  By designing tailor-made resonance modes with structured atoms, metamaterials
allow us to obtain constitutive parameters outside their limited range from
natural or composite materials. Nonetheless, tuning the constitutive parameters
relies much on our capability in modifying the physical structures or media in
constructing the metamaterial atoms, posing a fundamental challenge to the
range of tunability in many real-time applications. Here, we propose a
completely new notion of virtualized metamaterials to lift the traditional
boundary inherent to the physical structure of a metamaterial atom. By
replacing the resonating physical structure with a designer mathematical
convolution kernel with a fast digital signal processing circuit, we show that
a decoupled control of the effective bulk modulus and density of the
metamaterial is possible on-demand through a software-defined frequency
dispersion. Purely noninterfering to the incident wave in the off-mode
operation while providing freely reconfigurable amplitude, center frequency,
bandwidth, and phase delay of frequency dispersion in on-mode, our approach
adds an additional dimension to wave molding and can work as an essential
building block for time-varying metamaterials.
