Spin Hall Effect of Nonlinear Photons

Photonic spin Hall effect (SHE) refers to the transverse separation of spin photons in refraction and reflection phenomena. The photonic SHE has been investigated in various optical systems including air-glass interfaces, interfaces containing 2D materials, random media, etc. Here, the spin-orbit coupling (SOC) in nonlinear uniaxial crystals is investigated, and the SHE of second-harmonic photons is demonstrated theoretically and experimentally. The generation and evolution processes of nonlinear spin photons within the crystal are visualized by the derived four wave coupling equations and wavevector-varying Berry phases. For a focused fundamental beam, two cascaded SOCs occurring in the fundamental and second-harmonic fields are connected by the nonlinear wave mixing near the focal position. Thus the SHE of nonlinear photons depends on the focal position, different strongly from linear photons whose SHE is independent of the focal position. Similar to the focal-position-dependent SHE, the focal-position-dependent optical vortex generations are also demonstrated for the nonlinear fields. Finally, a high-speed modulation scheme for the SHE is proposed based on an electro-optical polarization controller, which routes nonlinear spin photons into different destinations. These findings deepen the understanding of spin-orbit coupling in nonlinear systems and facilitate the development of spin multiplexed electrooptic devices.