The study of the optical response of high refractive index nano-particles has revealed that these resonant structures are capable of controlling different degrees of freedom of light fields with unprecedented versatility . The ability of these particles to control the intensity, phase and polarization of light has unveiled a plethora of new physical effects and applications. To mention a few, these particles have allowed controlling the directionality of optical antennas in an unprecedented manner , they have shown promise in enhancing molecular circular dichroism spectroscopy  and all- optical chiral separation methods based on enantioselective photo-excitation of chiral molecules .
In this letter, we unveil a new phenomenon that to the best of our knowledge was not reported up to date; the natural emergence of an optical vortex in the back scattering of cylindrically symmetric high index resonators when illuminated at their first Kerker condition of anomalous scattering. Firstly, based on singular optics arguments , we deduce the emergence of the vortex for a high index nano-particle Illuminated by circularly polarized light at the first Kerker condition. Secondly, using the recently developed helicity and angular momentum conservation framework, we prove that the modulus of the topological charge of the vortex has to be equal to 2. Lastly, we verify our predictions through analytic and numerical calculations.
Moreover, we analize the emergence of polarization singularities (C lines and L surfaces) in the scattering of optical resonators excited by linearly polarized light. We demonstrate both analytically and numerically that high refractive index spherical resonators present such topologically protected features and calculating the polarization structure of light around the generated C lines, we unveil a Möbius strip structure in the main axis of the polarization ellipse when calculated on a closed path around the generated lines of circular polarization.
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