Search

Metalenses are nanostructured surfaces with great potential for delivering miniaturized and integrated optical systems. A key property of metalenses is that, by using a double layer configuration, or doublet, they can achieve both diffraction-limited resolution and wide field-of-view imaging. The physical operation and limitations of such doublet systems, however, are still not fully understood, and designs are still based on numerical optimization of the phase profiles. Here, we show the fundamental limits of doublet systems and provide a universal design strategy without any need to resort to numerical optimization. We find an analytical relationship between the focal length and the spacer thickness; we identify the physical principles underlying the limitations on performance and obtain a universal dependence of the field of view as a function of resolution (numerical aperture). Our results will allow researchers to appreciate the regimes of resolution and field of view that are accessible for specific applications, to identify the conditions for optimum performance (such as required spacer thickness), and to conveniently design doublets without needing to resort to numerical optimizations.

Diffractive approaches are needed when refractive microlenses reach their focusing limit at the micron-scale in visible light. Previously, we have reported on micron-sized optical lenses based on the diffraction of metallic nanowires. Here, we extend our study to lenses based on pairs of subwavelength dielectric scatterers. Using simulations by two-dimensional finite element method, we demonstrate that focusing holds for pair spacings as small as the wavelength-size. For pairs with distances between inner walls larger than about 1.2λ, the scattered waves generate a quadratic phase modulation on the total propagating field leading to a diffraction-limited focusing i.e. an effective optical lens effect with high numerical aperture. In addition, they have low sidelobe intensities, long depths of focus, and they have a low sensitivity with polarization. For pairs with inner wall distances smaller than about 1.2λ, the focusing phase modulation is accumulated during the propagation through the dielectric pair structure. In this work, we report only on the experimental demonstration for the case of larger wall separation to emphasize on the scattered wave effect on micro-focusing. A pair of parallel polymer lines (cylindrical lens), and a grid of polymer lines (square microlens array) with 2 μm-spacing were fabricated by two-photon induced polymerization. Their focal lengths are comparable to their separating distances, their spot-sizes are 0.37 μm and 0.28 μm at wavelength 530 nm, and their focusing efficiencies are 70% and 60%, respectively.