How to “digitize” metamaterials

Inspired by the Boolean algebra, the notion of digital electronics and the binary number theory, we have developed the methodologies to “digitize” metamaterials. We explore how an arbitrary value of the permittivity function can, in principle, be synthesized by judicious combinations of only two constituent materials with two different permittivity parameters. We have analyzed the conditions upon which one can achieve such synthesis, and have investigated theoretically issues such as the role of loss, shape and dimensions of the constituent elements. Two different digital systems have been considered: (1) the “rectangular bytes” and (2) the “core-shell bytes”. We have investigated the various features of these two systems, and their advantages and constraints. We present some of our theoretical results on this concept as utilized in several case studies.