  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.
