Effect of Finite Number of Nanoblocks in Metasurface Lens Design from Bloch-Mode Perspective and Its Experimental Verification

Metasurface lenses composed of nanoblocks with gradually changing sizes in a periodic lattice are generally designed based on the assumption that the properties of each nanoblock can be calculated based on an infinite array of periodically spaced same-sized nanoblocks. Here, we investigate the limits of a periodic calculation-based lens design starting from a Bloch approach. A modal analysis reveals possible parameters that can lead to discrepancies in the transmission response of actual meta-lenses. A hybrid mode composed of two propagating modes in the modal analysis requires a periodic structure. Therefore, if nanoblocks that exhibit hybrid modes are chosen as building blocks for meta-lenses containing a finite number of blocks, the transmission characteristics are different to the periodic calculation results. A dip in transmission is observed both numerically and experimentally. Mach-Zehnder interferometric microscopy and scattering contour mapping are used to experimentally visualize the transmittance and phase distributions. The results support the predictions of the calculations. This investigation provides deep insights into the design of meta-lenses with gradually varying nanoblock sizes.