Huygens' metasurfaces have demonstrated almost arbitrary control over the shape of a scattered beam, however its spatial profile is typically fixed at fabrication time. Dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens' condition across the tuning range. In this work, we experimentally demonstrate that a time-varying meta-device which performs frequency conversion, can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens' metadevice is made of both electric and magnetic meta-atoms with independently controlled modulation, and the phase of this modulation is imprinted on the scattered parametric waves, controlling their shapes and directions. We develop a theory which shows how the scattering directionality, phase and conversion efficiency of sidebands can be manipulated almost arbitrarily. We demonstrate novel effects including all-angle beam steering and frequency-multiplexed functionalities at microwave frequencies around 4 GHz, using varactor diodes as tunable elements. We believe that the concept can be extended to other frequency bands, enabling metasurfaces with arbitrary phase pattern that can be dynamically tuned over the complete 2π range. arXiv:1807.08873v3 [physics.app-ph] 2 Dec 2018 AUTHOR CONTRIBUTION M. Liu conceived the idea, performed the theoretical, numerical and experimental studies, with support from

The study of advanced artificial electromagnetic materials, known as metamaterials, provides a link from material science to theoretical and applied electrodynamics, as well as to electrical engineering. Being initially intended mainly to achieve negative refraction, the concept of metamaterials quickly covered a much broader range of applications, from microwaves to optics and even acoustics. In particular, nonlinear metamaterials established a new research direction giving rise to fruitful ideas for tunable and active artificial materials. Here we introduce the concept of magnetoelastic metamaterials, where a new type of nonlinear response emerges from mutual interaction. This is achieved by providing a mechanical degree of freedom so that the electromagnetic interaction in the metamaterial lattice is coupled to elastic interaction. This enables the electromagnetically induced forces to change the metamaterial structure, dynamically tuning its effective properties. This concept leads to a new generation of metamaterials, and can be compared to such fundamental concepts of modern physics as optomechanics of photonic structures or magnetoelasticity in magnetic materials.