# Spin and Orbital Angular Momentum of Light

## Universal spin-momentum locking of evanescent waves

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.

Van Mechelen, Todd, and Zubin Jacob. "Universal spin-momentum locking of evanescent waves." *Optica* 3, no. 2 (2016): 118-126.

## Quantum Field Theory for Angular Momentum of Light

All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open questions on the quantized description of spin of the gauge field particle—the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) SM=(1/c)∫d3xπ×A and orbital angular momentum (OAM) LM=−(1/c)∫d3xπμx×∇Aμ of the photon, where πμ is the conjugate canonical momentum of the gauge field Aμ. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above-defined quantum operators. Our work shows that the spin and OAM operators commute, which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon has applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.