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Novel rectangular waveguides with graphene inserts biased by light are proposed herein. The graphene films short the conductor plates of waveguides and support the localized transverse-electric modes. Their electric fields are parallel to the wide walls of these waveguides, and the eigenmodes have decreased conductor loss. The designs do not involve the conductor and graphene strips with their sharp edges, and the loss associated with the current crowding effect is excluded. The waveguides are treated in the quasi-linear regime using a rigorous field matching method, and the complex dispersion eigenmodal equation is solved using a validated iteration algorithm. At the terahertz frequencies of amplification, where the real part of graphene conductivity is negative, a gain increase is found with the eigenmodal number. This gain can be tuned by the waveguide geometry, dielectric filling, and the level of quasi-Fermi energy. The ideal waveguide theory is corrected using a perturbation approach and the Drude model of surface resistance of waveguide plates.

Terahertz rectangular waveguides with inserted graphene films biased by light and their quasi-linear electromagnetic modeling