New degrees of freedom in nonlinear metamaterials

This is an overview of the recent achievements in exploiting novel degrees of freedom in metamaterial design, which enable sophisticated nonlinear coupling mechanisms and bring enhancement to nonlinear behavior. One of the novel paradigms makes use of mechanical feedback, achieved by embedding electromagnetic resonators within elastic medium or engineering explicit elastic links between them, such as rotational feedback. These designs provide broad-band self-adjustable resonances, self-oscillations, chaotic regimes, nonlinear chirality and, spontaneous chiral symmetry breaking. With this respect, a range of implementations has been analyzed, from flexible helices for microwaves to artificial electrostriction in optics. Another concept benefits from multi-frequency operation, where the properties in completely distinct frequency ranges become entangled through specific metamaterial design -for example, direct optical coupling can be introduced between microwave resonators, providing an independent interaction channel. It was also found that hyperbolic metamaterials can bring notable benefits to classical nonlinear processes by imposing unusual phase matching solutions, with a rich choice of matching combinations. Finally, the boundary structure of metamaterials add yet another possibility to control their properties. Overall, the recent progress in these topics suggests a very positive outlook into the future of nonlinear metamaterials.