High-mobility field effect transistors can serve as resonant detectors of terahertz radiation due to excitation of plasmons in the channel. The modeling of these devices previously relied either on approximate techniques, or complex full-wave simulations. In this paper, we obtain an exact solution for driven electrical oscillations in plasmonic field-effect transistor with realistic contact geometry. The obtained solution highlights the importance of evanescent plasma waves excited near the contacts, which qualitatively modify the detector responsivity spectra. We derive the boundary condition on the ac floating electrodes of plasmonic FET which interpolates between open-circuit (Dyakonov-Shur) and short-circuit (clamped voltage) boundary conditions. In both limits, the FET photovoltage possesses resonant fringes, however, the absolute value of voltage is greater in the open-circuit regime.
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