Revealing the spin optics in conic-shaped metasurfaces

Ellipse and hyperbola are two well-known curves in mathematics with numerous applications in various fields, but their properties and inherent differences in spin optics are less understood. Here, we investigate the peculiar optical spin properties of the two curves and establish a connection between their foci and the spin states of incident light by introducing a geometric-phase distribution along the conic curve. We show that the optical spin Hall effect is the intrinsic optical spin property of ellipse, where photons with different spin states can be exactly separated to each of its two foci, while a hyperbola exhibits optical spin-selective effect, where only photons with one particular spin state can be accumulated at its foci. These properties are then experimentally demonstrated in near field by arranging nanoslits in conic shapes. Based on the spin properties of the curves, we design spin-based plasmonic devices with various functionalities. Our results reveal the intrinsic optical spin properties behind conic curves and provide a route for designing spin-based plasmonic devices.

Figure 1

(a),(b) Schematic of the ellipse (a) and hyperbola (b) with a geometric-phase distribution φ$(r_1,r_2)$ indicated with different colors along the conic traces. (c) Calculated normal component of the SPP electric field $E_z$ launched by a nanoslit perforated in an Au film. Red arrow: the polarization of incident light. φ: the azimuthal angle of the nanoslit. θ: the angle between the vector $OF$ and the short axis of the nanoslit. (d) Antiphase distributions ψ  of four nanoslits with different azimuthal angles.

Figure 2

(a),(b) Schematics of an ellipse-shaped (a) and a hyperbola-shaped (b) metasurface. Analytical model [(c)–(f)] and FDTD simulation (10 nm distance above the metasurface) [(g)–(j)] calculated near-field intensity $|E_z{|}^2$ of the two conic-shaped metasurfaces with $|{\sigma }_{\pm }\rangle$ illuminations. The FDTD simulated intensity is normalized to incident electric intensity $|E_0{|}^2$. The numerical values shown on the color bar apply only to the FDTD simulation intensity. The scale bars are 2 μm.

Figure 3

(a),(b) SEM images of the ellipse-shaped (a) and hyperbola-shaped (b) metasurfaces. The inset in (a) is a SEM image of a nanoslit with width of 50 nm and length of 200 nm (scale bar: 100 nm). The black dashed lines are a guide for the eye of the conic traces. (c)–(f) Measured near-field optical intensity profiles of the ellipse-shaped [(c),(d)] and hyperbola-shaped [(e),(f)] metasurfaces with $|{\sigma }_{\pm }\rangle$ illuminations. The spin states of incident photons are indicated in each panel.

Figure 4

(a) Design strategy of metasurfaces with different functionalities. (b),(c) SEM images of two metasurfaces, which can separate photons with opposite spin states at each side of it (b) or at the same (upper) side (c). (d)–(g) Measured near-field optical intensities for metasurfaces shown in (b) (upper row) and (c) (lower row) with $|{\sigma }_{\pm }\rangle$ illuminations. The spin states of incident photons are indicated in each panel.