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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., Comment: 23 pages, 10 figures

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., Comment: 19 pages, 6 figures

Optical fields can exert forces of chiral nature on molecules and nanoparticles, which would prove extremely valuable in the separation of enantiomers with pharmaceutical applications, yet it is inherently complex, and the varied frameworks used in the literature further complicate the theoretical understanding. This paper unifies existing approaches used to describe dipolar optical forces and introduces a new symmetry-based `force basis' consisting of twelve vector fields, each weighted by particle-specific coefficients, for a streamlined description of force patterns. The approach is rigorously applied to evanescent waves and dielectric nanofibres, yielding concise analytical expressions for optical forces. Through this, we identify optimal strategies for enantiomer separation, offering invaluable guidance for future experiments., Comment: 18 pages, 5 figures