Topological Shaping of Light by Closed-Path Nanoslits

We propose a discrete set of continuous deformation of a circular nanoslit to generate and control optical vortices at the microscopic scale. The process relies on the interplay between the spin and orbital angular momentum degrees of freedom of light mediated by appropriate closed-path nanoslits milled on a thin gold film. Topological shaping of light is experimentally demonstrated in the visible domain. Moreover, all experimental observations are quantitatively validated by a simple model that takes into account the transverse manipulation of the optical phase via the space-variant form birefringence of subwavelength slits.

Figure 1

(a) Geometry and definition of characteristic angles $\beta$ and $\varphi$ for a closed-path nanoslit circuit $\mathcal{C}$ homeomorphic to the circle. (b) Illustration of the experimental setup. A circularly polarized collimated Gaussian beam with wave vector $\mathbf{k}$, waist diameter $2w$, and helicity $\sigma =\pm 1$ impinges at normal incidence on the nanoslit plane.

Figure 2

(a) Closed-path topological nanoslit of order $m$, here with $m=5$ (thick curve), where $R$ is the radius of the circle in which is inscribed the structure and $R_m$ is the radius of the circles that generate the design. (b),(c) Scanning electron microscope (SEM) image of the case $m=3$ in its open and closed forms, with $R=10\mu \mathrm{m}$ and slit width $e=150–200\mathrm{nm}$. The scale bar is $5\mu \mathrm{m}$. The contrast difference of the two SEM images is due to different electrical charging effects between the two kinds of structures.

Figure 3

Upper row: SEM images of closed loop nanoslits of order $m=3$ to 8 with $R=10\mu \mathrm{m}$ (see dashed circle) and slit width $e=150–200\mathrm{nm}$. Bottom row: Optical imaging of the slit at 532 nm wavelength under crossed circular polarizers. Insets: Calculated convoluted nanoslit images accounting for the numerical aperture of the imaging system.

Figure 4

Polarization conversion efficiency $\eta$ of nanoslit structures of different order ($m$), size ($R$), and nature (open or closed forms). The dashed line is the mean value, and the gray area refers to the standard deviation range.

Figure 5

Map of the phase distribution of the generated optical vortices for nanoslits of order $m=3$ to 8, in the plane of the nanoslit, with $\sigma =-1$. Upper row: Experimental data with $R=10\mu \mathrm{m}$. The shown data refer to the location where intensity is measured for the contracircularly polarized field component; see Fig. 3. Bottom row: Model.

Figure 6

Nonuniform azimuthal phase profile ${\Phi }_m(\varphi )$ of the generated optical vortices for nanoslits of order $m=3$, 4, and 5 with $R=10\mu \mathrm{m}$ and $\sigma =-1$. Markers: Experimental data averaged over three different structures (one in open form and two in closed form). Curve: Model.

Figure 7

Propagation of the contracircularly polarized optical field component for the fundamental nanoslit structure $m=3$ with $R=5\mu \mathrm{m}$. The first image refers to the nanoslit plane ($z=0$), and others, from left to right, correspond to $dz=20R$ propagating steps. All images are on the same scale, and acquisition time increases with $z$.

Figure 8

Characteristic single beam self-spiraling optical textures for nanoslits of order $m=3$, 4, 5, 6, 7, and 8. The number of spiral arms is $m-2$, which corresponds to the topological charge of the optical vortex generated by the closed loop nanoslit. Upper row: Experimental data with $R=10\mu \mathrm{m}$. Bottom row: Model.

Figure 9

Polarization switching of the topological charge for nanoslits of order $m=3$ and 4 with $R=10\mu \mathrm{m}$, where $\sigma =\pm 1$ refers to the helicity of the incident beam on the structures.

Figure 10

Far-field characteristics for $m=3$, 4, 5, 6, 7, and 8. First and second rows: Fraunhofer diffraction intensity and phase patterns in the reciprocal coordinate system, here displayed in the range $-0.1\le (\mu ,\nu )\le 0.1$. Third row: Azimuthal dependence of the phase along the circle that passes by the intensity maxima. Simulation parameters: $\sigma =-1$, $w/R=0.02$, $\lambda =500\mathrm{nm}$, and $R=10\mu \mathrm{m}$.