*Optica*3 (2): 118-26.

## Abstract

We show the existence of an inherent property of evanescent electromagnetic waves: spin-momentum locking, where the direction of momentum fundamentally locks the polarization of the wave. We trace the ultimate origin of this phenomenon to complex dispersion and causality requirements on evanescent waves. We demonstrate that every case of evanescent waves in total internal reflection (TIR), surface states, and optical fibers/waveguides possesses this intrinsic spin-momentum locking. We also introduce a universal right-handed triplet consisting of momentum, decay, and spin for evanescent waves. We derive the Stokes parameters for evanescent waves, which reveal an intriguing result—every fast decaying evanescent wave is inherently circularly polarized with its handedness tied to the direction of propagation. We also show the existence of a fundamental angle associated with TIR such that propagating waves locally inherit perfect circular polarized characteristics from the evanescent wave. This circular TIR condition occurs if and only if the ratio of permittivities of the two dielectric media exceeds the golden ratio. Our work leads to a unified understanding of this spin-momentum locking in various nanophotonic experiments and sheds light on the electromagnetic analogy with the quantum spin-Hall state for electrons.

*Last updated on 03/01/2022*