Spin-orbit interaction of light induced by transverse spin angular momentum engineering

Abstract

The investigations on optical angular momenta and their interactions have broadened our knowledge of light's behavior at sub-wavelength scales. Recent studies further unveil the extraordinary characteristics of transverse spin angular momentum in confined light fields and orbital angular momentum in optical vortices. Here we demonstrate a direct interaction between these two intrinsic quantities of light. By engineering the transverse spin in the evanescent wave of a whispering-gallery-mode-based optical vortex emitter, a spin-orbit interaction is observed in generated vortex beams. Inversely, this unconventional spin-orbit interplay further gives rise to an enhanced spin-direction locking effect in which waveguide modes are unidirectionally excited, with the directionality jointly controlled by the spin and orbital angular momenta states of light. The identification of this previously unknown pathway between the polarization and spatial degrees of freedom of light enriches the spin-orbit interaction phenomena, and can enable various functionalities in applications such as communications and quantum information processing.

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

Fig. 2

Numerically calculated field component distributions and their dependence on waveguide dimensions. a The cross-sectional field distribution of the transverse component E_trans of the fundamental quasi-TE mode in a SiN_x waveguide, and the dashed rectangular indicates the waveguide of 0.8 μm width and 0.6 μm height. The results in b and c are obtained with the same waveguide mode. b The field distribution of the longitudinal component (multiplied with the imaginary unit) iE_long. c The distribution of the component ratio iE_long/E_trans over the waveguide cross section and evanescent region. d The contour map of the ratio iE_long/E_trans over variable waveguide dimensions. Among all the waveguide designs calculated, eight waveguide dimensions marked in the map are employed for device fabrication and characterization, consisting of two different heights (0.4 and 0.6 μm) and four widths (0.8, 1.0, 1.2, and 1.4 μm) as indicated in the subscripts

Fig. 3

Calculated transverse-spin states of all designed devices and SEM images of fabricated device WG_6–8. a Calculated transverse-spin states in the evanescent region of all eight sample devices. b SEM image of the device WG_6–8. The inset shows a close-up of the coupling section between the access waveguide and the resonator. c Top: junction point of the tapered coupler consisting of a tapered SiN_x waveguide and a SU8 waveguide. Bottom: cross-section views at various positions of the tapered coupler. The minimum width of the SiN_x taper (shown in the right-hand side image) is 130 nm

Fig. 4

Characterization of average polarization state in CVVs. a, b Measured squared polarization ellipticity ε² (solid markers) of the CVVs from the devices of height 0.4 and 0.6 μm, respectively. The prediction of κ² from numerical calculations is plotted with dashed lines, and the measured and calculated results for the same device are marked in the same color

Fig. 5

Stokes polarimetry of near-field polarization of CVVs. a–d Measured two-dimensional maps of near-field Stokes parameters and the comparison with theoretical prediction for devices WG_6–8, WG_6–10, WG_6–12, and WG_6–14, respectively. In each case, the four maps show the measured near-field intensity profile of the device with l_TC = +4, and the normalized Stokes parameters S₁, S₂, and S₃, respectively. The curves in each case show the comparison between the measured results (dots) sampled from the maps and the corresponding prediction (solid curves) from Eq. (7). For each set of measured data, 288 pixels intersecting with the circle of 80 μm radius along the azimuthal direction (φ) from 0 to 2π are sampled from the corresponding map. For each solid curve, the data are calculated by substituting the transverse-spin state σ from Fig. 3a into Eq. (7)

Fig. 6

Characterization of OAM components in CVVs. a–d The measured OAM spectra for the devices WG_6–8, WG_6–10, WG_6–12, and WG_6–14, respectively. For each device, the wavelengths of l_TC = −5 to +5 are considered, and each column represents a spectrum of measured OAM components with the corresponding l_TC

Fig. 7

Proof-of-principle demonstration of spin-orbit jointly controlled unidirectional coupling of waveguide modes. a Schematic of platform for receiving CVVs via spin-orbit unidirectional coupling effect. For devices of unity transverse-spin states in the evanescent region (σ_res = ±1), the propagation direction of coupled light in the waveguide, or the ratio of received power at the two ports P₁/P₂, is first subject to the sign of incident SAM state, sgn(σ_in). Meanwhile, at a given wavelength (λ_res), the incident spin-orbit states 〈σ_in, l_in〉 must obey the phase-matching condition l_in + σ_in = l_res for high-efficiency coupling. b–d Received power at Port 1 (P₁, blue bars) and Port 2 (P₂, red bars) of device WG_4–10 when the SAM state of incident wave σ_in = +1, 0, and −1, respectively. For each σ_in, CVVs at 5 resonance wavelengths of WG_4–10 (1578.61, 1583.11, 1587.59, 1592.11, and 1596.66 nm) and 11 OAM states (l_in = −5, −4, …, and +5) are illuminated on the device. At these five wavelengths, the CVVs emitted from the device would carry the topological charges of l_res = ±4, ±2, 0, ∓2, ∓4, respectively, when injecting light into Port 1 (2), as marked in blue (red) on the l_res axis in b–d. All measured power has been calibrated with respect to the lensed fiber coupling loss (Supplementary Note 10), and all data are normalized to the highest value in each l_res group