  Photons can undergo spin-orbit coupling, by which the polarization (spin) and
spatial profile (orbit) of the electromagnetic field interact and mix. Strong
photonic spin-orbit coupling may reportedly arise from light propagation
confined in a small cross-section, where the optical modes feature spin-orbit
entanglement. However, while photonic Hamiltonians generally exhibit
nonlinearity, the role and implication of spin-orbit entanglement in nonlinear
optics have received little attention and are still elusive. Here, we report
the first experimental demonstration of nonlinear optical frequency conversion,
where spin-orbit entanglement facilitates spin-to-orbit transfer among
different optical frequencies. By pumping a multimode optical nanofiber with a
spin-polarized Gaussian pump beam, we produce an optical vortex at the third
harmonic, which has long been regarded as a forbidden process in isotropic
media. Our findings offer a unique and powerful means for efficient optical
vortex generation that only incorporates a single Gaussian pump beam, in sharp
contrast to any other approaches employing structured pump fields or
sophisticatedly designed media. Our work opens up new possibilities of
spin-orbit-coupling subwavelength waveguides, inspiring fundamental studies of
nonlinear optics involving various types of structured light, as well as paving
the way for the realization of hybrid quantum systems comprised of telecom
photonic networks and long-lived quantum memories.
