Digital metamaterials

Balancing complexity and simplicity has played an important role in the development of many fields in science and engineering. One of the well-known and powerful examples of such balance can be found in Boolean algebra and its impact on the birth of digital electronics and the digital information age. The simplicity of using only two numbers, '0' and '1', in a binary system for describing an arbitrary quantity made the fields of digital electronics and digital signal processing powerful and ubiquitous. Here, inspired by the binary concept, we propose to develop the notion of digital metamaterials. Specifically, we investigate how one can synthesize an electromagnetic metamaterial with a desired permittivity, using as building blocks only two elemental materials, which we call 'metamaterial bits', with two distinct permittivity functions. We demonstrate, analytically and numerically, how proper spatial mixtures of such metamaterial bits lead to elemental 'metamaterial bytes' with effective material parameters that are different from the parameters of the metamaterial bits. We then apply this methodology to several design examples of optical elements, such as digital convex lenses, flat graded-index digital lenses, digital constructs for epsilon-near-zero (ENZ) supercoupling and digital hyperlenses, thus highlighting the power and simplicity of the methodology.