Fig. 1

Illustration of the concepts. a Schematic of the platform for the investigation of transverse spin-induced SOI effect. b The clockwise (CW) and counter-clockwise (CCW) WGMs present opposite transverse spins on each side of the resonator. c Illustration of the transverse-spin-dependent geometric phase acquired by the vector evanescent wave as the WGM travels around the resonator. For the CCW WGM shown here, a rotation angle of φ·z is experienced by the local coordinates from point (r′, φ′) to (r″, φ″), and the geometric phase imparted on the evanescent wave with a transverse-spin state σ is Φ_G = −σφ