Transverse spin-orbit interaction of light

Light carries both longitudinal and transverse spin angular momentum. The spin can couple with its orbital counterpart via the Berry phase, known as the spin-orbit interaction (SOI) of light. The SOI of light discovered previously belongs to the longitudinal one, which relies on the Berry phase in momentum space, such as the optical Magnus effect and the spin Hall effect. Here, we show that transverse SOI, relying on the Berry phase in real space, is inherent in the Helmholtz equation when transverse spinning light propagates in curved paths. The transverse SOI lifts the degeneracy of dispersion relations of light for opposite transverse spin states, analogous to the Dresselhaus effect. Transverse SOI is ubiquitous in nanophotonic systems where transverse spin and optical path bending are inevitable. It can also explain anomalous effects like the dispersion relation of surface plasmon polariton on curved paths and the energy level of whispering gallery modes. Our results reveal the analogies of spin photonics and spintronics and offer a new degree of freedom for integrated photonics, spin photonics, and astrophysics.