Modulation of TE propagation modes in rectangular metal waveguide with integrated graphene structure in the sub-terahertz frequency range

Abstract

The propagation of TE modes in a rectangular metal waveguide with an integrated structure of finite length containing a graphene monolayer was studied by a modal decomposition method. The modal decomposition method generates a number of linear algebraic equations related to waveguide modes taken into account. The system of linear algebraic equations for the amplitudes of all modes was derived taking into account the propagation as well as a number of local evanescent modes. Truncation errors in the function of the number of modes taken were quantified by using the discontinuities of the boundary conditions for the transverse electric and magnetic field components at the interface of the discontinuities of the structure. The transmitted and reflected TE01 mode amplitudes were calculated versus the graphene layer length, its position inside the waveguide cavity and the graphene electrons chemical potential. It was shown that the symmetrical positioning of the graphene layer inside the waveguide cavity is the most suitable to achieve the largest amplitude modulation, whereas an asymmetrical positioning is suitable to achieve a large phase modulation of the transmitted mode. It was shown that the phase modulation increases with a transmission coefficient modulation increase and decreases with a transmission coefficient increase. It was found that the phase modulation firstly increases almost proportionally with the graphene layer length for relatively short structures; however, after passing through a maximum, the phase modulation becomes almost constant and hence only weakly dependent on the graphene layer length. Typical phase modulation values turn out to be about 15–20 degrees for minimal transmission coefficients of about 0.6–0.4; however, the phase modulation reaches a value of about 45 degrees if the transmission coefficient modulation equals 50%.