Metasurfaces with Nonlinear Berry Phases in Space and Time

For efficient nonlinear processes, the engineering of the nonlinear optical properties of media becomes important. The most well-known technique for spatially engineering nonlinear properties is the quasi-phase matching scheme... [ view full abstract ]

For efficient nonlinear processes, the engineering of the nonlinear optical properties of media becomes important. The most well-known technique for spatially engineering nonlinear properties is the quasi-phase matching scheme for second-order processes like second harmonic generation. However, the widely used technique of periodic polling of natural crystals to obtain quasi-phase matching only provides a binary state for the nonlinear material polarization, which is equivalent to a discrete phase change of π of the nonlinear polarization. A continuous tailoring of the phase of the nonlinear susceptibility would greatly enhance flexibility in the design and reduce parasitic effects.

Here we will discuss a novel nonlinear metamaterial with homogeneous linear optical properties but continuously controllable phase of the local effective nonlinear polarizability. For the demonstration, we use plasmonic metasurfaces with various designs for the meta-atom geometry together with circular polarized light states. The controllable nonlinearity phase results from the phase accumulation due to the polarization change along the polarization path on the Poincare Sphere (the so-called Pancharatnam-Berry phase) and depends therefore only on the spatial geometry of the metasurface. By using a fixed orientation of the meta-atom the nonlinear phase can be spatially arbitrarily tailored over the entire range from 0 to 2π. In contrast to the quasi-phase matching scheme the continuous phase engineering of the effective nonlinear polarizability enables complete control of the propagation of harmonic generation signals, and therefore, it seamlessly combines the generation and manipulation of the harmonic waves for highly compact nonlinear nanophotonic devices. We will demonstrate the concept of phase engineering for the manipulation of second- and third-harmonic generation from metasurfaces and the restriction with respect to symmetry and geometry of meta-atoms. Furthermore, we will discuss a nonlinear Berry phase in the time domain, which arises from the rotational Doppler shift that is observed on spinning objects. Our findings are of fundamental significance in nonlinear optics and for tailored nonlinearities, as they provide a further degree of freedom in the design of nonlinear materials.