We consider gold plasmonic nanorods in the infrared domain. Such elements are very anisotropic and only polarizable along their longer dimension. Varying the nanorod length from 150 to 500 nm changes the resonant frequency of the element, which allows us to tune the phase-shift provided to an incident plane wave which electric field is parallel to the long axis. On the contrary, the nanorod is transparent to an incoming plane wave with a polarization perpendicular to its main axis. In order to provide a 0 to 2pi phase shift, we chose to work in reflection with metasurfaces made of elements with random positions and orientation. We emphasize that the length of each nanorod is not random, but strongly depends on the position of the element. It is chosen accordingly so that the reflected phase shift follows a parabolic law.
The focusing efficiency strongly depends on the density of nanorods but also of the dimensionality and of the symmetry of the metasurface. Using full wave simulations, we design ordered and random metalens and compare their characteristics. Unfortunately, simulating 2D large area metasurface is numerically challenging. Hence, we extract the transmission matrix parameters for single elements from our FDTD simulation, and model the metasurface as an array of two level atom scatterers
Finally, we present an experimental realization of such random metalens. The latter is made with conventional top-down fabrication techniques and e-beam lithography. We will show that the resulting lens focus light on diffraction limited focal spots for the two polarizations.