In this paper, we report the design, simulation, and some applications of a tunable graphene-based cylindrical resonator by analytical and numerical two-dimensional finite-difference time-domain methods. The base structure operates as a bandpass filter in the mid-infrared region. The tunability of the filter is achieved by changing the radius and/or the chemical potential of the graphene cylinder. Based on the proposed cylindrical resonator, a two-channel wavelength selector and some novel linear plasmonic logic gates are designed and proposed. The even- and the odd-order resonance modes are separated in the two-channel wavelength selector and are transmitted to the output graphene waveguides. Moreover, the plasmonic logic gates including XOR, XNOR, NAND, and NOT having the significant features such as linearity, compact size, and low loss are proposed. The analytical approach and the numerical simulations prove the excellent performance of the logic gates in comparison to the reported ones in the literature. The simulation results demonstrate that the maximum ON/OFF ratios for these plasmonic logic gates are 29.09, 28.78, 28.78, and 29.09 dB, respectively. The proposed functional ultra-compact nano-scale graphene-based structures offer potential basic blocks for mid-infrared optical computing and signal processing.
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