Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices

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The potential of graphene for use in photonic applications was evidenced by recent demonstrations of modulators, polarisation rotators, and isolators. These promising yet preliminary results raise crucial questions: what is the optimal performance achievable by more complex designs using multilayer structures, graphene patterning, metal additions, or a combination of these approaches, and how can this optimum design be achieved in practice? Today, the complexity of the problem, which is magnified by the variability in graphene parameters, leaves the design of these new devices to time-consuming and suboptimal trial-and-error procedures. We address this issue by first demonstrating that the relevant figures of merit for the devices above are subject to absolute theoretical upper bounds. Strikingly these limits are related only to the conductivity tensor of graphene; thus, we can provide essential roadmap information such as the best possible device performance versus wavelength and graphene quality. Second, based on the theory developed, physical insight, and detailed simulations, we demonstrate how structures closely approaching these fundamental limits can be designed, demonstrating the possibility of significant improvement. These results are believed to be of paramount importance for the design of graphene-based modulators, rotators, and isolators and are also directly applicable to other 2-dimensional materials.