  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.
