Mie theory describes how electromagnetic waves scatter at the interface between a homogeneous spherical dielectric particle surrounded by a material of a different optical index. Numerical improvements have allowed studying more complicated geometries with the multipole decomposition of the spherical harmonics. Hence, Mie theory is widely applied in theoretical and applied physics, to enable novel light manipulation, to model Fano resonances, nonlinear optics, or to design dielectric metamaterials. Recently, the anapole state has brought attention to the community as one of the most interesting phenomena. It can be interpreted as a destructive interference in the far field between the fields scattered by the toroidal and electrical dipoles at a given frequency. Such element is therefore transparent to any incoming plane wave. However, things are different if the element is excited in its near field, where it can be excited by an internal source. In this work, we experimentally demonstrate a semiconductor laser based on a single cylindrical resonator suspended in air. An epitaxially grown InGaAsP layer on an InP substrate is patterned by e-beam lithography. We study the shift of the Mie resonance as geometrical parameters are varied, and show how it affects the shift of the lasing frequency. Our investigation of Mie resonances from an active gain medium would is a rich platform to study nontrivial excitation of a complex field and paves the way to designing active devices exploiting Mie theory.
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.