, from pharmacology to chemistry. Longitudinal chiral forces are especially promising for tackling the challenging scenario of separating particles of realistically small chiralities. In this work, we study the longitudinal chiral forces arising in dielectric integrated waveguides when the quasi-TE and quasi-TM modes are combined as well as their application to separate absorbing and non-absorbing chiral particles. We show that chiral gradient forces dominate in the scenario of beating of non-denegerate TE and TM modes when considering non-absorbing particles. For absorbing particles, the superposition of degenerate TE and TM modes can lead to chiral forces that are kept along the whole waveguide length. We accompany the calculations of the forces with particle tracking simulations for specific radii and chirality parameters. We show that longitudinal forces can separate non-absorbing chiral nanoparticles in water even for relatively low values of the particle chirality and absorbing particles with arbitrarily low values of chirality can be effectively separated after enough interaction time.