Analytical formulation of spatiotemporal modulated graphene-based waveguides using Floquet-Bloch theory

In this work, an analytical model to study graphene-based spatiotemporal modulated structures is developed and verified through comparison with full wave numerical simulations. Graphene is an ideal material for realizing spatiotemporal modulated structures at high frequencies of THz and optics. In this analysis, the electromagnetic response of studied structures is expressed in terms of weighted Floquet-Bloch modes supported by the structure, while graphene is modeled by a spatiotemporal modulated surface current that imposes certain boundary conditions on the modes. The developed analytical technique is a comprehensive tool and can be used for accurate modeling of different kinds of spatiotemporal devices including lossy, guided, and leaky wave structures. To demonstrate the accuracy of the model, two plasmonic waveguides with space and time modulated graphene conductivity are analyzed and their interband and intraband transition between modes are thoroughly investigated. Using the developed analytical model, spatiotemporal modulation phenomena such as mode conversion, wave amplification and nonreciprocal response are explored and discussed for the studied structures.