Fig. 1. Multilayered periodic photonic nanostructure supporting robust phase singularity. (a) Schematic of the periodic bilayer structure enabling robust phase singularity; the array is made of two plasmonic resonators with detuned resonances and twisted angle θ. The first layer of resonators is embedded in a 60-nm-thick polymer spacer (SU-8), whereas the second layer of resonators is on top of the polymer and is exposed to the air, making its surface available for chiral analyte detection. Panel (b) illustrates the unit cell consisting of two spatially separated plasmonic nanorods twisted at an angle (θ=30deg). Ltop represents the lengths of top bars while Lbottom represents the length of the bottom bars. The structures are fabricated using two-step electron beam lithography (EBL) and metal lift-off on a glass substrate (nsub=1.50). Finally, the second layer was fabricated using the same method but included a precise alignment process. (c) Top-view scanning electron microscope (SEM) image of the fabricated multilayer structure, with dx=80nm and twisted angle θ=30deg, showing the quality of the fabricated structures.

Fig. 2. Hybridized plasmonic arrays of spatially separated plasmonic twisted resonators with two different incident beams (RCP and LCP). (a) Schematic of a bilayer unit cell structure made of two plasmonic resonators in an array with twisted resonators at a twisted angle (θ=30deg). RCP light (red color) and LCP light (blue color) are incident onto the front side of the bilayer plasmonic nanostructure, and transmitted through the substrate. The unit cell dimensions consist of dissimilar gold nanorods with different parameters Ltop=170nm, Lbottom=120nm, W=50nm, and t=40nm. The phase response is designed using the same configuration with two different incident beams RCP and LCP. (b) Numerical simulation shows the existence of phase singularity when incident light is RCP, thus highlighting the phase singularity in a chiral medium (red box). The phase singularity occurs around dx=53nm. Panel (c) represents a regular phase when illuminated by a left circularly polarized light (blue box). Panel (d) represents the comparison between the numerical simulation and the developed model (see Supplementary Material). (e) The polar plot illustrates the complex amplitudes of the transmission. In this chart, the dots represent the numerical simulation, whereas solid lines depict the fits obtained through the model (with polar angles in deg).

Fig. 3. Experimental observation of phase singularity in a chiral medium. Panels (a) and (b) present the comparison between numerical simulations and experimental phase responses of the hybridized plasmonic arrays of two spatially separated plasmonic twisted resonators at a twisted angle (θ=30deg) with RCP (a) and LCP (b) as the incident beams. Dimensions are chosen to support a phase jump (dx=58nm, Ltop=170nm, Lbottom=120nm, W=50nm, θ=30deg). Left and right circularly polarized lights are incident onto the front side of the bilayer plasmonic nanostructure and transmitted through the substrate. By varying the offset dx as a function of the frequency, the phase jump occurs at zero transmission (see Supplementary Material). The phase singularity occurs between dx=48 and 58 nm. Error bars indicate the standard deviation of measured phases.

Fig. 4. Robustness of phase singularity in a chiral medium using three primary parameters, width (W), length (L), and twisted angle (θ), as well as the effects of various combinations of these parameters on the performance of the devices. The sweeping ranges are width from 50 to 70 nm (ΔW=−10 to 10 nm, Wcenter=60nm), length from 170 to 190 nm (ΔL=−10 to 10 nm, Lcenter=180nm), and twisted angle from 30 deg to 50 deg (Δθ=−10deg to 10 deg, θcenter=40deg). Panel (a) represents configuration I where θ=30deg with varying L and W. Panel (b) represents configuration II where L=170nm with varying θ and W. Panel (c) illustrates configuration III where W=50nm with varying L and W. The insets are 2D plots including regular phase (dx=0nm, blue) and phase jump (dx=80nm, red) such as in Fig. 3(a). The insets in panel (a) are the case of ΔW=0nm with ΔL=−10, 0, and 10 nm. The insets in panel (b) are the case of Δθ=0deg with ΔW=−10, 0, and 10 nm. The insets in panel (c) are the case of Δθ=0deg with ΔL=−10, 0, and 10 nm. The lines are simulations, and dots/squares are experimental data with an error bar. The error bar indicates the standard deviation of measured phases. A max phase difference is calculated by subtracting the phase of the regular case from the phase jump case at the highest frequency. When a phase singularity exists in the system, the max phase difference is close to 2π. We can observe the max phase difference/π in the 3D plots of different sweeping variables in Fig. 4 are all close to 2 (surfaces are simulations, and dots are measurements). Thus, the proposed photonic device is robust, as fabrication imperfections cannot hinder the existence of phase singularities.